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And we did one chi-square test for", "tokens": [400, 264, 661, 10024, 307, 577, 281, 764, 13228, 12, 33292, 543, 6921, 337, 27820, 3020, 8020, 13, 400, 321, 630, 472, 13228, 12, 33292, 543, 1500, 337], "avg_logprob": -0.21551723932397776, "compression_ratio": 1.2954545454545454, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 27.93, "end": 28.33, "word": " And", "probability": 0.6455078125}, {"start": 28.33, "end": 28.45, "word": " the", "probability": 0.71240234375}, {"start": 28.45, "end": 28.63, "word": " other", "probability": 0.89501953125}, {"start": 28.63, "end": 29.05, "word": " objective", "probability": 0.9384765625}, {"start": 29.05, "end": 29.35, "word": " is", "probability": 0.9169921875}, {"start": 29.35, "end": 29.55, "word": " how", "probability": 0.81982421875}, {"start": 29.55, "end": 29.73, "word": " to", "probability": 0.91552734375}, {"start": 29.73, "end": 29.95, "word": " use", "probability": 0.8525390625}, {"start": 29.95, "end": 30.17, "word": " chi", "probability": 0.40380859375}, {"start": 30.17, "end": 30.45, "word": "-square", "probability": 0.8818359375}, {"start": 30.45, "end": 30.81, "word": " tests", "probability": 0.5}, {"start": 30.81, "end": 31.07, "word": " for", "probability": 0.8916015625}, {"start": 31.07, "end": 31.73, "word": " contingency", "probability": 0.81298828125}, {"start": 31.73, "end": 32.03, "word": " tables.", "probability": 0.81396484375}, {"start": 32.59, "end": 32.99, "word": " And", "probability": 0.93798828125}, {"start": 32.99, "end": 33.19, "word": " we", "probability": 0.9365234375}, {"start": 33.19, "end": 33.49, "word": " did", "probability": 0.95458984375}, {"start": 33.49, "end": 34.33, "word": " one", "probability": 0.90576171875}, {"start": 34.33, "end": 34.63, "word": " chi", "probability": 0.8466796875}, {"start": 34.63, "end": 34.93, "word": "-square", "probability": 0.966796875}, {"start": 34.93, "end": 35.41, "word": " test", "probability": 0.88037109375}, {"start": 35.41, "end": 37.03, "word": " for", "probability": 0.89111328125}], "temperature": 1.0}, {"id": 3, "seek": 6515, "start": 37.93, "end": 65.15, "text": " the difference between two proportions. 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This quantity under the square root, where b dash", "tokens": [1176, 29588, 11, 597, 307, 272, 16, 3175, 272, 17, 3175, 288, 16, 3175, 288, 17, 6666, 538, 272, 8240, 1413, 502, 3175, 272, 8240, 17207, 538, 502, 670, 297, 16, 1804, 502, 670, 297, 17, 13, 639, 11275, 833, 264, 3732, 5593, 11, 689, 272, 8240], "avg_logprob": -0.28824869729578495, "compression_ratio": 1.4596774193548387, "no_speech_prob": 0.0, "words": [{"start": 67.68, "end": 67.96, "word": " Z", "probability": 0.25390625}, {"start": 67.96, "end": 68.46, "word": " statistic,", "probability": 0.572265625}, {"start": 69.36, "end": 69.78, "word": " which", "probability": 0.955078125}, {"start": 69.78, "end": 70.1, "word": " is", "probability": 0.95263671875}, {"start": 70.1, "end": 71.76, "word": " b1", "probability": 0.6927490234375}, {"start": 71.76, "end": 72.08, "word": " minus", "probability": 0.97119140625}, {"start": 72.08, "end": 72.56, "word": " b2", "probability": 0.987060546875}, {"start": 72.56, "end": 74.38, "word": " minus", "probability": 0.8828125}, {"start": 74.38, "end": 75.2, "word": " y1", "probability": 0.74169921875}, {"start": 75.2, "end": 75.52, "word": " minus", "probability": 0.986328125}, {"start": 75.52, "end": 76.08, "word": " y2", "probability": 0.997802734375}, {"start": 76.08, "end": 77.92, "word": " divided", "probability": 0.57177734375}, {"start": 77.92, "end": 78.34, "word": " by", "probability": 0.978515625}, {"start": 78.34, "end": 81.84, "word": " b", "probability": 0.76025390625}, {"start": 81.84, "end": 82.22, "word": " dash", "probability": 0.82470703125}, {"start": 82.22, "end": 84.18, "word": " times", "probability": 0.86328125}, {"start": 84.18, "end": 84.42, "word": " 1", "probability": 0.85595703125}, {"start": 84.42, "end": 84.7, "word": " minus", "probability": 0.9892578125}, {"start": 84.7, "end": 84.9, "word": " b", "probability": 0.84619140625}, {"start": 84.9, "end": 85.2, "word": " dash", "probability": 0.869140625}, {"start": 85.2, "end": 86.46, "word": " multiplied", "probability": 0.46630859375}, {"start": 86.46, "end": 86.78, "word": " by", "probability": 0.9658203125}, {"start": 86.78, "end": 87.0, "word": " 1", "probability": 0.94921875}, {"start": 87.0, "end": 87.22, "word": " over", "probability": 0.8662109375}, {"start": 87.22, "end": 87.5, "word": " n1", "probability": 0.570068359375}, {"start": 87.5, "end": 87.76, "word": " plus", "probability": 0.931640625}, {"start": 87.76, "end": 87.94, "word": " 1", "probability": 0.96044921875}, {"start": 87.94, "end": 88.12, "word": " over", "probability": 0.87841796875}, {"start": 88.12, "end": 88.76, "word": " n2.", "probability": 0.9921875}, {"start": 89.34, "end": 89.98, "word": " This", "probability": 0.298095703125}, {"start": 89.98, "end": 90.38, "word": " quantity", "probability": 0.445068359375}, {"start": 90.38, "end": 90.86, "word": " under", "probability": 0.52685546875}, {"start": 90.86, "end": 91.02, "word": " the", "probability": 0.72998046875}, {"start": 91.02, "end": 91.2, "word": " square", "probability": 0.82470703125}, {"start": 91.2, "end": 91.42, "word": " root,", "probability": 0.9140625}, {"start": 92.26, "end": 92.5, "word": " where", "probability": 0.921875}, {"start": 92.5, "end": 92.72, "word": " b", "probability": 0.97900390625}, {"start": 92.72, "end": 93.08, "word": " dash", "probability": 0.89990234375}], "temperature": 1.0}, {"id": 5, "seek": 13094, "start": 102.18, "end": 130.94, "text": " Or proportionally, where P dash equals X1 plus X2 divided by N1 plus N2. Or, in this chapter, we are going to use chi-square statistic, which is given by this equation. Chi-square statistic is just sum of observed frequency, FO.", "tokens": [1610, 16068, 379, 11, 689, 430, 8240, 6915, 1783, 16, 1804, 1783, 17, 6666, 538, 426, 16, 1804, 426, 17, 13, 1610, 11, 294, 341, 7187, 11, 321, 366, 516, 281, 764, 13228, 12, 33292, 543, 29588, 11, 597, 307, 2212, 538, 341, 5367, 13, 17730, 12, 33292, 543, 29588, 307, 445, 2408, 295, 13095, 7893, 11, 23501, 13], "avg_logprob": -0.27916665573914845, "compression_ratio": 1.4049079754601228, "no_speech_prob": 0.0, "words": [{"start": 102.18, "end": 102.48, "word": " Or", "probability": 0.51708984375}, {"start": 102.48, "end": 103.24, "word": " proportionally,", "probability": 0.52294921875}, {"start": 103.54, "end": 105.84, "word": " where", "probability": 0.8271484375}, {"start": 105.84, "end": 106.12, "word": " P", "probability": 0.343017578125}, {"start": 106.12, "end": 106.4, "word": " dash", "probability": 0.6044921875}, {"start": 106.4, "end": 107.0, "word": " equals", "probability": 0.896484375}, {"start": 107.0, "end": 107.64, "word": " X1", "probability": 0.73974609375}, {"start": 107.64, "end": 107.92, "word": " plus", "probability": 0.93505859375}, {"start": 107.92, "end": 108.58, "word": " X2", "probability": 0.9951171875}, {"start": 108.58, "end": 110.08, "word": " divided", "probability": 0.57373046875}, {"start": 110.08, "end": 110.56, "word": " by", "probability": 0.97119140625}, {"start": 110.56, "end": 111.88, "word": " N1", "probability": 0.942138671875}, {"start": 111.88, "end": 113.18, "word": " plus", "probability": 0.953125}, {"start": 113.18, "end": 114.28, "word": " N2.", "probability": 0.992919921875}, {"start": 115.06, "end": 115.56, "word": " Or,", "probability": 0.9345703125}, {"start": 118.7, "end": 118.88, "word": " in", "probability": 0.85986328125}, {"start": 118.88, "end": 119.04, "word": " this", "probability": 0.9404296875}, {"start": 119.04, "end": 119.3, "word": " chapter,", "probability": 0.86572265625}, {"start": 119.36, "end": 119.46, "word": " we", "probability": 0.958984375}, {"start": 119.46, "end": 119.58, "word": " are", "probability": 0.92431640625}, {"start": 119.58, "end": 119.82, "word": " going", "probability": 0.947265625}, {"start": 119.82, "end": 119.98, "word": " to", "probability": 0.9619140625}, {"start": 119.98, "end": 120.2, "word": " use", "probability": 0.84521484375}, {"start": 120.2, "end": 120.4, "word": " chi", "probability": 0.306640625}, {"start": 120.4, "end": 120.72, "word": "-square", "probability": 0.7600911458333334}, {"start": 120.72, "end": 121.02, "word": " statistic,", "probability": 0.347900390625}, {"start": 121.5, "end": 121.7, "word": " which", "probability": 0.94189453125}, {"start": 121.7, "end": 121.84, "word": " is", "probability": 0.947265625}, {"start": 121.84, "end": 122.04, "word": " given", "probability": 0.89404296875}, {"start": 122.04, "end": 122.48, "word": " by", "probability": 0.96826171875}, {"start": 122.48, "end": 123.02, "word": " this", "probability": 0.95068359375}, {"start": 123.02, "end": 123.58, "word": " equation.", "probability": 0.96826171875}, {"start": 124.3, "end": 124.52, "word": " Chi", "probability": 0.6875}, {"start": 124.52, "end": 124.82, "word": "-square", "probability": 0.93994140625}, {"start": 124.82, "end": 125.2, "word": " statistic", "probability": 0.89208984375}, {"start": 125.2, "end": 125.68, "word": " is", "probability": 0.9033203125}, {"start": 125.68, "end": 125.98, "word": " just", "probability": 0.91259765625}, {"start": 125.98, "end": 126.46, "word": " sum", "probability": 0.8212890625}, {"start": 126.46, "end": 127.3, "word": " of", "probability": 0.94580078125}, {"start": 127.3, "end": 129.62, "word": " observed", "probability": 0.72021484375}, {"start": 129.62, "end": 130.36, "word": " frequency,", "probability": 0.9404296875}, {"start": 130.54, "end": 130.94, "word": " FO.", "probability": 0.366455078125}], "temperature": 1.0}, {"id": 6, "seek": 16027, "start": 135.53, "end": 160.27, "text": " minus expected frequency squared divided by expected frequency for all cells. Chi squared, this statistic is given by this equation. If there are two by two rows and columns, I mean there are two rows and two columns. So in this case, my table is two by two.", "tokens": [3175, 5176, 7893, 8889, 6666, 538, 5176, 7893, 337, 439, 5438, 13, 17730, 8889, 11, 341, 29588, 307, 2212, 538, 341, 5367, 13, 759, 456, 366, 732, 538, 732, 13241, 293, 13766, 11, 286, 914, 456, 366, 732, 13241, 293, 732, 13766, 13, 407, 294, 341, 1389, 11, 452, 3199, 307, 732, 538, 732, 13], "avg_logprob": -0.19349888233201845, "compression_ratio": 1.6602564102564104, "no_speech_prob": 0.0, "words": [{"start": 135.53000000000003, "end": 136.17000000000002, "word": " minus", "probability": 0.2366943359375}, {"start": 136.17000000000002, "end": 136.81, "word": " expected", "probability": 0.86767578125}, {"start": 136.81, "end": 137.49, "word": " frequency", "probability": 0.9599609375}, {"start": 137.49, "end": 138.57, "word": " squared", "probability": 0.826171875}, {"start": 138.57, "end": 139.77, "word": " divided", "probability": 0.438232421875}, {"start": 139.77, "end": 140.07, "word": " by", "probability": 0.97265625}, {"start": 140.07, "end": 140.59, "word": " expected", "probability": 0.91064453125}, {"start": 140.59, "end": 141.17, "word": " frequency", "probability": 0.9609375}, {"start": 141.17, "end": 141.89, "word": " for", "probability": 0.92626953125}, {"start": 141.89, "end": 142.17, "word": " all", "probability": 0.91162109375}, {"start": 142.17, "end": 142.49, "word": " cells.", "probability": 0.76123046875}, {"start": 145.21, "end": 145.77, "word": " Chi", "probability": 0.44384765625}, {"start": 145.77, "end": 146.23, "word": " squared,", "probability": 0.56396484375}, {"start": 147.71, "end": 147.91, "word": " this", "probability": 0.61181640625}, {"start": 147.91, "end": 148.27, "word": " statistic", "probability": 0.85009765625}, {"start": 148.27, "end": 148.47, "word": " is", "probability": 0.93603515625}, {"start": 148.47, "end": 148.63, "word": " given", "probability": 0.8935546875}, {"start": 148.63, "end": 148.85, "word": " by", "probability": 0.96826171875}, {"start": 148.85, "end": 149.07, "word": " this", "probability": 0.947265625}, {"start": 149.07, "end": 149.55, "word": " equation.", "probability": 0.97900390625}, {"start": 150.49, "end": 150.79, "word": " If", "probability": 0.9697265625}, {"start": 150.79, "end": 151.05, "word": " there", "probability": 0.912109375}, {"start": 151.05, "end": 151.45, "word": " are", "probability": 0.9453125}, {"start": 151.45, "end": 153.03, "word": " two", "probability": 0.65869140625}, {"start": 153.03, "end": 153.19, "word": " by", "probability": 0.9296875}, {"start": 153.19, "end": 153.39, "word": " two", "probability": 0.92919921875}, {"start": 153.39, "end": 153.77, "word": " rows", "probability": 0.9140625}, {"start": 153.77, "end": 154.19, "word": " and", "probability": 0.91943359375}, {"start": 154.19, "end": 154.61, "word": " columns,", "probability": 0.94970703125}, {"start": 154.79, "end": 154.87, "word": " I", "probability": 0.97412109375}, {"start": 154.87, "end": 155.05, "word": " mean", "probability": 0.96923828125}, {"start": 155.05, "end": 155.27, "word": " there", "probability": 0.54150390625}, {"start": 155.27, "end": 155.45, "word": " are", "probability": 0.94189453125}, {"start": 155.45, "end": 155.65, "word": " two", "probability": 0.91943359375}, {"start": 155.65, "end": 155.93, "word": " rows", "probability": 0.900390625}, {"start": 155.93, "end": 156.11, "word": " and", "probability": 0.93798828125}, {"start": 156.11, "end": 156.29, "word": " two", "probability": 0.91943359375}, {"start": 156.29, "end": 156.71, "word": " columns.", "probability": 0.962890625}, {"start": 157.01, "end": 157.35, "word": " So", "probability": 0.88427734375}, {"start": 157.35, "end": 157.49, "word": " in", "probability": 0.7822265625}, {"start": 157.49, "end": 157.67, "word": " this", "probability": 0.94775390625}, {"start": 157.67, "end": 158.03, "word": " case,", "probability": 0.91162109375}, {"start": 158.79, "end": 159.13, "word": " my", "probability": 0.96826171875}, {"start": 159.13, "end": 159.47, "word": " table", "probability": 0.892578125}, {"start": 159.47, "end": 159.67, "word": " is", "probability": 0.94677734375}, {"start": 159.67, "end": 159.81, "word": " two", "probability": 0.904296875}, {"start": 159.81, "end": 159.97, "word": " by", "probability": 0.96435546875}, {"start": 159.97, "end": 160.27, "word": " two.", "probability": 0.93310546875}], "temperature": 1.0}, {"id": 7, "seek": 18794, "start": 162.12, "end": 187.94, "text": " In this case, you have only one degree of freedom. Always degrees of freedom equals number of rows minus one multiplied by number of columns minus one. So for two by two tables, there are two rows and two columns, so two minus one.", "tokens": [682, 341, 1389, 11, 291, 362, 787, 472, 4314, 295, 5645, 13, 11270, 5310, 295, 5645, 6915, 1230, 295, 13241, 3175, 472, 17207, 538, 1230, 295, 13766, 3175, 472, 13, 407, 337, 732, 538, 732, 8020, 11, 456, 366, 732, 13241, 293, 732, 13766, 11, 370, 732, 3175, 472, 13], "avg_logprob": -0.19316788689762937, "compression_ratio": 1.6223776223776223, "no_speech_prob": 0.0, "words": [{"start": 162.12, "end": 162.34, "word": " In", "probability": 0.74853515625}, {"start": 162.34, "end": 162.56, "word": " this", "probability": 0.9482421875}, {"start": 162.56, "end": 162.82, "word": " case,", "probability": 0.91748046875}, {"start": 162.9, "end": 162.96, "word": " you", "probability": 0.951171875}, {"start": 162.96, "end": 163.16, "word": " have", "probability": 0.8876953125}, {"start": 163.16, "end": 163.44, "word": " only", "probability": 0.91943359375}, {"start": 163.44, "end": 163.68, "word": " one", "probability": 0.79638671875}, {"start": 163.68, "end": 163.88, "word": " degree", "probability": 0.97802734375}, {"start": 163.88, "end": 164.08, "word": " of", "probability": 0.955078125}, {"start": 164.08, "end": 164.36, "word": " freedom.", "probability": 0.92919921875}, {"start": 164.64, "end": 165.1, "word": " Always", "probability": 0.8193359375}, {"start": 165.1, "end": 166.46, "word": " degrees", "probability": 0.68212890625}, {"start": 166.46, "end": 166.74, "word": " of", "probability": 0.9697265625}, {"start": 166.74, "end": 167.18, "word": " freedom", "probability": 0.923828125}, {"start": 167.18, "end": 169.02, "word": " equals", "probability": 0.7763671875}, {"start": 169.02, "end": 169.86, "word": " number", "probability": 0.865234375}, {"start": 169.86, "end": 170.1, "word": " of", "probability": 0.96337890625}, {"start": 170.1, "end": 170.44, "word": " rows", "probability": 0.87060546875}, {"start": 170.44, "end": 171.18, "word": " minus", "probability": 0.410888671875}, {"start": 171.18, "end": 173.34, "word": " one", "probability": 0.599609375}, {"start": 173.34, "end": 173.92, "word": " multiplied", "probability": 0.4482421875}, {"start": 173.92, "end": 175.8, "word": " by", "probability": 0.970703125}, {"start": 175.8, "end": 176.1, "word": " number", "probability": 0.67822265625}, {"start": 176.1, "end": 176.3, "word": " of", "probability": 0.96044921875}, {"start": 176.3, "end": 176.82, "word": " columns", "probability": 0.94140625}, {"start": 176.82, "end": 180.32, "word": " minus", "probability": 0.9462890625}, {"start": 180.32, "end": 180.78, "word": " one.", "probability": 0.927734375}, {"start": 181.88, "end": 182.42, "word": " So", "probability": 0.87841796875}, {"start": 182.42, "end": 182.68, "word": " for", "probability": 0.673828125}, {"start": 182.68, "end": 182.86, "word": " two", "probability": 0.81982421875}, {"start": 182.86, "end": 183.02, "word": " by", "probability": 0.89306640625}, {"start": 183.02, "end": 183.22, "word": " two", "probability": 0.9384765625}, {"start": 183.22, "end": 183.72, "word": " tables,", "probability": 0.826171875}, {"start": 184.26, "end": 185.54, "word": " there", "probability": 0.8798828125}, {"start": 185.54, "end": 185.72, "word": " are", "probability": 0.94091796875}, {"start": 185.72, "end": 185.9, "word": " two", "probability": 0.92431640625}, {"start": 185.9, "end": 186.14, "word": " rows", "probability": 0.9130859375}, {"start": 186.14, "end": 186.28, "word": " and", "probability": 0.9248046875}, {"start": 186.28, "end": 186.46, "word": " two", "probability": 0.92822265625}, {"start": 186.46, "end": 186.88, "word": " columns,", "probability": 0.96240234375}, {"start": 187.0, "end": 187.1, "word": " so", "probability": 0.927734375}, {"start": 187.1, "end": 187.24, "word": " two", "probability": 0.87841796875}, {"start": 187.24, "end": 187.48, "word": " minus", "probability": 0.98046875}, {"start": 187.48, "end": 187.94, "word": " one.", "probability": 0.92529296875}], "temperature": 1.0}, {"id": 8, "seek": 21636, "start": 190.48, "end": 216.36, "text": " times 2 minus 1, so your degrees of freedom in this case is 1. Here the assumption is we assume that the expected frequency is at least 5, in order to use Chi-square statistic. Chi-square is always positive, I mean, Chi-square value is always greater than 0. It's one TLTS to the right one.", "tokens": [1413, 568, 3175, 502, 11, 370, 428, 5310, 295, 5645, 294, 341, 1389, 307, 502, 13, 1692, 264, 15302, 307, 321, 6552, 300, 264, 5176, 7893, 307, 412, 1935, 1025, 11, 294, 1668, 281, 764, 17730, 12, 33292, 543, 29588, 13, 17730, 12, 33292, 543, 307, 1009, 3353, 11, 286, 914, 11, 17730, 12, 33292, 543, 2158, 307, 1009, 5044, 813, 1958, 13, 467, 311, 472, 40277, 7327, 281, 264, 558, 472, 13], "avg_logprob": -0.21959459479596163, "compression_ratio": 1.5235602094240839, "no_speech_prob": 0.0, "words": [{"start": 190.48, "end": 190.96, "word": " times", "probability": 0.2900390625}, {"start": 190.96, "end": 191.26, "word": " 2", "probability": 0.70361328125}, {"start": 191.26, "end": 191.56, "word": " minus", "probability": 0.83203125}, {"start": 191.56, "end": 191.98, "word": " 1,", "probability": 0.9814453125}, {"start": 192.7, "end": 192.9, "word": " so", "probability": 0.7001953125}, {"start": 192.9, "end": 193.14, "word": " your", 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"probability": 0.96728515625}, {"start": 202.06, "end": 202.44, "word": " use", "probability": 0.87744140625}, {"start": 202.44, "end": 202.94, "word": " Chi", "probability": 0.470703125}, {"start": 202.94, "end": 203.3, "word": "-square", "probability": 0.7542317708333334}, {"start": 203.3, "end": 203.8, "word": " statistic.", "probability": 0.446044921875}, {"start": 205.44, "end": 206.0, "word": " Chi", "probability": 0.73828125}, {"start": 206.0, "end": 206.28, "word": "-square", "probability": 0.9451497395833334}, {"start": 206.28, "end": 206.44, "word": " is", "probability": 0.93310546875}, {"start": 206.44, "end": 206.78, "word": " always", "probability": 0.8994140625}, {"start": 206.78, "end": 207.2, "word": " positive,", "probability": 0.931640625}, {"start": 207.68, "end": 207.76, "word": " I", "probability": 0.97900390625}, {"start": 207.76, "end": 208.02, "word": " mean,", "probability": 0.9677734375}, {"start": 208.22, "end": 208.5, "word": " Chi", "probability": 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216.04, "word": " right", "probability": 0.92822265625}, {"start": 216.04, "end": 216.36, "word": " one.", "probability": 0.92041015625}], "temperature": 1.0}, {"id": 9, "seek": 24581, "start": 217.21, "end": 245.81, "text": " We reject F0 if your chi-square statistic falls in the rejection region. That means we reject the null hypothesis if chi-square statistic greater than chi-square alpha. Alpha can be determined by using chi-square table. So we reject in this case F0, otherwise, sorry, we don't reject F0. 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X1 is 12, this 12, plus 24 divided by 300. That will give 12%. So let me just write this notation, B dash.", "tokens": [823, 11, 428, 363, 8240, 307, 2212, 538, 1783, 16, 1804, 1783, 17, 6666, 538, 426, 16, 1804, 426, 17, 13, 1783, 16, 307, 2272, 11, 341, 2272, 11, 1804, 4022, 6666, 538, 6641, 13, 663, 486, 976, 2272, 6856, 407, 718, 385, 445, 2464, 341, 24657, 11, 363, 8240, 13], "avg_logprob": -0.19936898809212905, "compression_ratio": 1.328125, "no_speech_prob": 0.0, "words": [{"start": 332.81, "end": 333.17, "word": " Now,", "probability": 0.8427734375}, {"start": 333.65, "end": 334.21, "word": " your", "probability": 0.87060546875}, {"start": 334.21, "end": 334.43, "word": " B", "probability": 0.76171875}, {"start": 334.43, "end": 334.81, "word": " dash", "probability": 0.53662109375}, {"start": 334.81, "end": 337.83, "word": " is", "probability": 0.66943359375}, {"start": 337.83, "end": 338.07, "word": " given", "probability": 0.892578125}, {"start": 338.07, "end": 338.39, "word": " by", "probability": 0.966796875}, {"start": 338.39, "end": 338.83, "word": " X1", "probability": 0.6044921875}, {"start": 338.83, "end": 339.05, "word": " plus", "probability": 0.8154296875}, {"start": 339.05, "end": 339.43, "word": " X2", "probability": 0.9912109375}, {"start": 339.43, "end": 339.71, "word": " divided", "probability": 0.75244140625}, {"start": 339.71, "end": 339.87, "word": " by", "probability": 0.96923828125}, {"start": 339.87, "end": 340.19, "word": " N1", "probability": 0.962890625}, {"start": 340.19, "end": 340.53, "word": " plus", "probability": 0.95849609375}, {"start": 340.53, "end": 340.97, "word": " N2.", "probability": 0.998291015625}, {"start": 341.53, "end": 342.11, "word": " X1", "probability": 0.990966796875}, {"start": 342.11, "end": 342.25, "word": " is", "probability": 0.93017578125}, {"start": 342.25, "end": 342.83, "word": " 12,", "probability": 0.92041015625}, {"start": 344.05, "end": 344.35, "word": " this", "probability": 0.79931640625}, {"start": 344.35, "end": 344.73, "word": " 12,", "probability": 0.73046875}, {"start": 345.67, "end": 346.63, "word": " plus", "probability": 0.94921875}, {"start": 346.63, "end": 347.35, "word": " 24", "probability": 0.97900390625}, {"start": 347.35, "end": 348.73, "word": " divided", "probability": 0.65283203125}, {"start": 348.73, "end": 349.17, "word": " by", "probability": 0.97412109375}, {"start": 349.17, "end": 350.51, "word": " 300.", "probability": 0.97216796875}, {"start": 351.17, "end": 351.73, "word": " That", "probability": 0.90380859375}, {"start": 351.73, "end": 351.93, "word": " will", "probability": 0.8935546875}, {"start": 351.93, "end": 352.25, "word": " give", "probability": 0.8720703125}, {"start": 352.25, "end": 353.31, "word": " 12%.", "probability": 0.622802734375}, {"start": 353.31, "end": 353.93, "word": " So", "probability": 0.96044921875}, {"start": 353.93, "end": 354.09, "word": " let", "probability": 0.8505859375}, {"start": 354.09, "end": 354.19, "word": " me", "probability": 0.96337890625}, {"start": 354.19, "end": 354.43, "word": " just", "probability": 0.91796875}, {"start": 354.43, "end": 354.73, "word": " write", "probability": 0.87451171875}, {"start": 354.73, "end": 354.97, "word": " this", "probability": 0.9453125}, {"start": 354.97, "end": 355.51, "word": " notation,", "probability": 0.955078125}, {"start": 356.83, "end": 357.31, "word": " B", "probability": 0.79443359375}, {"start": 357.31, "end": 357.71, "word": " dash.", "probability": 0.92919921875}], "temperature": 1.0}, {"id": 14, "seek": 39068, "start": 365.56, "end": 390.68, "text": " equals 36 by 300, so that's 12%. So the expected frequency in this case for female, 0.12 times 120, because there are 120 females in the data you have, so that will give 14.4. So the expected frequency is 0.12 times 180, 120, I'm sorry,", "tokens": [6915, 8652, 538, 6641, 11, 370, 300, 311, 2272, 6856, 407, 264, 5176, 7893, 294, 341, 1389, 337, 6556, 11, 1958, 13, 4762, 1413, 10411, 11, 570, 456, 366, 10411, 21529, 294, 264, 1412, 291, 362, 11, 370, 300, 486, 976, 3499, 13, 19, 13, 407, 264, 5176, 7893, 307, 1958, 13, 4762, 1413, 11971, 11, 10411, 11, 286, 478, 2597, 11], "avg_logprob": -0.1927083328602806, "compression_ratio": 1.5192307692307692, "no_speech_prob": 0.0, "words": [{"start": 365.55999999999995, "end": 366.21999999999997, "word": " equals", "probability": 0.33544921875}, {"start": 366.21999999999997, "end": 366.88, "word": " 36", "probability": 0.9326171875}, {"start": 366.88, "end": 368.92, "word": " by", "probability": 0.88720703125}, {"start": 368.92, "end": 369.46, "word": " 300,", "probability": 0.95947265625}, {"start": 369.66, "end": 369.86, "word": " so", "probability": 0.939453125}, {"start": 369.86, "end": 370.34, "word": " that's", "probability": 0.956787109375}, {"start": 370.34, "end": 371.26, "word": " 12%.", "probability": 0.862548828125}, {"start": 371.26, "end": 373.22, "word": " So", "probability": 0.96142578125}, {"start": 373.22, "end": 373.38, "word": " the", "probability": 0.69970703125}, {"start": 373.38, "end": 373.74, "word": " expected", "probability": 0.91650390625}, {"start": 373.74, "end": 374.38, "word": " frequency", "probability": 0.94970703125}, {"start": 374.38, "end": 375.68, "word": " in", "probability": 0.57177734375}, {"start": 375.68, "end": 375.88, "word": " this", "probability": 0.94775390625}, {"start": 375.88, "end": 376.14, "word": " case", "probability": 0.90234375}, {"start": 376.14, "end": 376.32, "word": " for", "probability": 0.8603515625}, {"start": 376.32, "end": 376.78, "word": " female,", "probability": 0.7919921875}, {"start": 378.04, "end": 378.46, "word": " 0", "probability": 0.7490234375}, {"start": 378.46, "end": 378.78, "word": ".12", "probability": 0.96484375}, {"start": 378.78, "end": 379.08, "word": " times", "probability": 0.85595703125}, {"start": 379.08, "end": 379.5, "word": " 120,", "probability": 0.90966796875}, {"start": 379.68, "end": 379.9, "word": " because", "probability": 0.90478515625}, {"start": 379.9, "end": 380.06, "word": " there", "probability": 0.9091796875}, {"start": 380.06, "end": 380.18, "word": " are", "probability": 0.94287109375}, {"start": 380.18, "end": 380.58, "word": " 120", "probability": 0.91162109375}, {"start": 380.58, "end": 381.18, "word": " females", "probability": 0.9580078125}, {"start": 381.18, "end": 381.56, "word": " in", "probability": 0.91748046875}, {"start": 381.56, "end": 381.7, "word": " the", "probability": 0.921875}, {"start": 381.7, "end": 381.94, "word": " data", "probability": 0.9365234375}, {"start": 381.94, "end": 382.14, "word": " you", "probability": 0.94677734375}, {"start": 382.14, "end": 382.46, "word": " have,", "probability": 0.93994140625}, {"start": 382.86, "end": 382.98, "word": " so", "probability": 0.9423828125}, {"start": 382.98, "end": 383.16, "word": " that", "probability": 0.93603515625}, {"start": 383.16, "end": 383.32, "word": " will", "probability": 0.8603515625}, {"start": 383.32, "end": 383.5, "word": " give", "probability": 0.497802734375}, {"start": 383.5, "end": 383.84, "word": " 14", "probability": 0.6376953125}, {"start": 383.84, "end": 384.32, "word": ".4.", "probability": 0.99462890625}, {"start": 384.66, "end": 384.82, "word": " So", "probability": 0.96630859375}, {"start": 384.82, "end": 384.98, "word": " the", "probability": 0.837890625}, {"start": 384.98, "end": 385.52, "word": " expected", "probability": 0.90478515625}, {"start": 385.52, "end": 386.7, "word": " frequency", "probability": 0.73681640625}, {"start": 386.7, "end": 386.9, "word": " is", "probability": 0.8701171875}, {"start": 386.9, "end": 387.16, "word": " 0", "probability": 0.93701171875}, {"start": 387.16, "end": 387.58, "word": ".12", "probability": 0.992919921875}, {"start": 387.58, "end": 388.46, "word": " times", "probability": 0.87841796875}, {"start": 388.46, "end": 389.02, "word": " 180,", "probability": 0.5751953125}, {"start": 389.76, "end": 390.2, "word": " 120,", "probability": 0.72998046875}, {"start": 390.44, "end": 390.52, "word": " I'm", "probability": 0.92138671875}, {"start": 390.52, "end": 390.68, "word": " sorry,", "probability": 0.8466796875}], "temperature": 1.0}, {"id": 15, "seek": 41843, "start": 394.81, "end": 418.43, "text": " That will give 14.4. Similarly, for male to be left-handed is 0.12 times number of females in the sample, which is 180, and that will give 21.6. Now, since you compute the expected for the first cell, the second one direct is just the complement 120.", "tokens": [663, 486, 976, 3499, 13, 19, 13, 13157, 11, 337, 7133, 281, 312, 1411, 12, 25407, 307, 1958, 13, 4762, 1413, 1230, 295, 21529, 294, 264, 6889, 11, 597, 307, 11971, 11, 293, 300, 486, 976, 5080, 13, 21, 13, 823, 11, 1670, 291, 14722, 264, 5176, 337, 264, 700, 2815, 11, 264, 1150, 472, 2047, 307, 445, 264, 17103, 10411, 13], "avg_logprob": -0.2214781760223328, "compression_ratio": 1.4101123595505618, "no_speech_prob": 0.0, "words": [{"start": 394.81, "end": 395.07, "word": " That", "probability": 0.3037109375}, {"start": 395.07, "end": 395.27, "word": " will", "probability": 0.8125}, {"start": 395.27, "end": 395.49, "word": " give", "probability": 0.6005859375}, {"start": 395.49, "end": 395.89, "word": " 14", "probability": 0.70556640625}, {"start": 395.89, "end": 396.27, "word": ".4.", "probability": 0.9267578125}, {"start": 396.55, "end": 397.09, "word": " Similarly,", "probability": 0.84228515625}, {"start": 398.05, "end": 398.37, "word": " for", "probability": 0.94140625}, {"start": 398.37, "end": 398.73, "word": " male", "probability": 0.72119140625}, {"start": 398.73, "end": 399.43, "word": " to", "probability": 0.75732421875}, {"start": 399.43, "end": 399.59, "word": " be", "probability": 0.95947265625}, {"start": 399.59, "end": 399.81, "word": " left", "probability": 0.9267578125}, {"start": 399.81, "end": 400.31, "word": "-handed", "probability": 0.755615234375}, {"start": 400.31, "end": 401.09, "word": " is", "probability": 0.470947265625}, {"start": 401.09, "end": 401.33, "word": " 0", "probability": 0.79345703125}, {"start": 401.33, "end": 401.65, "word": ".12", "probability": 0.994140625}, {"start": 401.65, "end": 402.09, "word": " times", "probability": 0.8251953125}, {"start": 402.09, "end": 402.45, "word": " number", "probability": 0.77978515625}, {"start": 402.45, "end": 402.63, "word": " of", "probability": 0.9697265625}, {"start": 402.63, "end": 403.03, "word": " females", "probability": 0.94677734375}, {"start": 403.03, "end": 403.23, "word": " in", "probability": 0.93408203125}, {"start": 403.23, "end": 403.39, "word": " the", "probability": 0.837890625}, {"start": 403.39, "end": 403.65, "word": " sample,", "probability": 0.85595703125}, {"start": 403.81, "end": 403.93, "word": " which", "probability": 0.94775390625}, {"start": 403.93, "end": 404.11, "word": " is", "probability": 0.94482421875}, {"start": 404.11, "end": 404.49, "word": " 180,", "probability": 0.89404296875}, {"start": 404.93, "end": 405.13, "word": " and", "probability": 0.88720703125}, {"start": 405.13, "end": 405.29, "word": " that", "probability": 0.88037109375}, {"start": 405.29, "end": 405.43, "word": " will", "probability": 0.87109375}, {"start": 405.43, "end": 405.59, "word": " give", "probability": 0.87939453125}, {"start": 405.59, "end": 405.89, "word": " 21", "probability": 0.568359375}, {"start": 405.89, "end": 406.69, "word": ".6.", "probability": 0.997314453125}, {"start": 408.67, "end": 409.31, "word": " Now,", "probability": 0.9345703125}, {"start": 409.95, "end": 410.29, "word": " since", "probability": 0.8623046875}, {"start": 410.29, "end": 410.51, "word": " you", "probability": 0.9384765625}, {"start": 410.51, "end": 411.09, "word": " compute", "probability": 0.88720703125}, {"start": 411.09, "end": 412.05, "word": " the", "probability": 0.7529296875}, {"start": 412.05, "end": 412.51, "word": " expected", "probability": 0.96826171875}, {"start": 412.51, "end": 412.75, "word": " for", "probability": 0.93994140625}, {"start": 412.75, "end": 412.93, "word": " the", "probability": 0.919921875}, {"start": 412.93, "end": 413.19, "word": " first", "probability": 0.8681640625}, {"start": 413.19, "end": 413.45, "word": " cell,", "probability": 0.93408203125}, {"start": 413.53, "end": 413.65, "word": " the", "probability": 0.90869140625}, {"start": 413.65, "end": 413.95, "word": " second", "probability": 0.8876953125}, {"start": 413.95, "end": 414.37, "word": " one", "probability": 0.9228515625}, {"start": 414.37, "end": 415.05, "word": " direct", "probability": 0.60888671875}, {"start": 415.05, "end": 415.87, "word": " is", "probability": 0.74755859375}, {"start": 415.87, "end": 416.19, "word": " just", "probability": 0.72607421875}, {"start": 416.19, "end": 417.19, "word": " the", "probability": 0.75732421875}, {"start": 417.19, "end": 417.59, "word": " complement", "probability": 0.78271484375}, {"start": 417.59, "end": 418.43, "word": " 120.", "probability": 0.611328125}], "temperature": 1.0}, {"id": 16, "seek": 43562, "start": 419.48, "end": 435.62, "text": " 120 is sample size for the Rome. I mean female total 120 minus 14.4 will give 105.6. Or 0.88 times 120 will give the same value.", "tokens": [10411, 307, 6889, 2744, 337, 264, 12043, 13, 286, 914, 6556, 3217, 10411, 3175, 3499, 13, 19, 486, 976, 33705, 13, 21, 13, 1610, 1958, 13, 16919, 1413, 10411, 486, 976, 264, 912, 2158, 13], "avg_logprob": -0.2858072850439284, "compression_ratio": 1.18348623853211, "no_speech_prob": 0.0, "words": [{"start": 419.48, "end": 420.08, "word": " 120", "probability": 0.5}, {"start": 420.08, "end": 420.56, "word": " is", "probability": 0.7939453125}, {"start": 420.56, "end": 421.14, "word": " sample", "probability": 0.363525390625}, {"start": 421.14, "end": 421.6, "word": " size", "probability": 0.8408203125}, {"start": 421.6, "end": 421.82, "word": " for", "probability": 0.8896484375}, {"start": 421.82, "end": 421.98, "word": " the", "probability": 0.880859375}, {"start": 421.98, "end": 422.24, "word": " Rome.", "probability": 0.1212158203125}, {"start": 422.78, "end": 422.84, "word": " I", "probability": 0.87109375}, {"start": 422.84, "end": 423.02, "word": " mean", "probability": 0.96923828125}, {"start": 423.02, "end": 423.64, "word": " female", "probability": 0.4296875}, {"start": 423.64, "end": 424.16, "word": " total", "probability": 0.55859375}, {"start": 424.16, "end": 424.74, "word": " 120", "probability": 0.7978515625}, {"start": 424.74, "end": 425.76, "word": " minus", "probability": 0.90478515625}, {"start": 425.76, "end": 426.74, "word": " 14", "probability": 0.9443359375}, {"start": 426.74, "end": 427.2, "word": ".4", "probability": 0.975341796875}, {"start": 427.2, "end": 427.34, "word": " will", "probability": 0.7666015625}, {"start": 427.34, "end": 427.6, "word": " give", "probability": 0.841796875}, {"start": 427.6, "end": 428.4, "word": " 105", "probability": 0.93798828125}, {"start": 428.4, "end": 429.02, "word": ".6.", "probability": 0.98876953125}, {"start": 429.72, "end": 430.06, "word": " Or", "probability": 0.90625}, {"start": 430.06, "end": 432.2, "word": " 0", "probability": 0.6171875}, {"start": 432.2, "end": 432.82, "word": ".88", "probability": 0.994140625}, {"start": 432.82, "end": 434.06, "word": " times", "probability": 0.76708984375}, {"start": 434.06, "end": 434.54, "word": " 120", "probability": 0.9013671875}, {"start": 434.54, "end": 434.8, "word": " will", "probability": 0.86376953125}, {"start": 434.8, "end": 434.94, "word": " give", "probability": 0.8798828125}, {"start": 434.94, "end": 435.1, "word": " the", "probability": 0.904296875}, {"start": 435.1, "end": 435.3, "word": " same", "probability": 0.9091796875}, {"start": 435.3, "end": 435.62, "word": " value.", "probability": 0.96044921875}], "temperature": 1.0}, {"id": 17, "seek": 45967, "start": 437.15, "end": 459.67, "text": " Here, the expected is 21.6, so the compliment is the, I'm sorry, the expected is just the compliment, which is 180 minus 21.6 will give 158.4. Or 0.88 is the compliment of that one multiplied by 180 will give the same value. So that's the one we had discussed before.", "tokens": [1692, 11, 264, 5176, 307, 5080, 13, 21, 11, 370, 264, 16250, 307, 264, 11, 286, 478, 2597, 11, 264, 5176, 307, 445, 264, 16250, 11, 597, 307, 11971, 3175, 5080, 13, 21, 486, 976, 2119, 23, 13, 19, 13, 1610, 1958, 13, 16919, 307, 264, 16250, 295, 300, 472, 17207, 538, 11971, 486, 976, 264, 912, 2158, 13, 407, 300, 311, 264, 472, 321, 632, 7152, 949, 13], "avg_logprob": -0.1891741116132055, "compression_ratio": 1.5952380952380953, "no_speech_prob": 0.0, "words": [{"start": 437.15, "end": 437.63, "word": " Here,", "probability": 0.5859375}, {"start": 437.77, "end": 438.05, "word": " the", "probability": 0.82080078125}, {"start": 438.05, "end": 438.45, "word": " expected", "probability": 0.70947265625}, {"start": 438.45, "end": 438.67, "word": " is", "probability": 0.83544921875}, {"start": 438.67, "end": 439.01, "word": " 21", "probability": 0.96435546875}, {"start": 439.01, "end": 439.67, "word": ".6,", "probability": 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value of chi-square statistic by using this equation. Sum of F observed minus F expected squared divided by F expected for each cell. You have to compute the value of chi-square for each cell. In this case, the simplest case is just 2 by 2 table. So 12 minus 14.4 squared divided by 14.4.", "tokens": [1282, 341, 1874, 11, 291, 393, 6997, 264, 2158, 295, 13228, 12, 33292, 543, 29588, 538, 1228, 341, 5367, 13, 8626, 295, 479, 13095, 3175, 479, 5176, 8889, 6666, 538, 479, 5176, 337, 1184, 2815, 13, 509, 362, 281, 14722, 264, 2158, 295, 13228, 12, 33292, 543, 337, 1184, 2815, 13, 682, 341, 1389, 11, 264, 22811, 1389, 307, 445, 568, 538, 568, 3199, 13, 407, 2272, 3175, 3499, 13, 19, 8889, 6666, 538, 3499, 13, 19, 13], "avg_logprob": -0.15852453172961367, "compression_ratio": 1.694300518134715, "no_speech_prob": 0.0, "words": [{"start": 462.41, "end": 462.83, "word": " On", "probability": 0.8798828125}, {"start": 462.83, "end": 463.57, "word": " this", "probability": 0.94580078125}, {"start": 463.57, "end": 464.01, "word": " result,", "probability": 0.95068359375}, {"start": 464.55, "end": 465.11, "word": " you", "probability": 0.955078125}, {"start": 465.11, "end": 465.35, "word": " can", "probability": 0.943359375}, {"start": 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result. Now my chi-square value is 0.7576. And in this case, if chi-square value is very small, I mean it's close to zero, then we don't reject the null hypothesis.", "tokens": [7721, 264, 1150, 472, 41342, 3175, 33705, 8889, 6666, 538, 33705, 493, 281, 264, 1036, 472, 11, 291, 486, 483, 341, 1874, 13, 823, 452, 13228, 12, 33292, 543, 2158, 307, 1958, 13, 11901, 25026, 13, 400, 294, 341, 1389, 11, 498, 13228, 12, 33292, 543, 2158, 307, 588, 1359, 11, 286, 914, 309, 311, 1998, 281, 4018, 11, 550, 321, 500, 380, 8248, 264, 18184, 17291, 13], "avg_logprob": -0.20629528467205988, "compression_ratio": 1.4285714285714286, "no_speech_prob": 0.0, "words": [{"start": 489.32, "end": 489.72, "word": " Plus", "probability": 0.441650390625}, {"start": 489.72, "end": 489.98, "word": " the", "probability": 0.87548828125}, {"start": 489.98, "end": 490.32, "word": " second", "probability": 0.8701171875}, {"start": 490.32, "end": 490.68, "word": " one", "probability": 0.916015625}, {"start": 490.68, "end": 491.18, "word": " 108", "probability": 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So here if you look carefully for the observed and expected frequencies, you can tell if you can reject or don't reject the number. Now the difference between these values looks small, so that's lead to small chi-square.", "tokens": [1436, 264, 16998, 2158, 295, 13228, 12, 33292, 543, 307, 4018, 11, 293, 4018, 2314, 787, 498, 283, 13095, 307, 1998, 281, 283, 5176, 13, 407, 510, 498, 291, 574, 7500, 337, 264, 13095, 293, 5176, 20250, 11, 291, 393, 980, 498, 291, 393, 8248, 420, 500, 380, 8248, 264, 1230, 13, 823, 264, 2649, 1296, 613, 4190, 1542, 1359, 11, 370, 300, 311, 1477, 281, 1359, 13228, 12, 33292, 543, 13], "avg_logprob": -0.2043022292934052, "compression_ratio": 1.6225490196078431, "no_speech_prob": 0.0, "words": [{"start": 513.3, "end": 513.64, "word": " Because", "probability": 0.529296875}, {"start": 513.64, "end": 513.8, "word": " the", "probability": 0.8515625}, {"start": 513.8, "end": 514.14, "word": " smallest", "probability": 0.92333984375}, {"start": 514.14, "end": 514.44, "word": " value", "probability": 0.9697265625}, {"start": 514.44, "end": 514.56, "word": " of", "probability": 0.8720703125}, 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Because your chi-square value is very small. So we don't reject the null hypothesis. Or if you look carefully at the table, for the table we have here, for chi-square table. 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It's smaller than 1.32. 1.32 is a very small value. Then we don't reject. Then we don't reject x0. That's always, always true. 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Imagine that we are talking about alpha is 5%. So alpha is 5, so your critical value, the smallest one for 1 degrees of freedom, is 3.84. So that's my smallest, if alpha", "tokens": [1222, 13228, 12, 33292, 543, 307, 1998, 281, 4018, 11, 420, 4356, 813, 502, 13, 11440, 11, 570, 264, 7285, 2158, 295, 4924, 2158, 307, 502, 13, 11440, 13, 11739, 300, 321, 366, 1417, 466, 8961, 307, 1025, 6856, 407, 8961, 307, 1025, 11, 370, 428, 4924, 2158, 11, 264, 16998, 472, 337, 502, 5310, 295, 5645, 11, 307, 805, 13, 25494, 13, 407, 300, 311, 452, 16998, 11, 498, 8961], "avg_logprob": -0.2881944473418925, "compression_ratio": 1.5136612021857923, "no_speech_prob": 0.0, "words": [{"start": 627.7100000000002, "end": 628.3900000000001, "word": " My", "probability": 0.1014404296875}, {"start": 628.3900000000001, "end": 629.07, "word": " chi", "probability": 0.234130859375}, {"start": 629.07, "end": 629.39, "word": "-square", "probability": 0.793212890625}, {"start": 629.39, "end": 629.61, "word": " is", "probability": 0.8720703125}, {"start": 629.61, "end": 630.07, "word": " close", "probability": 0.81591796875}, {"start": 630.07, "end": 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And that's only true, only true for 2 by 2 table. That means this square is just Chi square 1.", "tokens": [5264, 565, 321, 2835, 300, 341, 2158, 307, 445, 502, 13, 22962, 8889, 13, 400, 300, 311, 787, 2074, 11, 787, 2074, 337, 568, 538, 568, 3199, 13, 663, 1355, 341, 3732, 307, 445, 17730, 3732, 502, 13], "avg_logprob": -0.3555689041431134, "compression_ratio": 1.3220338983050848, "no_speech_prob": 0.0, "words": [{"start": 663.7400000000001, "end": 664.5400000000001, "word": " Last", "probability": 0.0347900390625}, {"start": 664.5400000000001, "end": 665.34, "word": " time", "probability": 0.8681640625}, {"start": 665.34, "end": 665.48, "word": " we", "probability": 0.77783203125}, {"start": 665.48, "end": 665.82, "word": " mentioned", "probability": 0.7626953125}, {"start": 665.82, "end": 666.22, "word": " that", "probability": 0.91015625}, {"start": 666.22, "end": 666.58, "word": " this", "probability": 0.89404296875}, {"start": 666.58, "end": 666.94, "word": " value", "probability": 0.97412109375}, {"start": 666.94, "end": 667.16, "word": " is", "probability": 0.9404296875}, {"start": 667.16, "end": 667.6, "word": " just", "probability": 0.8876953125}, {"start": 667.6, "end": 668.68, "word": " 1", "probability": 0.923828125}, {"start": 668.68, "end": 669.68, "word": ".96", "probability": 0.9755859375}, {"start": 669.68, "end": 671.32, "word": " squared.", "probability": 0.6103515625}, {"start": 672.3, "end": 672.5, "word": " And", "probability": 0.74560546875}, {"start": 672.5, "end": 672.94, "word": " that's", "probability": 0.904541015625}, {"start": 672.94, "end": 673.34, "word": " only", "probability": 0.90673828125}, {"start": 673.34, "end": 673.7, "word": " true,", "probability": 0.953125}, {"start": 673.9, "end": 675.24, "word": " only", "probability": 0.91748046875}, {"start": 675.24, "end": 675.62, "word": " true", "probability": 0.96044921875}, {"start": 675.62, "end": 676.14, "word": " for", "probability": 0.9443359375}, {"start": 676.14, "end": 677.76, "word": " 2", "probability": 0.6044921875}, {"start": 677.76, "end": 677.98, "word": " by", "probability": 0.462890625}, {"start": 677.98, "end": 678.18, "word": " 2", "probability": 0.982421875}, {"start": 678.18, "end": 678.5, "word": " table.", "probability": 0.60693359375}, {"start": 680.74, "end": 681.54, "word": " That", "probability": 0.8408203125}, {"start": 681.54, "end": 682.02, "word": " means", "probability": 0.92578125}, {"start": 682.02, "end": 682.74, "word": " this", "probability": 0.396484375}, {"start": 682.74, "end": 683.32, "word": " square", "probability": 0.849609375}, {"start": 683.32, "end": 683.68, "word": " is", "probability": 0.9423828125}, {"start": 683.68, "end": 683.98, "word": " just", "probability": 0.8994140625}, {"start": 683.98, "end": 684.18, "word": " Chi", "probability": 0.431640625}, {"start": 684.18, "end": 684.48, "word": " square", "probability": 0.440673828125}, {"start": 684.48, "end": 684.8, "word": " 1.", "probability": 0.6923828125}], "temperature": 1.0}, {"id": 26, "seek": 70967, "start": 685.97, "end": 709.67, "text": " For this reason, we can test by one equal by two, by two methods, either this statistic or chi-square statistic. Both of them will give the same result. So let's go back to the question we have. My chi-square value is 0.77576.", "tokens": [1171, 341, 1778, 11, 321, 393, 1500, 538, 472, 2681, 538, 732, 11, 538, 732, 7150, 11, 2139, 341, 29588, 420, 13228, 12, 33292, 543, 29588, 13, 6767, 295, 552, 486, 976, 264, 912, 1874, 13, 407, 718, 311, 352, 646, 281, 264, 1168, 321, 362, 13, 1222, 13228, 12, 33292, 543, 2158, 307, 1958, 13, 22, 11901, 25026, 13], "avg_logprob": -0.18186474921273404, "compression_ratio": 1.41875, "no_speech_prob": 0.0, "words": [{"start": 685.97, "end": 686.23, "word": " For", "probability": 0.78466796875}, {"start": 686.23, "end": 686.49, "word": " this", "probability": 0.943359375}, {"start": 686.49, "end": 686.91, "word": " reason,", "probability": 0.97314453125}, {"start": 687.03, "end": 687.17, "word": " we", "probability": 0.958984375}, {"start": 687.17, "end": 687.63, "word": " can", "probability": 0.94775390625}, {"start": 687.63, "end": 688.97, "word": " test", "probability": 0.8427734375}, {"start": 688.97, "end": 689.19, "word": " by", "probability": 0.45458984375}, {"start": 689.19, "end": 689.47, "word": " one", "probability": 0.73828125}, {"start": 689.47, "end": 689.75, "word": " equal", "probability": 0.65771484375}, {"start": 689.75, "end": 690.03, "word": " by", "probability": 0.93896484375}, {"start": 690.03, "end": 690.45, "word": " two,", "probability": 0.93505859375}, {"start": 691.11, "end": 691.35, "word": " by", "probability": 0.96826171875}, {"start": 691.35, "end": 691.53, "word": " two", "probability": 0.9462890625}, {"start": 691.53, "end": 691.89, "word": " methods,", "probability": 0.8095703125}, {"start": 692.05, "end": 692.31, "word": " either", "probability": 0.9365234375}, {"start": 692.31, "end": 693.33, "word": " this", "probability": 0.50732421875}, {"start": 693.33, "end": 693.95, "word": " statistic", "probability": 0.90673828125}, {"start": 693.95, "end": 694.99, "word": " or", "probability": 0.88525390625}, {"start": 694.99, "end": 695.29, "word": " chi", "probability": 0.4228515625}, {"start": 695.29, "end": 695.63, "word": "-square", "probability": 0.8292643229166666}, {"start": 695.63, "end": 696.07, "word": " statistic.", "probability": 0.6591796875}, {"start": 696.87, "end": 697.37, "word": " Both", "probability": 0.77294921875}, {"start": 697.37, "end": 697.57, "word": " of", "probability": 0.96484375}, {"start": 697.57, "end": 697.75, "word": " them", "probability": 0.89599609375}, {"start": 697.75, "end": 697.89, "word": " will", "probability": 0.880859375}, {"start": 697.89, "end": 698.05, "word": " give", "probability": 0.89599609375}, {"start": 698.05, "end": 698.23, "word": " the", "probability": 0.91552734375}, {"start": 698.23, "end": 698.53, "word": " same", "probability": 0.900390625}, {"start": 698.53, "end": 699.43, "word": " result.", "probability": 0.92138671875}, {"start": 700.07, "end": 700.23, "word": " So", "probability": 0.94921875}, {"start": 700.23, "end": 700.47, "word": " let's", "probability": 0.865478515625}, {"start": 700.47, "end": 700.63, "word": " go", "probability": 0.96435546875}, {"start": 700.63, "end": 700.97, "word": " back", "probability": 0.86962890625}, {"start": 700.97, "end": 701.85, "word": " to", "probability": 0.9560546875}, {"start": 701.85, "end": 701.97, "word": " the", "probability": 0.92041015625}, {"start": 701.97, "end": 702.27, "word": " question", "probability": 0.91650390625}, {"start": 702.27, "end": 702.45, "word": " we", "probability": 0.94384765625}, {"start": 702.45, "end": 702.69, "word": " have.", "probability": 0.62548828125}, {"start": 703.13, "end": 703.33, "word": " My", "probability": 0.974609375}, {"start": 703.33, "end": 703.57, "word": " chi", "probability": 0.8662109375}, {"start": 703.57, "end": 703.87, "word": "-square", "probability": 0.9627278645833334}, {"start": 703.87, "end": 704.25, "word": " value", "probability": 0.96533203125}, {"start": 704.25, "end": 704.61, "word": " is", "probability": 0.95068359375}, {"start": 704.61, "end": 705.29, "word": " 0", "probability": 0.69970703125}, {"start": 705.29, "end": 709.67, "word": ".77576.", "probability": 0.8465576171875}], "temperature": 1.0}, {"id": 27, "seek": 72218, "start": 712.16, "end": 722.18, "text": " So that's your chi-square statistic. Again, degrees of freedom 1 to chi-square, the critical value is 3.841.", "tokens": [407, 300, 311, 428, 13228, 12, 33292, 543, 29588, 13, 3764, 11, 5310, 295, 5645, 502, 281, 13228, 12, 33292, 543, 11, 264, 4924, 2158, 307, 805, 13, 23, 17344, 13], "avg_logprob": -0.24304199498146772, "compression_ratio": 1.1237113402061856, "no_speech_prob": 0.0, "words": [{"start": 712.16, "end": 712.46, "word": " So", "probability": 0.8955078125}, {"start": 712.46, "end": 712.82, "word": " that's", "probability": 0.8974609375}, {"start": 712.82, "end": 713.04, "word": " your", "probability": 0.876953125}, {"start": 713.04, "end": 713.3, "word": " chi", "probability": 0.338623046875}, {"start": 713.3, "end": 713.6, "word": "-square", "probability": 0.7390950520833334}, {"start": 713.6, "end": 714.14, "word": " statistic.", "probability": 0.80517578125}, {"start": 716.28, "end": 716.94, "word": " Again,", "probability": 0.91552734375}, {"start": 717.5, "end": 717.76, "word": " degrees", "probability": 0.95068359375}, {"start": 717.76, "end": 717.94, "word": " of", "probability": 0.9501953125}, {"start": 717.94, "end": 718.22, "word": " freedom", "probability": 0.9453125}, {"start": 718.22, "end": 718.56, "word": " 1", "probability": 0.3466796875}, {"start": 718.56, "end": 718.74, "word": " to", "probability": 0.65087890625}, {"start": 718.74, "end": 719.0, "word": " chi", "probability": 0.7685546875}, {"start": 719.0, "end": 719.36, "word": "-square,", "probability": 0.93017578125}, {"start": 719.78, "end": 719.92, "word": " the", "probability": 0.41552734375}, {"start": 719.92, "end": 720.24, "word": " critical", "probability": 0.95166015625}, {"start": 720.24, "end": 720.72, "word": " value", "probability": 0.974609375}, {"start": 720.72, "end": 721.16, "word": " is", "probability": 0.900390625}, {"start": 721.16, "end": 721.42, "word": " 3", "probability": 0.99267578125}, {"start": 721.42, "end": 722.18, "word": ".841.", "probability": 0.9163411458333334}], "temperature": 1.0}, {"id": 28, "seek": 75320, "start": 724.12, "end": 753.2, "text": " So my decision is we don't reject the null hypothesis. My conclusion is there is not sufficient evidence that two proportions are different. So you don't have sufficient evidence in order to support that the two proportions are different at 5% level of significance. We stopped last time at this point. Now suppose we are testing", "tokens": [407, 452, 3537, 307, 321, 500, 380, 8248, 264, 18184, 17291, 13, 1222, 10063, 307, 456, 307, 406, 11563, 4467, 300, 732, 32482, 366, 819, 13, 407, 291, 500, 380, 362, 11563, 4467, 294, 1668, 281, 1406, 300, 264, 732, 32482, 366, 819, 412, 1025, 4, 1496, 295, 17687, 13, 492, 5936, 1036, 565, 412, 341, 935, 13, 823, 7297, 321, 366, 4997], "avg_logprob": -0.11767577973660082, "compression_ratio": 1.7010309278350515, "no_speech_prob": 0.0, "words": [{"start": 724.12, "end": 724.38, "word": " So", "probability": 0.85986328125}, {"start": 724.38, "end": 724.56, "word": " my", "probability": 0.7529296875}, {"start": 724.56, "end": 724.92, "word": " decision", "probability": 0.92822265625}, {"start": 724.92, "end": 725.38, "word": " is", "probability": 0.95166015625}, {"start": 725.38, "end": 727.9, "word": " we", "probability": 0.41796875}, {"start": 727.9, "end": 728.14, "word": " don't", "probability": 0.9609375}, {"start": 728.14, "end": 728.5, 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The same steps, we have to extend in this case chi-square. Your null hypothesis, by one equal by two, all the way up to by C. So in this case, there are C columns. 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So pi 1 equals pi 2, all the way up to pi C. So null hypothesis for the columns we have. There are C columns. Again, it's the alternative, not all of the pi J are equal, and J equals 1 up to C. Now, the only difference here, the degrees of freedom.", "tokens": [407, 1230, 295, 13766, 6915, 383, 11, 293, 456, 366, 787, 732, 13241, 13, 407, 3895, 502, 6915, 3895, 568, 11, 439, 264, 636, 493, 281, 3895, 383, 13, 407, 18184, 17291, 337, 264, 13766, 321, 362, 13, 821, 366, 383, 13766, 13, 3764, 11, 309, 311, 264, 8535, 11, 406, 439, 295, 264, 3895, 508, 366, 2681, 11, 293, 508, 6915, 502, 493, 281, 383, 13, 823, 11, 264, 787, 2649, 510, 11, 264, 5310, 295, 5645, 13], "avg_logprob": -0.20136718079447746, "compression_ratio": 1.592783505154639, "no_speech_prob": 0.0, "words": [{"start": 782.54, "end": 782.76, "word": " So", "probability": 0.927734375}, {"start": 782.76, "end": 783.04, "word": " number", "probability": 0.76611328125}, {"start": 783.04, "end": 783.24, "word": " of", "probability": 0.96875}, {"start": 783.24, "end": 783.68, "word": " columns", "probability": 0.94091796875}, {"start": 783.68, "end": 784.26, "word": " equals", "probability": 0.83740234375}, {"start": 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There are two rows, so 2 minus 1 times number of columns minus 1. 2 minus 1 is 1, c minus 1, 1 times c minus 1, c minus 1. So your degrees of freedom in this case is c minus 1.", "tokens": [1171, 568, 538, 269, 3199, 11, 568, 538, 269, 11, 5310, 295, 5645, 6915, 1230, 295, 13241, 3175, 502, 13, 821, 366, 732, 13241, 11, 370, 568, 3175, 502, 1413, 1230, 295, 13766, 3175, 502, 13, 568, 3175, 502, 307, 502, 11, 269, 3175, 502, 11, 502, 1413, 269, 3175, 502, 11, 269, 3175, 502, 13, 407, 428, 5310, 295, 5645, 294, 341, 1389, 307, 269, 3175, 502, 13], "avg_logprob": -0.15636160842009952, "compression_ratio": 1.8333333333333333, "no_speech_prob": 0.0, "words": [{"start": 811.37, "end": 811.69, "word": " For", "probability": 0.7646484375}, {"start": 811.69, "end": 811.97, "word": " 2", "probability": 0.615234375}, {"start": 811.97, "end": 812.19, "word": " by", "probability": 0.86328125}, {"start": 812.19, "end": 812.41, "word": " c", "probability": 0.611328125}, {"start": 812.41, "end": 812.85, "word": " table,", "probability": 0.80517578125}, {"start": 815.71, "end": 815.81, "word": " 2", "probability": 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For two by two table, degrees of freedom is just one. If there are C columns and we have the same number of rows, degrees of freedom is C minus one. And we have the same chi squared statistic, the same equation I mean.", "tokens": [407, 300, 311, 264, 787, 2649, 13, 1171, 732, 538, 732, 3199, 11, 5310, 295, 5645, 307, 445, 472, 13, 759, 456, 366, 383, 13766, 293, 321, 362, 264, 912, 1230, 295, 13241, 11, 5310, 295, 5645, 307, 383, 3175, 472, 13, 400, 321, 362, 264, 912, 13228, 8889, 29588, 11, 264, 912, 5367, 286, 914, 13], "avg_logprob": -0.18547952123757067, "compression_ratio": 1.5923566878980893, "no_speech_prob": 0.0, "words": [{"start": 840.07, "end": 840.27, "word": " So", "probability": 0.89404296875}, {"start": 840.27, "end": 840.57, "word": " that's", "probability": 0.87353515625}, {"start": 840.57, "end": 840.73, "word": " the", "probability": 0.91748046875}, {"start": 840.73, "end": 840.99, "word": " only", "probability": 0.94091796875}, {"start": 840.99, "end": 841.61, "word": " difference.", "probability": 0.857421875}, {"start": 842.57, "end": 842.71, "word": " For", "probability": 0.95556640625}, {"start": 842.71, "end": 842.87, "word": " two", "probability": 0.55078125}, {"start": 842.87, "end": 843.01, "word": " by", "probability": 0.8037109375}, {"start": 843.01, "end": 843.19, "word": " two", "probability": 0.943359375}, {"start": 843.19, "end": 843.49, "word": " table,", "probability": 0.7373046875}, {"start": 843.95, "end": 844.33, "word": " degrees", "probability": 0.85302734375}, {"start": 844.33, "end": 844.43, "word": " of", "probability": 0.90576171875}, {"start": 844.43, "end": 844.59, "word": " freedom", "probability": 0.93212890625}, {"start": 844.59, "end": 844.79, "word": " is", "probability": 0.8056640625}, {"start": 844.79, "end": 844.99, "word": " just", "probability": 0.9140625}, {"start": 844.99, "end": 845.25, "word": " one.", "probability": 0.8671875}, {"start": 846.51, "end": 846.89, "word": " If", "probability": 0.96826171875}, {"start": 846.89, "end": 847.13, "word": " there", "probability": 0.89453125}, {"start": 847.13, "end": 847.55, "word": " are", "probability": 0.94970703125}, {"start": 847.55, "end": 847.97, "word": " C", "probability": 0.5966796875}, {"start": 847.97, "end": 848.53, "word": " columns", "probability": 0.93994140625}, {"start": 848.53, "end": 849.35, "word": " and", "probability": 0.6142578125}, {"start": 849.35, "end": 849.47, "word": " we", "probability": 0.93701171875}, {"start": 849.47, "end": 849.59, "word": " have", "probability": 0.94921875}, {"start": 849.59, "end": 849.75, "word": " the", "probability": 0.9072265625}, {"start": 849.75, "end": 849.93, "word": " same", "probability": 0.90966796875}, {"start": 849.93, "end": 850.19, "word": " number", "probability": 0.93359375}, {"start": 850.19, "end": 850.35, "word": " of", "probability": 0.96484375}, {"start": 850.35, "end": 850.67, "word": " rows,", "probability": 0.904296875}, {"start": 851.45, "end": 851.73, "word": " degrees", "probability": 0.95068359375}, {"start": 851.73, "end": 851.93, "word": " of", "probability": 0.96630859375}, {"start": 851.93, "end": 852.17, "word": " freedom", "probability": 0.9150390625}, {"start": 852.17, "end": 852.43, "word": " is", "probability": 0.783203125}, {"start": 852.43, "end": 852.59, "word": " C", "probability": 0.92138671875}, {"start": 852.59, "end": 852.85, "word": " minus", "probability": 0.86474609375}, {"start": 852.85, "end": 853.25, "word": " one.", "probability": 0.75341796875}, {"start": 854.07, "end": 854.33, "word": " And", "probability": 0.94580078125}, {"start": 854.33, "end": 854.45, "word": " we", "probability": 0.93994140625}, {"start": 854.45, "end": 854.57, "word": " have", "probability": 0.9482421875}, {"start": 854.57, "end": 854.81, "word": " the", "probability": 0.9072265625}, {"start": 854.81, "end": 855.23, "word": " same", "probability": 0.90478515625}, {"start": 855.23, "end": 856.09, "word": " chi", "probability": 0.37744140625}, {"start": 856.09, "end": 856.35, "word": " squared", "probability": 0.353759765625}, {"start": 856.35, "end": 857.09, "word": " statistic,", "probability": 0.80224609375}, {"start": 858.09, "end": 858.39, "word": " the", "probability": 0.82666015625}, {"start": 858.39, "end": 858.55, "word": " same", "probability": 0.91552734375}, {"start": 858.55, "end": 858.97, "word": " equation", "probability": 0.970703125}, {"start": 858.97, "end": 859.19, "word": " I", "probability": 0.76904296875}, {"start": 859.19, "end": 859.39, "word": " mean.", "probability": 0.9677734375}], "temperature": 1.0}, {"id": 33, "seek": 88191, "start": 861.05, "end": 881.91, "text": " And we have to extend also the overall proportion instead of x1 plus x2 divided by n1 plus n2. It becomes x1 plus x2 plus x3 all the way up to xc because there are c columns divided by n1 plus n2 all the way up to nc. So that's x over n.", "tokens": [400, 321, 362, 281, 10101, 611, 264, 4787, 16068, 2602, 295, 2031, 16, 1804, 2031, 17, 6666, 538, 297, 16, 1804, 297, 17, 13, 467, 3643, 2031, 16, 1804, 2031, 17, 1804, 2031, 18, 439, 264, 636, 493, 281, 2031, 66, 570, 456, 366, 269, 13766, 6666, 538, 297, 16, 1804, 297, 17, 439, 264, 636, 493, 281, 297, 66, 13, 407, 300, 311, 2031, 670, 297, 13], "avg_logprob": -0.13937953157701355, "compression_ratio": 1.6081081081081081, "no_speech_prob": 0.0, "words": [{"start": 861.05, "end": 861.31, "word": " And", "probability": 0.86572265625}, {"start": 861.31, "end": 861.43, "word": " we", "probability": 0.91943359375}, {"start": 861.43, "end": 861.55, "word": " have", "probability": 0.9384765625}, {"start": 861.55, "end": 861.67, "word": " to", "probability": 0.96435546875}, {"start": 861.67, "end": 862.07, "word": " extend", "probability": 0.8798828125}, {"start": 862.07, "end": 862.63, "word": " also", "probability": 0.85595703125}, {"start": 862.63, "end": 863.41, "word": " the", "probability": 0.7294921875}, {"start": 863.41, "end": 863.89, "word": " overall", "probability": 0.892578125}, {"start": 863.89, "end": 864.37, "word": " proportion", "probability": 0.77099609375}, {"start": 864.37, "end": 865.13, "word": " instead", "probability": 0.484130859375}, {"start": 865.13, "end": 865.47, "word": " of", "probability": 0.96240234375}, {"start": 865.47, "end": 865.83, "word": " x1", "probability": 0.702880859375}, {"start": 865.83, "end": 866.11, "word": " plus", "probability": 0.82861328125}, {"start": 866.11, "end": 866.45, "word": " x2", "probability": 0.99609375}, {"start": 866.45, "end": 866.79, "word": " divided", "probability": 0.7080078125}, {"start": 866.79, "end": 867.01, "word": " by", "probability": 0.96484375}, {"start": 867.01, "end": 867.33, "word": " n1", "probability": 0.90966796875}, {"start": 867.33, "end": 867.65, "word": " plus", "probability": 0.958984375}, {"start": 867.65, "end": 868.05, "word": " n2.", "probability": 0.998046875}, {"start": 868.37, "end": 868.95, "word": " It", "probability": 0.94580078125}, {"start": 868.95, "end": 869.45, "word": " becomes", "probability": 0.88623046875}, {"start": 869.45, "end": 870.11, "word": " x1", "probability": 0.99169921875}, {"start": 870.11, "end": 870.39, "word": " plus", "probability": 0.951171875}, {"start": 870.39, "end": 870.89, "word": " x2", "probability": 0.993896484375}, {"start": 870.89, "end": 871.27, "word": " plus", "probability": 0.947265625}, {"start": 871.27, "end": 871.85, "word": " x3", "probability": 0.99609375}, {"start": 871.85, "end": 872.29, "word": " all", "probability": 0.787109375}, {"start": 872.29, "end": 872.45, "word": " the", "probability": 0.9208984375}, {"start": 872.45, "end": 872.61, "word": " way", "probability": 0.9541015625}, {"start": 872.61, "end": 872.83, "word": " up", "probability": 0.9580078125}, {"start": 872.83, "end": 872.99, "word": " to", "probability": 0.96923828125}, {"start": 872.99, "end": 873.57, "word": " xc", "probability": 0.8232421875}, {"start": 873.57, "end": 874.41, "word": " because", "probability": 0.5439453125}, {"start": 874.41, "end": 874.65, "word": " there", "probability": 0.8857421875}, {"start": 874.65, "end": 874.89, "word": " are", "probability": 0.9453125}, {"start": 874.89, "end": 875.37, "word": " c", "probability": 0.91064453125}, {"start": 875.37, "end": 876.49, "word": " columns", "probability": 0.90234375}, {"start": 876.49, "end": 877.75, "word": " divided", "probability": 0.3671875}, {"start": 877.75, "end": 877.99, "word": " by", "probability": 0.96484375}, {"start": 877.99, "end": 878.33, "word": " n1", "probability": 0.984130859375}, {"start": 878.33, "end": 878.69, "word": " plus", "probability": 0.95556640625}, {"start": 878.69, "end": 879.05, "word": " n2", "probability": 0.996337890625}, {"start": 879.05, "end": 879.29, "word": " all", "probability": 0.876953125}, {"start": 879.29, "end": 879.43, "word": " the", "probability": 0.916015625}, {"start": 879.43, "end": 879.55, "word": " way", "probability": 0.94921875}, {"start": 879.55, "end": 879.71, "word": " up", "probability": 0.95068359375}, {"start": 879.71, "end": 879.83, "word": " to", "probability": 0.96044921875}, {"start": 879.83, "end": 880.25, "word": " nc.", "probability": 0.90185546875}, {"start": 880.63, "end": 880.85, "word": " So", "probability": 0.9384765625}, {"start": 880.85, "end": 881.15, "word": " that's", "probability": 0.890869140625}, {"start": 881.15, "end": 881.41, "word": " x", "probability": 0.99169921875}, {"start": 881.41, "end": 881.71, "word": " over", "probability": 0.8681640625}, {"start": 881.71, "end": 881.91, "word": " n.", "probability": 0.7392578125}], "temperature": 1.0}, {"id": 34, "seek": 91130, "start": 883.54, "end": 911.3, "text": " So similarly we can reject the null hypothesis if the value of chi-square statistic lies or falls in the rejection region. Other type of chi-square test is called chi-square test of independence. Generally speaking, most of the time there are more than two columns or more than two rows.", "tokens": [407, 14138, 321, 393, 8248, 264, 18184, 17291, 498, 264, 2158, 295, 13228, 12, 33292, 543, 29588, 9134, 420, 8804, 294, 264, 26044, 4458, 13, 5358, 2010, 295, 13228, 12, 33292, 543, 1500, 307, 1219, 13228, 12, 33292, 543, 1500, 295, 14640, 13, 21082, 4124, 11, 881, 295, 264, 565, 456, 366, 544, 813, 732, 13766, 420, 544, 813, 732, 13241, 13], "avg_logprob": -0.15141368905703226, "compression_ratio": 1.6551724137931034, "no_speech_prob": 0.0, "words": [{"start": 883.5400000000001, "end": 884.2, "word": " So", "probability": 0.90185546875}, {"start": 884.2, "end": 884.86, "word": " similarly", "probability": 0.720703125}, {"start": 884.86, "end": 885.32, "word": " we", "probability": 0.50927734375}, {"start": 885.32, "end": 885.6, "word": " can", "probability": 0.94189453125}, {"start": 885.6, "end": 886.42, "word": " reject", "probability": 0.89013671875}, {"start": 886.42, "end": 886.7, "word": " the", "probability": 0.85107421875}, {"start": 886.7, "end": 886.88, "word": " null", "probability": 0.95263671875}, {"start": 886.88, "end": 887.34, "word": " hypothesis", "probability": 0.88671875}, {"start": 887.34, "end": 888.4, "word": " if", "probability": 0.8603515625}, {"start": 888.4, "end": 888.6, "word": " the", "probability": 0.91259765625}, {"start": 888.6, "end": 888.84, "word": " value", "probability": 0.96533203125}, {"start": 888.84, "end": 889.02, "word": " of", "probability": 0.9443359375}, {"start": 889.02, "end": 889.16, "word": " chi", "probability": 0.390625}, {"start": 889.16, "end": 889.42, "word": "-square", "probability": 0.8240559895833334}, {"start": 889.42, "end": 889.8, "word": " statistic", "probability": 0.45751953125}, {"start": 889.8, "end": 890.7, "word": " lies", "probability": 0.90576171875}, {"start": 890.7, "end": 891.0, "word": " or", "probability": 0.89599609375}, {"start": 891.0, "end": 891.44, "word": " falls", "probability": 0.77783203125}, {"start": 891.44, "end": 892.26, "word": " in", "probability": 0.9306640625}, {"start": 892.26, "end": 892.62, "word": " the", "probability": 0.92041015625}, {"start": 892.62, "end": 893.32, "word": " rejection", "probability": 0.94140625}, {"start": 893.32, "end": 894.16, "word": " region.", "probability": 0.85595703125}, {"start": 898.12, "end": 898.78, "word": " Other", "probability": 0.7314453125}, {"start": 898.78, "end": 899.18, "word": " type", "probability": 0.9609375}, {"start": 899.18, "end": 899.38, "word": " of", "probability": 0.97314453125}, {"start": 899.38, "end": 899.6, "word": " chi", "probability": 0.736328125}, {"start": 899.6, "end": 900.0, "word": "-square", "probability": 0.9532877604166666}, {"start": 900.0, "end": 900.6, "word": " test", "probability": 0.82861328125}, {"start": 900.6, "end": 901.06, "word": " is", "probability": 0.94140625}, {"start": 901.06, "end": 901.4, "word": " called", "probability": 0.91552734375}, {"start": 901.4, "end": 901.66, "word": " chi", "probability": 0.78173828125}, {"start": 901.66, "end": 901.98, "word": "-square", "probability": 0.9695638020833334}, {"start": 901.98, "end": 902.26, "word": " test", "probability": 0.900390625}, {"start": 902.26, "end": 902.44, "word": " of", "probability": 0.966796875}, {"start": 902.44, "end": 902.9, "word": " independence.", "probability": 0.8955078125}, {"start": 905.3, "end": 905.76, "word": " Generally", "probability": 0.57666015625}, {"start": 905.76, "end": 906.4, "word": " speaking,", "probability": 0.86279296875}, {"start": 907.08, "end": 907.24, "word": " most", "probability": 0.70654296875}, {"start": 907.24, "end": 907.38, "word": " of", "probability": 0.96728515625}, {"start": 907.38, "end": 907.46, "word": " the", "probability": 0.9189453125}, {"start": 907.46, "end": 907.7, "word": " time", "probability": 0.85693359375}, {"start": 907.7, "end": 907.92, "word": " there", "probability": 0.75048828125}, {"start": 907.92, "end": 908.26, "word": " are", "probability": 0.93896484375}, {"start": 908.26, "end": 908.54, "word": " more", "probability": 0.94287109375}, {"start": 908.54, "end": 908.8, "word": " than", "probability": 0.953125}, {"start": 908.8, "end": 909.08, "word": " two", "probability": 0.9072265625}, {"start": 909.08, "end": 909.58, "word": " columns", "probability": 0.9580078125}, {"start": 909.58, "end": 910.16, "word": " or", "probability": 0.83837890625}, {"start": 910.16, "end": 910.44, "word": " more", "probability": 0.94091796875}, {"start": 910.44, "end": 910.64, "word": " than", "probability": 0.95166015625}, {"start": 910.64, "end": 910.86, "word": " two", "probability": 0.92626953125}, {"start": 910.86, "end": 911.3, "word": " rows.", "probability": 0.9111328125}], "temperature": 1.0}, {"id": 35, "seek": 93351, "start": 912.95, "end": 933.51, "text": " Now, suppose we have contingency table that has R rows and C columns. And we are interested to test to see whether the two categorical variables are independent. 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That means there is a relationship between them. So test of independence. Null hypothesis is always the two variables, I mean, the two categorical variables are independent. So it's zero. 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So tests of independence for chi-square test to see whether or not the two variables are independent. So your null, two variables are independent against they are not independent. 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So, this statistic is no longer appropriate or valid for more than two proportions.", "tokens": [407, 11, 294, 1668, 281, 1500, 281, 536, 498, 544, 813, 732, 32482, 366, 2681, 11, 291, 2644, 764, 341, 29588, 13, 407, 11, 341, 29588, 307, 572, 2854, 6854, 420, 7363, 337, 544, 813, 732, 32482, 13], "avg_logprob": -0.1678685882152655, "compression_ratio": 1.564102564102564, "no_speech_prob": 0.0, "words": [{"start": 1021.14, "end": 1021.52, "word": " So,", "probability": 0.7177734375}, {"start": 1021.66, "end": 1021.74, "word": " in", "probability": 0.90966796875}, {"start": 1021.74, "end": 1021.94, "word": " order", "probability": 0.92236328125}, {"start": 1021.94, "end": 1022.16, "word": " to", "probability": 0.96875}, {"start": 1022.16, "end": 1022.44, "word": " test", "probability": 0.8671875}, {"start": 1022.44, "end": 1022.64, "word": " to", "probability": 0.75732421875}, {"start": 1022.64, "end": 1022.86, "word": " see", "probability": 0.92626953125}, {"start": 1022.86, "end": 1023.16, "word": " if", "probability": 0.92431640625}, {"start": 1023.16, "end": 1023.44, "word": " more", "probability": 0.9267578125}, {"start": 1023.44, "end": 1023.66, "word": " than", "probability": 0.9404296875}, {"start": 1023.66, "end": 1023.88, "word": " two", "probability": 0.73486328125}, {"start": 1023.88, "end": 1024.42, "word": " proportions", "probability": 0.76904296875}, {"start": 1024.42, "end": 1024.74, "word": " are", "probability": 0.9482421875}, {"start": 1024.74, "end": 1025.08, "word": " equal,", "probability": 0.880859375}, {"start": 1025.7, "end": 1026.02, "word": " you", "probability": 0.94482421875}, {"start": 1026.02, "end": 1026.36, "word": " cannot", "probability": 0.8125}, {"start": 1026.36, "end": 1026.72, "word": " use", "probability": 0.8798828125}, {"start": 1026.72, "end": 1026.9, "word": " this", "probability": 0.77294921875}, {"start": 1026.9, "end": 1027.34, "word": " statistic.", "probability": 0.8583984375}, {"start": 1028.3, "end": 1028.58, "word": " So,", "probability": 0.927734375}, {"start": 1028.68, "end": 1028.86, "word": " this", "probability": 0.93603515625}, {"start": 1028.86, "end": 1029.42, "word": " statistic", "probability": 0.9111328125}, {"start": 1029.42, "end": 1035.7, "word": " is", "probability": 0.5341796875}, {"start": 1035.7, "end": 1036.24, "word": " no", "probability": 0.935546875}, {"start": 1036.24, "end": 1036.8, "word": " longer", "probability": 0.93310546875}, {"start": 1036.8, "end": 1039.66, "word": " appropriate", "probability": 0.7490234375}, {"start": 1039.66, "end": 1041.92, "word": " or", "probability": 0.9052734375}, {"start": 1041.92, "end": 1042.36, "word": " valid", "probability": 0.966796875}, {"start": 1042.36, "end": 1043.5, "word": " for", "probability": 0.94287109375}, {"start": 1043.5, "end": 1045.54, "word": " more", "probability": 0.93798828125}, {"start": 1045.54, "end": 1045.94, "word": " than", "probability": 0.95068359375}, {"start": 1045.94, "end": 1047.6, "word": " two", "probability": 0.89990234375}, {"start": 1047.6, "end": 1048.16, "word": " proportions.", "probability": 0.85791015625}], "temperature": 1.0}, {"id": 40, "seek": 107610, "start": 1049.51, "end": 1076.11, "text": " In this case, you have to use chi-square test. So this statistic can be used only to test the difference between two proportions. But for more than two, you have to use chi-square test. So similar, chi-square test of independence is similar to chi-square test for equality of more than two proportions. But extend the concept.", "tokens": [682, 341, 1389, 11, 291, 362, 281, 764, 13228, 12, 33292, 543, 1500, 13, 407, 341, 29588, 393, 312, 1143, 787, 281, 1500, 264, 2649, 1296, 732, 32482, 13, 583, 337, 544, 813, 732, 11, 291, 362, 281, 764, 13228, 12, 33292, 543, 1500, 13, 407, 2531, 11, 13228, 12, 33292, 543, 1500, 295, 14640, 307, 2531, 281, 13228, 12, 33292, 543, 1500, 337, 14949, 295, 544, 813, 732, 32482, 13, 583, 10101, 264, 3410, 13], "avg_logprob": -0.15848214130897026, "compression_ratio": 1.9349112426035502, "no_speech_prob": 0.0, "words": [{"start": 1049.51, "end": 1049.79, "word": " In", "probability": 0.79248046875}, {"start": 1049.79, "end": 1050.05, "word": " this", "probability": 0.94580078125}, {"start": 1050.05, "end": 1050.37, "word": " case,", "probability": 0.916015625}, {"start": 1050.49, "end": 1050.55, "word": " you", "probability": 0.95751953125}, {"start": 1050.55, "end": 1050.77, "word": " have", "probability": 0.93896484375}, {"start": 1050.77, "end": 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So one more time, this statistic is valid only for two by two tables. So that means we can use z or chi-square to test if there is no difference between two population proportions. But for more than that, you have to use chi-square.", "tokens": [407, 294, 341, 1389, 11, 291, 2644, 764, 341, 29588, 13, 407, 472, 544, 565, 11, 341, 29588, 307, 7363, 787, 337, 732, 538, 732, 8020, 13, 407, 300, 1355, 321, 393, 764, 710, 420, 13228, 12, 33292, 543, 281, 1500, 498, 456, 307, 572, 2649, 1296, 732, 4415, 32482, 13, 583, 337, 544, 813, 300, 11, 291, 362, 281, 764, 13228, 12, 33292, 543, 13], "avg_logprob": -0.15671641524158306, "compression_ratio": 1.6242774566473988, "no_speech_prob": 0.0, "words": [{"start": 1107.08, "end": 1107.36, "word": " So", "probability": 0.908203125}, {"start": 1107.36, "end": 1107.48, "word": " in", "probability": 0.61279296875}, {"start": 1107.48, "end": 1107.62, "word": " this", "probability": 0.94287109375}, {"start": 1107.62, "end": 1107.82, "word": " case,", "probability": 0.9248046875}, {"start": 1107.92, "end": 1108.0, "word": " you", "probability": 0.9609375}, {"start": 1108.0, "end": 1108.3, "word": " cannot", "probability": 0.88623046875}, {"start": 1108.3, "end": 1108.84, "word": " use", "probability": 0.86279296875}, {"start": 1108.84, "end": 1109.22, "word": " this", "probability": 0.48779296875}, {"start": 1109.22, "end": 1109.72, "word": " statistic.", "probability": 0.79052734375}, {"start": 1110.34, "end": 1110.52, "word": " So", "probability": 0.95751953125}, {"start": 1110.52, "end": 1110.7, "word": " one", "probability": 0.8564453125}, {"start": 1110.7, "end": 1110.86, "word": " more", "probability": 0.92822265625}, {"start": 1110.86, "end": 1111.14, "word": " time,", "probability": 0.86767578125}, {"start": 1111.2, "end": 1111.34, "word": " this", "probability": 0.89306640625}, {"start": 1111.34, "end": 1111.86, "word": " statistic", "probability": 0.91845703125}, {"start": 1111.86, "end": 1112.22, "word": " is", "probability": 0.94775390625}, {"start": 1112.22, "end": 1112.54, "word": " valid", "probability": 0.96044921875}, {"start": 1112.54, "end": 1112.96, "word": " only", "probability": 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1121.9, "word": " population", "probability": 0.78955078125}, {"start": 1121.9, "end": 1122.4, "word": " proportions.", "probability": 0.47412109375}, {"start": 1123.1, "end": 1123.28, "word": " But", "probability": 0.9462890625}, {"start": 1123.28, "end": 1123.54, "word": " for", "probability": 0.93359375}, {"start": 1123.54, "end": 1123.78, "word": " more", "probability": 0.93896484375}, {"start": 1123.78, "end": 1123.96, "word": " than", "probability": 0.9501953125}, {"start": 1123.96, "end": 1124.28, "word": " that,", "probability": 0.931640625}, {"start": 1124.56, "end": 1124.72, "word": " you", "probability": 0.95654296875}, {"start": 1124.72, "end": 1124.94, "word": " have", "probability": 0.94384765625}, {"start": 1124.94, "end": 1125.08, "word": " to", "probability": 0.96923828125}, {"start": 1125.08, "end": 1125.42, "word": " use", "probability": 0.88330078125}, {"start": 1125.42, "end": 1126.34, "word": " chi", "probability": 0.88916015625}, {"start": 1126.34, "end": 1126.7, "word": "-square.", "probability": 0.9684244791666666}], "temperature": 1.0}, {"id": 43, "seek": 115599, "start": 1129.95, "end": 1155.99, "text": " Now still we have the same equation, Chi-square statistic is just sum F observed minus F expected quantity squared divided by F expected. In this case, Chi-square statistic for R by C case has degrees of freedom R minus 1 multiplied by C minus 1.", "tokens": [823, 920, 321, 362, 264, 912, 5367, 11, 17730, 12, 33292, 543, 29588, 307, 445, 2408, 479, 13095, 3175, 479, 5176, 11275, 8889, 6666, 538, 479, 5176, 13, 682, 341, 1389, 11, 17730, 12, 33292, 543, 29588, 337, 497, 538, 383, 1389, 575, 5310, 295, 5645, 497, 3175, 502, 17207, 538, 383, 3175, 502, 13], "avg_logprob": -0.20521763579121657, "compression_ratio": 1.5534591194968554, "no_speech_prob": 0.0, "words": [{"start": 1129.95, "end": 1130.27, "word": " Now", "probability": 0.93408203125}, {"start": 1130.27, "end": 1130.69, "word": " still", "probability": 0.76513671875}, {"start": 1130.69, "end": 1130.97, "word": " we", "probability": 0.69189453125}, {"start": 1130.97, "end": 1131.33, "word": " have", "probability": 0.94873046875}, {"start": 1131.33, "end": 1131.69, "word": " the", "probability": 0.8564453125}, {"start": 1131.69, "end": 1131.99, "word": " same", "probability": 0.916015625}, {"start": 1131.99, "end": 1132.57, "word": " equation,", "probability": 0.966796875}, {"start": 1132.87, "end": 1133.05, "word": " Chi", "probability": 0.37158203125}, {"start": 1133.05, "end": 1133.31, "word": "-square", "probability": 0.7174479166666666}, {"start": 1133.31, "end": 1133.85, "word": " statistic", "probability": 0.5263671875}, {"start": 1133.85, "end": 1134.27, "word": " is", "probability": 0.841796875}, {"start": 1134.27, "end": 1134.57, "word": " just", "probability": 0.90478515625}, {"start": 1134.57, "end": 1135.01, "word": " sum", "probability": 0.69287109375}, {"start": 1135.01, "end": 1136.07, "word": " F", "probability": 0.285888671875}, {"start": 1136.07, "end": 1136.57, "word": " observed", "probability": 0.8017578125}, {"start": 1136.57, "end": 1136.99, "word": " minus", "probability": 0.958984375}, {"start": 1136.99, "end": 1137.39, "word": " F", "probability": 0.943359375}, {"start": 1137.39, "end": 1137.87, "word": " expected", "probability": 0.91015625}, {"start": 1137.87, "end": 1138.31, "word": " quantity", "probability": 0.814453125}, {"start": 1138.31, "end": 1138.83, "word": " squared", "probability": 0.8564453125}, {"start": 1138.83, "end": 1139.81, "word": " divided", "probability": 0.48876953125}, {"start": 1139.81, "end": 1140.01, "word": " by", "probability": 0.97607421875}, {"start": 1140.01, "end": 1140.21, "word": " F", "probability": 0.92041015625}, {"start": 1140.21, "end": 1140.69, "word": " expected.", "probability": 0.9267578125}, {"start": 1143.49, "end": 1144.25, "word": " In", "probability": 0.712890625}, {"start": 1144.25, "end": 1144.47, "word": " this", "probability": 0.9482421875}, {"start": 1144.47, "end": 1144.73, "word": " case,", "probability": 0.9453125}, {"start": 1144.79, "end": 1144.97, "word": " Chi", "probability": 0.79248046875}, {"start": 1144.97, "end": 1145.35, "word": "-square", "probability": 0.8841145833333334}, {"start": 1145.35, "end": 1146.15, "word": " statistic", "probability": 0.86376953125}, {"start": 1146.15, "end": 1146.47, "word": " for", "probability": 0.9345703125}, {"start": 1146.47, "end": 1146.71, "word": " R", "probability": 0.720703125}, {"start": 1146.71, "end": 1146.91, "word": " by", "probability": 0.95849609375}, {"start": 1146.91, "end": 1147.13, "word": " C", "probability": 0.986328125}, {"start": 1147.13, "end": 1147.55, "word": " case", "probability": 0.92138671875}, {"start": 1147.55, "end": 1148.13, "word": " has", "probability": 0.91162109375}, {"start": 1148.13, "end": 1149.73, "word": " degrees", "probability": 0.935546875}, {"start": 1149.73, "end": 1150.03, "word": " of", "probability": 0.97119140625}, {"start": 1150.03, "end": 1150.47, "word": " freedom", "probability": 0.9404296875}, {"start": 1150.47, "end": 1152.97, "word": " R", "probability": 0.56298828125}, {"start": 1152.97, "end": 1153.29, "word": " minus", "probability": 0.9384765625}, {"start": 1153.29, "end": 1153.69, "word": " 1", "probability": 0.76611328125}, {"start": 1153.69, "end": 1154.77, "word": " multiplied", "probability": 0.67578125}, {"start": 1154.77, "end": 1155.13, "word": " by", "probability": 0.97021484375}, {"start": 1155.13, "end": 1155.43, "word": " C", "probability": 0.97509765625}, {"start": 1155.43, "end": 1155.69, "word": " minus", "probability": 0.98681640625}, {"start": 1155.69, "end": 1155.99, "word": " 1.", "probability": 0.99169921875}], "temperature": 1.0}, {"id": 44, "seek": 118619, "start": 1157.03, "end": 1186.19, "text": " In this case, each cell in the contingency table has expected frequency at least one instead of five. Now let's see how can we compute the expected cell frequency for each cell. The expected frequency is given by row total multiplied by colon total divided by n. So that's my new equation to determine", "tokens": [682, 341, 1389, 11, 1184, 2815, 294, 264, 27820, 3020, 3199, 575, 5176, 7893, 412, 1935, 472, 2602, 295, 1732, 13, 823, 718, 311, 536, 577, 393, 321, 14722, 264, 5176, 2815, 7893, 337, 1184, 2815, 13, 440, 5176, 7893, 307, 2212, 538, 5386, 3217, 17207, 538, 8255, 3217, 6666, 538, 297, 13, 407, 300, 311, 452, 777, 5367, 281, 6997], "avg_logprob": -0.1730090660914298, "compression_ratio": 1.641304347826087, "no_speech_prob": 0.0, "words": [{"start": 1157.03, "end": 1157.29, "word": " In", "probability": 0.72607421875}, {"start": 1157.29, "end": 1157.49, "word": " this", "probability": 0.94384765625}, {"start": 1157.49, "end": 1157.77, "word": " case,", "probability": 0.91796875}, {"start": 1157.91, "end": 1158.05, "word": " each", "probability": 0.927734375}, {"start": 1158.05, "end": 1158.27, "word": " cell", "probability": 0.884765625}, {"start": 1158.27, "end": 1158.43, "word": " in", "probability": 0.9150390625}, {"start": 1158.43, "end": 1158.57, "word": " the", "probability": 0.91943359375}, {"start": 1158.57, "end": 1159.15, "word": " contingency", "probability": 0.8076171875}, {"start": 1159.15, "end": 1159.47, "word": " table", "probability": 0.888671875}, {"start": 1159.47, "end": 1159.77, "word": " has", "probability": 0.8876953125}, {"start": 1159.77, "end": 1160.25, "word": " expected", "probability": 0.79541015625}, {"start": 1160.25, "end": 1160.81, "word": " frequency", "probability": 0.92822265625}, {"start": 1160.81, "end": 1161.03, "word": " at", "probability": 0.8095703125}, {"start": 1161.03, "end": 1161.23, "word": " least", "probability": 0.96240234375}, {"start": 1161.23, "end": 1161.53, "word": " one", "probability": 0.74755859375}, {"start": 1161.53, "end": 1163.21, "word": " instead", "probability": 0.4404296875}, {"start": 1163.21, "end": 1163.45, "word": " of", "probability": 0.9697265625}, {"start": 1163.45, "end": 1163.77, "word": " five.", "probability": 0.87158203125}, {"start": 1165.39, "end": 1165.99, "word": " Now", "probability": 0.94287109375}, {"start": 1165.99, "end": 1166.27, "word": " let's", "probability": 0.820556640625}, {"start": 1166.27, "end": 1166.39, "word": " see", "probability": 0.91650390625}, {"start": 1166.39, "end": 1166.51, "word": " how", "probability": 0.9150390625}, {"start": 1166.51, "end": 1166.73, "word": " can", "probability": 0.7705078125}, {"start": 1166.73, "end": 1166.91, "word": " we", "probability": 0.95703125}, {"start": 1166.91, "end": 1167.49, "word": " compute", "probability": 0.88916015625}, {"start": 1167.49, "end": 1169.01, "word": " the", "probability": 0.822265625}, {"start": 1169.01, "end": 1169.61, "word": " expected", "probability": 0.92138671875}, {"start": 1169.61, "end": 1170.03, "word": " cell", "probability": 0.88427734375}, {"start": 1170.03, "end": 1170.75, "word": " frequency", "probability": 0.95166015625}, {"start": 1170.75, "end": 1171.13, "word": " for", "probability": 0.94384765625}, {"start": 1171.13, "end": 1171.39, "word": " each", "probability": 0.939453125}, {"start": 1171.39, "end": 1171.69, "word": " cell.", "probability": 0.81884765625}, {"start": 1172.95, "end": 1173.19, "word": " The", "probability": 0.84814453125}, {"start": 1173.19, "end": 1173.67, "word": " expected", "probability": 0.9208984375}, {"start": 1173.67, "end": 1174.37, "word": " frequency", "probability": 0.9619140625}, {"start": 1174.37, "end": 1174.69, "word": " is", "probability": 0.94970703125}, {"start": 1174.69, "end": 1174.93, "word": " given", "probability": 0.89404296875}, {"start": 1174.93, "end": 1175.37, "word": " by", "probability": 0.970703125}, {"start": 1175.37, "end": 1177.07, "word": " row", "probability": 0.2861328125}, {"start": 1177.07, "end": 1177.53, "word": " total", "probability": 0.8251953125}, {"start": 1177.53, "end": 1179.37, "word": " multiplied", "probability": 0.57470703125}, {"start": 1179.37, "end": 1179.71, "word": " by", "probability": 0.97216796875}, {"start": 1179.71, "end": 1180.07, "word": " colon", "probability": 0.8095703125}, {"start": 1180.07, "end": 1180.59, "word": " total", "probability": 0.87109375}, {"start": 1180.59, "end": 1181.29, "word": " divided", "probability": 0.708984375}, {"start": 1181.29, "end": 1181.57, "word": " by", "probability": 0.9677734375}, {"start": 1181.57, "end": 1181.79, "word": " n.", "probability": 0.66650390625}, {"start": 1182.33, "end": 1182.65, "word": " So", "probability": 0.9619140625}, {"start": 1182.65, "end": 1182.95, "word": " that's", "probability": 0.911376953125}, {"start": 1182.95, "end": 1183.19, "word": " my", "probability": 0.96630859375}, {"start": 1183.19, "end": 1183.79, "word": " new", "probability": 0.89697265625}, {"start": 1183.79, "end": 1184.67, "word": " equation", "probability": 0.9619140625}, {"start": 1184.67, "end": 1185.63, "word": " to", "probability": 0.95068359375}, {"start": 1185.63, "end": 1186.19, "word": " determine", "probability": 0.908203125}], "temperature": 1.0}, {"id": 45, "seek": 121556, "start": 1188.62, "end": 1215.56, "text": " I've expected it. So the expected value for each cell is given by Rho total multiplied by Kono, total divided by N. Also, this equation is true for the previous example. If you go back a little bit here, now the", "tokens": [286, 600, 5176, 309, 13, 407, 264, 5176, 2158, 337, 1184, 2815, 307, 2212, 538, 497, 1289, 3217, 17207, 538, 591, 8957, 11, 3217, 6666, 538, 426, 13, 2743, 11, 341, 5367, 307, 2074, 337, 264, 3894, 1365, 13, 759, 291, 352, 646, 257, 707, 857, 510, 11, 586, 264], "avg_logprob": -0.34007354109894994, "compression_ratio": 1.394736842105263, "no_speech_prob": 0.0, "words": [{"start": 1188.62, "end": 1188.98, "word": " I've", "probability": 0.3450927734375}, {"start": 1188.98, "end": 1189.44, "word": " expected", "probability": 0.80322265625}, {"start": 1189.44, "end": 1189.92, "word": " it.", "probability": 0.5888671875}, {"start": 1190.4, "end": 1190.7, "word": " So", "probability": 0.75927734375}, {"start": 1190.7, "end": 1190.82, "word": " the", "probability": 0.744140625}, {"start": 1190.82, "end": 1191.22, "word": " expected", "probability": 0.869140625}, {"start": 1191.22, "end": 1191.7, "word": " value", "probability": 0.9697265625}, {"start": 1191.7, "end": 1192.12, "word": " for", "probability": 0.74072265625}, {"start": 1192.12, "end": 1192.36, "word": " each", "probability": 0.8857421875}, {"start": 1192.36, "end": 1192.62, "word": " cell", "probability": 0.908203125}, {"start": 1192.62, "end": 1192.8, "word": " is", "probability": 0.93017578125}, {"start": 1192.8, "end": 1193.02, "word": " given", "probability": 0.85302734375}, {"start": 1193.02, "end": 1193.44, "word": " by", "probability": 0.96728515625}, {"start": 1193.44, "end": 1196.44, "word": " Rho", "probability": 0.4947509765625}, {"start": 1196.44, "end": 1196.84, "word": " total", "probability": 0.572265625}, {"start": 1196.84, "end": 1199.44, "word": " multiplied", "probability": 0.5234375}, {"start": 1199.44, "end": 1199.76, "word": " by", "probability": 0.9619140625}, {"start": 1199.76, "end": 1200.26, "word": " Kono,", "probability": 0.5438232421875}, {"start": 1201.34, "end": 1201.98, "word": " total", "probability": 0.74755859375}, {"start": 1201.98, "end": 1202.94, "word": " divided", "probability": 0.771484375}, {"start": 1202.94, "end": 1203.16, "word": " by", "probability": 0.96826171875}, {"start": 1203.16, "end": 1203.38, "word": " N.", "probability": 0.611328125}, {"start": 1205.16, "end": 1206.0, "word": " Also,", "probability": 0.921875}, {"start": 1206.26, "end": 1206.52, "word": " this", "probability": 0.93603515625}, {"start": 1206.52, "end": 1207.04, "word": " equation", "probability": 0.97509765625}, {"start": 1207.04, "end": 1207.98, "word": " is", "probability": 0.86279296875}, {"start": 1207.98, "end": 1208.42, "word": " true", "probability": 0.9560546875}, {"start": 1208.42, "end": 1208.88, "word": " for", "probability": 0.94580078125}, {"start": 1208.88, "end": 1209.06, "word": " the", "probability": 0.91796875}, {"start": 1209.06, "end": 1209.54, "word": " previous", "probability": 0.8447265625}, {"start": 1209.54, "end": 1210.86, "word": " example.", "probability": 0.96923828125}, {"start": 1211.02, "end": 1211.1, "word": " If", "probability": 0.92578125}, {"start": 1211.1, "end": 1211.2, "word": " you", "probability": 0.6943359375}, {"start": 1211.2, "end": 1211.36, "word": " go", "probability": 0.94580078125}, {"start": 1211.36, "end": 1211.6, "word": " back", "probability": 0.8759765625}, {"start": 1211.6, "end": 1211.74, "word": " a", "probability": 0.81298828125}, {"start": 1211.74, "end": 1211.88, "word": " little", "probability": 0.8662109375}, {"start": 1211.88, "end": 1212.26, "word": " bit", "probability": 0.95263671875}, {"start": 1212.26, "end": 1212.94, "word": " here,", "probability": 0.53662109375}, {"start": 1213.7, "end": 1214.9, "word": " now", "probability": 0.9052734375}, {"start": 1214.9, "end": 1215.56, "word": " the", "probability": 0.705078125}], "temperature": 1.0}, {"id": 46, "seek": 124031, "start": 1216.65, "end": 1240.31, "text": " Expected for this cell was 40.4. Now let's see how can we compute the same value by using this equation. So it's equal to row total 120 multiplied by column total 36 divided by 300.", "tokens": [2111, 10729, 337, 341, 2815, 390, 3356, 13, 19, 13, 823, 718, 311, 536, 577, 393, 321, 14722, 264, 912, 2158, 538, 1228, 341, 5367, 13, 407, 309, 311, 2681, 281, 5386, 3217, 10411, 17207, 538, 7738, 3217, 8652, 6666, 538, 6641, 13], "avg_logprob": -0.1922940347682346, "compression_ratio": 1.2907801418439717, "no_speech_prob": 0.0, "words": [{"start": 1216.65, "end": 1217.25, "word": " Expected", "probability": 0.6572265625}, {"start": 1217.25, "end": 1217.71, "word": " for", "probability": 0.9189453125}, {"start": 1217.71, "end": 1217.95, "word": " this", "probability": 0.927734375}, {"start": 1217.95, "end": 1218.15, "word": " cell", "probability": 0.94873046875}, {"start": 1218.15, "end": 1218.47, "word": " was", "probability": 0.94140625}, {"start": 1218.47, "end": 1218.87, "word": " 40", "probability": 0.72314453125}, {"start": 1218.87, "end": 1219.53, "word": ".4.", "probability": 0.98486328125}, {"start": 1220.45, "end": 1221.17, "word": " Now", "probability": 0.939453125}, {"start": 1221.17, "end": 1221.45, "word": " let's", "probability": 0.79296875}, {"start": 1221.45, "end": 1221.53, "word": " see", "probability": 0.908203125}, {"start": 1221.53, "end": 1221.65, "word": " how", "probability": 0.91064453125}, {"start": 1221.65, "end": 1221.85, "word": " can", "probability": 0.796875}, {"start": 1221.85, "end": 1222.53, "word": " we", "probability": 0.94189453125}, {"start": 1222.53, "end": 1223.05, "word": " compute", "probability": 0.900390625}, {"start": 1223.05, "end": 1223.29, "word": " the", "probability": 0.8212890625}, {"start": 1223.29, "end": 1224.25, "word": " same", "probability": 0.83251953125}, {"start": 1224.25, "end": 1224.63, "word": " value", "probability": 0.96923828125}, {"start": 1224.63, "end": 1224.83, "word": " by", "probability": 0.95068359375}, {"start": 1224.83, "end": 1225.19, "word": " using", "probability": 0.9306640625}, {"start": 1225.19, "end": 1225.47, "word": " this", "probability": 0.92431640625}, {"start": 1225.47, "end": 1225.95, "word": " equation.", "probability": 0.92822265625}, {"start": 1226.15, "end": 1227.07, "word": " So", "probability": 0.8291015625}, {"start": 1227.07, "end": 1227.33, "word": " it's", "probability": 0.894775390625}, {"start": 1227.33, "end": 1227.63, "word": " equal", "probability": 0.90380859375}, {"start": 1227.63, "end": 1228.41, "word": " to", "probability": 0.97216796875}, {"start": 1228.41, "end": 1229.45, "word": " row", "probability": 0.284912109375}, {"start": 1229.45, "end": 1229.77, "word": " total", "probability": 0.8046875}, {"start": 1229.77, "end": 1230.25, "word": " 120", "probability": 0.46533203125}, {"start": 1230.25, "end": 1232.67, "word": " multiplied", "probability": 0.42041015625}, {"start": 1232.67, "end": 1233.29, "word": " by", "probability": 0.97265625}, {"start": 1233.29, "end": 1234.23, "word": " column", "probability": 0.8544921875}, {"start": 1234.23, "end": 1234.69, "word": " total", "probability": 0.890625}, {"start": 1234.69, "end": 1235.49, "word": " 36", "probability": 0.96533203125}, {"start": 1235.49, "end": 1238.41, "word": " divided", "probability": 0.5927734375}, {"start": 1238.41, "end": 1238.85, "word": " by", "probability": 0.97509765625}, {"start": 1238.85, "end": 1240.31, "word": " 300.", "probability": 0.97705078125}], "temperature": 1.0}, {"id": 47, "seek": 126982, "start": 1243.58, "end": 1269.82, "text": " Now before we compute this value by using B dash first, 300 divided by, I'm sorry, 36 divided by 300. So that's your B dash. Then we multiply this B dash by N, and this is your N. So it's similar equation. So either you use row total multiplied by column total.", "tokens": [823, 949, 321, 14722, 341, 2158, 538, 1228, 363, 8240, 700, 11, 6641, 6666, 538, 11, 286, 478, 2597, 11, 8652, 6666, 538, 6641, 13, 407, 300, 311, 428, 363, 8240, 13, 1396, 321, 12972, 341, 363, 8240, 538, 426, 11, 293, 341, 307, 428, 426, 13, 407, 309, 311, 2531, 5367, 13, 407, 2139, 291, 764, 5386, 3217, 17207, 538, 7738, 3217, 13], "avg_logprob": -0.21995192307692307, "compression_ratio": 1.497142857142857, "no_speech_prob": 0.0, "words": [{"start": 1243.58, "end": 1243.82, "word": " Now", "probability": 0.6923828125}, {"start": 1243.82, "end": 1244.22, "word": " before", "probability": 0.58203125}, {"start": 1244.22, "end": 1244.46, "word": " we", "probability": 0.82373046875}, {"start": 1244.46, "end": 1244.82, "word": " compute", "probability": 0.845703125}, {"start": 1244.82, "end": 1245.1, "word": " this", "probability": 0.94140625}, {"start": 1245.1, "end": 1245.42, "word": " value", "probability": 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{"start": 1250.7, "end": 1250.9, "word": " by", "probability": 0.96337890625}, {"start": 1250.9, "end": 1251.32, "word": " 300.", "probability": 0.9775390625}, {"start": 1252.34, "end": 1252.82, "word": " So", "probability": 0.9443359375}, {"start": 1252.82, "end": 1253.36, "word": " that's", "probability": 0.932861328125}, {"start": 1253.36, "end": 1254.44, "word": " your", "probability": 0.89892578125}, {"start": 1254.44, "end": 1254.64, "word": " B", "probability": 0.98095703125}, {"start": 1254.64, "end": 1254.94, "word": " dash.", "probability": 0.89453125}, {"start": 1256.56, "end": 1257.12, "word": " Then", "probability": 0.449462890625}, {"start": 1257.12, "end": 1257.36, "word": " we", "probability": 0.8759765625}, {"start": 1257.36, "end": 1257.86, "word": " multiply", "probability": 0.88525390625}, {"start": 1257.86, "end": 1258.52, "word": " this", "probability": 0.94482421875}, {"start": 1258.52, "end": 1258.76, "word": " B", "probability": 0.9853515625}, {"start": 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"word": " So", "probability": 0.92626953125}, {"start": 1264.6, "end": 1264.82, "word": " either", "probability": 0.91455078125}, {"start": 1264.82, "end": 1265.04, "word": " you", "probability": 0.95166015625}, {"start": 1265.04, "end": 1265.46, "word": " use", "probability": 0.87548828125}, {"start": 1265.46, "end": 1266.36, "word": " row", "probability": 0.438232421875}, {"start": 1266.36, "end": 1266.76, "word": " total", "probability": 0.8525390625}, {"start": 1266.76, "end": 1268.54, "word": " multiplied", "probability": 0.595703125}, {"start": 1268.54, "end": 1269.02, "word": " by", "probability": 0.97021484375}, {"start": 1269.02, "end": 1269.42, "word": " column", "probability": 0.755859375}, {"start": 1269.42, "end": 1269.82, "word": " total.", "probability": 0.87939453125}], "temperature": 1.0}, {"id": 48, "seek": 129998, "start": 1271.28, "end": 1299.98, "text": " then divide by overall sample size you will get the same result by using the overall proportion 12% times 120 so each one will give the same answer so from now we are going to use this equation in order to compute the expected frequency for each cell so again expected frequency is rho total times", "tokens": [550, 9845, 538, 4787, 6889, 2744, 291, 486, 483, 264, 912, 1874, 538, 1228, 264, 4787, 16068, 2272, 4, 1413, 10411, 370, 1184, 472, 486, 976, 264, 912, 1867, 370, 490, 586, 321, 366, 516, 281, 764, 341, 5367, 294, 1668, 281, 14722, 264, 5176, 7893, 337, 1184, 2815, 370, 797, 5176, 7893, 307, 20293, 3217, 1413], "avg_logprob": -0.20662715774157953, "compression_ratio": 1.664804469273743, "no_speech_prob": 0.0, "words": [{"start": 1271.28, "end": 1271.62, "word": " then", "probability": 0.329833984375}, {"start": 1271.62, "end": 1271.96, "word": " divide", "probability": 0.6259765625}, {"start": 1271.96, "end": 1272.28, "word": " by", "probability": 0.8916015625}, {"start": 1272.28, "end": 1273.72, "word": " overall", "probability": 0.65869140625}, {"start": 1273.72, "end": 1274.06, "word": 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"probability": 0.92236328125}, {"start": 1287.52, "end": 1288.44, "word": " so", "probability": 0.5576171875}, {"start": 1288.44, "end": 1288.72, "word": " from", "probability": 0.84423828125}, {"start": 1288.72, "end": 1289.02, "word": " now", "probability": 0.92724609375}, {"start": 1289.02, "end": 1289.28, "word": " we", "probability": 0.84619140625}, {"start": 1289.28, "end": 1289.42, "word": " are", "probability": 0.88623046875}, {"start": 1289.42, "end": 1289.7, "word": " going", "probability": 0.943359375}, {"start": 1289.7, "end": 1289.86, "word": " to", "probability": 0.96728515625}, {"start": 1289.86, "end": 1290.18, "word": " use", "probability": 0.88232421875}, {"start": 1290.18, "end": 1290.56, "word": " this", "probability": 0.94677734375}, {"start": 1290.56, "end": 1291.1, "word": " equation", "probability": 0.97802734375}, {"start": 1291.1, "end": 1292.14, "word": " in", "probability": 0.90380859375}, {"start": 1292.14, "end": 1292.46, "word": " order", "probability": 0.92236328125}, {"start": 1292.46, "end": 1292.72, "word": " to", "probability": 0.96875}, {"start": 1292.72, "end": 1293.12, "word": " compute", "probability": 0.912109375}, {"start": 1293.12, "end": 1293.44, "word": " the", "probability": 0.861328125}, {"start": 1293.44, "end": 1293.9, "word": " expected", "probability": 0.92138671875}, {"start": 1293.9, "end": 1294.6, "word": " frequency", "probability": 0.95703125}, {"start": 1294.6, "end": 1295.52, "word": " for", "probability": 0.92431640625}, {"start": 1295.52, "end": 1295.78, "word": " each", "probability": 0.931640625}, {"start": 1295.78, "end": 1296.02, "word": " cell", "probability": 0.8935546875}, {"start": 1296.02, "end": 1296.92, "word": " so", "probability": 0.75390625}, {"start": 1296.92, "end": 1297.22, "word": " again", "probability": 0.8828125}, {"start": 1297.22, "end": 1297.96, "word": " expected", "probability": 0.82421875}, {"start": 1297.96, "end": 1298.46, "word": " frequency", "probability": 0.95947265625}, {"start": 1298.46, "end": 1298.72, "word": " is", "probability": 0.9482421875}, {"start": 1298.72, "end": 1298.9, "word": " rho", "probability": 0.57666015625}, {"start": 1298.9, "end": 1299.24, "word": " total", "probability": 0.79443359375}, {"start": 1299.24, "end": 1299.98, "word": " times", "probability": 0.900390625}], "temperature": 1.0}, {"id": 49, "seek": 132018, "start": 1301.72, "end": 1320.18, "text": " Column total divided by N, N is the sample size. So row total it means sum of all frequencies in the row. Similarly column total is the sum of all frequencies in the column and N is over all sample size.", "tokens": [4004, 16449, 3217, 6666, 538, 426, 11, 426, 307, 264, 6889, 2744, 13, 407, 5386, 3217, 309, 1355, 2408, 295, 439, 20250, 294, 264, 5386, 13, 13157, 7738, 3217, 307, 264, 2408, 295, 439, 20250, 294, 264, 7738, 293, 426, 307, 670, 439, 6889, 2744, 13], "avg_logprob": -0.23986037804725321, "compression_ratio": 1.6585365853658536, "no_speech_prob": 0.0, "words": [{"start": 1301.72, "end": 1302.16, "word": " Column", "probability": 0.7080078125}, {"start": 1302.16, "end": 1302.48, "word": " total", "probability": 0.7109375}, {"start": 1302.48, "end": 1302.92, "word": " divided", "probability": 0.68603515625}, {"start": 1302.92, "end": 1303.52, "word": " by", "probability": 0.97314453125}, {"start": 1303.52, "end": 1304.58, "word": " N,", "probability": 0.59765625}, {"start": 1304.76, "end": 1304.84, "word": " N", "probability": 0.6337890625}, {"start": 1304.84, "end": 1305.06, "word": " is", "probability": 0.93994140625}, {"start": 1305.06, "end": 1305.26, "word": " the", "probability": 0.8271484375}, {"start": 1305.26, "end": 1305.46, "word": " sample", "probability": 0.9150390625}, {"start": 1305.46, "end": 1305.88, "word": " size.", "probability": 0.86376953125}, {"start": 1307.22, "end": 1307.76, "word": " So", "probability": 0.8232421875}, {"start": 1307.76, "end": 1307.94, "word": " row", "probability": 0.350341796875}, {"start": 1307.94, "end": 1308.18, "word": " total", "probability": 0.8486328125}, {"start": 1308.18, "end": 1308.4, "word": " it", "probability": 0.2412109375}, {"start": 1308.4, "end": 1308.62, "word": " means", "probability": 0.9072265625}, {"start": 1308.62, "end": 1309.0, "word": " sum", "probability": 0.81005859375}, {"start": 1309.0, "end": 1309.26, "word": " of", "probability": 0.96728515625}, {"start": 1309.26, "end": 1309.5, "word": " all", "probability": 0.951171875}, {"start": 1309.5, "end": 1310.06, "word": " frequencies", "probability": 0.8291015625}, {"start": 1310.06, "end": 1310.34, "word": " in", "probability": 0.94140625}, {"start": 1310.34, "end": 1310.5, "word": " the", "probability": 0.89697265625}, {"start": 1310.5, "end": 1310.72, "word": " row.", "probability": 0.9228515625}, {"start": 1311.72, "end": 1312.22, "word": " Similarly", "probability": 0.82568359375}, {"start": 1312.22, "end": 1312.66, "word": " column", "probability": 0.53466796875}, {"start": 1312.66, "end": 1313.02, "word": " total", "probability": 0.87109375}, {"start": 1313.02, "end": 1313.42, "word": " is", "probability": 0.93017578125}, {"start": 1313.42, "end": 1313.6, "word": " the", "probability": 0.87060546875}, {"start": 1313.6, "end": 1313.82, "word": " sum", "probability": 0.94970703125}, {"start": 1313.82, "end": 1313.98, "word": " of", "probability": 0.96728515625}, {"start": 1313.98, "end": 1314.16, "word": " all", "probability": 0.947265625}, {"start": 1314.16, "end": 1314.7, "word": " frequencies", "probability": 0.857421875}, {"start": 1314.7, "end": 1315.84, "word": " in", "probability": 0.93408203125}, {"start": 1315.84, "end": 1316.16, "word": " the", "probability": 0.90869140625}, {"start": 1316.16, "end": 1316.7, "word": " column", "probability": 0.8173828125}, {"start": 1316.7, "end": 1317.32, "word": " and", "probability": 0.58984375}, {"start": 1317.32, "end": 1317.56, "word": " N", "probability": 0.9541015625}, {"start": 1317.56, "end": 1317.78, "word": " is", "probability": 0.9521484375}, {"start": 1317.78, "end": 1318.2, "word": " over", "probability": 0.86962890625}, {"start": 1318.2, "end": 1318.92, "word": " all", "probability": 0.9521484375}, {"start": 1318.92, "end": 1319.76, "word": " sample", "probability": 0.86767578125}, {"start": 1319.76, "end": 1320.18, "word": " size.", "probability": 0.7236328125}], "temperature": 1.0}, {"id": 50, "seek": 134759, "start": 1323.03, "end": 1347.59, "text": " Again, we reject the null hypothesis if your chi-square statistic greater than chi-square alpha. Otherwise, you don't reject it. And keep in mind, chi-square statistic has degrees of freedom R minus 1 times C minus 1. That's all for chi-square as test of independence. Any question?", "tokens": [3764, 11, 321, 8248, 264, 18184, 17291, 498, 428, 13228, 12, 33292, 543, 29588, 5044, 813, 13228, 12, 33292, 543, 8961, 13, 10328, 11, 291, 500, 380, 8248, 309, 13, 400, 1066, 294, 1575, 11, 13228, 12, 33292, 543, 29588, 575, 5310, 295, 5645, 497, 3175, 502, 1413, 383, 3175, 502, 13, 663, 311, 439, 337, 13228, 12, 33292, 543, 382, 1500, 295, 14640, 13, 2639, 1168, 30], "avg_logprob": -0.20516304088675458, "compression_ratio": 1.554945054945055, "no_speech_prob": 0.0, "words": [{"start": 1323.03, "end": 1323.53, "word": " Again,", "probability": 0.916015625}, {"start": 1323.97, "end": 1324.19, "word": " we", "probability": 0.94873046875}, {"start": 1324.19, "end": 1324.67, "word": " reject", "probability": 0.8779296875}, {"start": 1324.67, "end": 1324.87, "word": " the", "probability": 0.8935546875}, {"start": 1324.87, "end": 1325.01, "word": " null", "probability": 0.9599609375}, {"start": 1325.01, "end": 1325.55, "word": " hypothesis", "probability": 0.84814453125}, {"start": 1325.55, "end": 1326.15, "word": " if", "probability": 0.65380859375}, {"start": 1326.15, "end": 1326.39, "word": " your", "probability": 0.8359375}, {"start": 1326.39, "end": 1326.63, "word": " chi", "probability": 0.35693359375}, {"start": 1326.63, "end": 1326.85, "word": "-square", "probability": 0.876953125}, {"start": 1326.85, "end": 1327.55, "word": " statistic", "probability": 0.61279296875}, {"start": 1327.55, "end": 1328.99, "word": " greater", "probability": 0.40966796875}, {"start": 1328.99, "end": 1329.41, "word": " than", "probability": 0.9453125}, {"start": 1329.41, "end": 1329.81, "word": " chi", "probability": 0.7578125}, {"start": 1329.81, "end": 1330.09, "word": "-square", "probability": 0.9583333333333334}, {"start": 1330.09, "end": 1330.43, "word": " alpha.", "probability": 0.88427734375}, {"start": 1330.59, "end": 1330.93, "word": " Otherwise,", "probability": 0.943359375}, {"start": 1331.21, "end": 1331.27, "word": " you", "probability": 0.927734375}, {"start": 1331.27, "end": 1331.53, "word": " don't", "probability": 0.97021484375}, {"start": 1331.53, "end": 1331.85, "word": " reject", "probability": 0.9169921875}, {"start": 1331.85, "end": 1332.25, "word": " it.", "probability": 0.59375}, {"start": 1332.51, "end": 1332.65, "word": " And", "probability": 0.939453125}, {"start": 1332.65, "end": 1332.83, "word": " keep", "probability": 0.900390625}, {"start": 1332.83, "end": 1332.99, "word": " in", "probability": 0.93994140625}, {"start": 1332.99, "end": 1333.37, "word": " mind,", "probability": 0.880859375}, {"start": 1334.27, "end": 1334.51, "word": " chi", "probability": 0.5419921875}, {"start": 1334.51, "end": 1334.79, "word": "-square", "probability": 0.9632161458333334}, {"start": 1334.79, "end": 1335.37, "word": " statistic", "probability": 0.84130859375}, {"start": 1335.37, "end": 1336.47, "word": " has", "probability": 0.9287109375}, {"start": 1336.47, "end": 1337.01, "word": " degrees", "probability": 0.94921875}, {"start": 1337.01, "end": 1337.23, "word": " of", "probability": 0.96875}, {"start": 1337.23, "end": 1337.61, "word": " freedom", "probability": 0.93017578125}, {"start": 1337.61, "end": 1338.39, "word": " R", "probability": 0.33349609375}, {"start": 1338.39, "end": 1338.69, "word": " minus", "probability": 0.8173828125}, {"start": 1338.69, "end": 1339.01, "word": " 1", "probability": 0.8447265625}, {"start": 1339.01, "end": 1339.55, "word": " times", "probability": 0.91845703125}, {"start": 1339.55, "end": 1339.97, "word": " C", "probability": 0.8076171875}, {"start": 1339.97, "end": 1340.27, "word": " minus", "probability": 0.96044921875}, {"start": 1340.27, "end": 1340.49, "word": " 1.", "probability": 0.97119140625}, {"start": 1341.37, "end": 1342.05, "word": " That's", "probability": 0.845947265625}, {"start": 1342.05, "end": 1342.51, "word": " all", "probability": 0.9306640625}, {"start": 1342.51, "end": 1342.89, "word": " for", "probability": 0.9501953125}, {"start": 1342.89, "end": 1343.25, "word": " chi", "probability": 0.81982421875}, {"start": 1343.25, "end": 1343.73, "word": "-square", "probability": 0.94384765625}, {"start": 1343.73, "end": 1344.27, "word": " as", "probability": 0.8525390625}, {"start": 1344.27, "end": 1344.69, "word": " test", "probability": 0.849609375}, {"start": 1344.69, "end": 1345.11, "word": " of", "probability": 0.95166015625}, {"start": 1345.11, "end": 1345.71, "word": " independence.", "probability": 0.1673583984375}, {"start": 1346.95, "end": 1347.29, "word": " Any", "probability": 0.9287109375}, {"start": 1347.29, "end": 1347.59, "word": " question?", "probability": 0.57275390625}], "temperature": 1.0}, {"id": 51, "seek": 137350, "start": 1351.22, "end": 1373.5, "text": " Here there is an example for applying chi-square test of independence. Meal plan selected by 200 students is shown in this table. So there are two variables of interest. The first one is number of meals per week.", "tokens": [1692, 456, 307, 364, 1365, 337, 9275, 13228, 12, 33292, 543, 1500, 295, 14640, 13, 1923, 304, 1393, 8209, 538, 2331, 1731, 307, 4898, 294, 341, 3199, 13, 407, 456, 366, 732, 9102, 295, 1179, 13, 440, 700, 472, 307, 1230, 295, 12832, 680, 1243, 13], "avg_logprob": -0.19514628293666433, "compression_ratio": 1.392156862745098, "no_speech_prob": 0.0, "words": [{"start": 1351.22, "end": 1351.98, "word": " Here", "probability": 0.83154296875}, {"start": 1351.98, "end": 1352.46, "word": " there", "probability": 0.496826171875}, {"start": 1352.46, "end": 1352.64, "word": " is", "probability": 0.92236328125}, {"start": 1352.64, "end": 1352.84, "word": " an", "probability": 0.96044921875}, {"start": 1352.84, "end": 1353.26, "word": " example", "probability": 0.978515625}, {"start": 1353.26, "end": 1354.82, "word": " for", "probability": 0.90771484375}, {"start": 1354.82, "end": 1355.38, "word": " applying", "probability": 0.87939453125}, {"start": 1355.38, "end": 1355.98, "word": " chi", "probability": 0.09808349609375}, {"start": 1355.98, "end": 1356.3, "word": "-square", "probability": 0.7794596354166666}, {"start": 1356.3, "end": 1356.56, "word": " test", "probability": 0.5390625}, {"start": 1356.56, "end": 1356.72, "word": " of", "probability": 0.9521484375}, {"start": 1356.72, "end": 1357.32, "word": " independence.", "probability": 0.9189453125}, {"start": 1358.28, "end": 1358.5, "word": " Meal", "probability": 0.94677734375}, {"start": 1358.5, "end": 1358.92, "word": " plan", "probability": 0.91796875}, {"start": 1358.92, "end": 1362.2, "word": " selected", "probability": 0.560546875}, {"start": 1362.2, "end": 1362.72, "word": " by", "probability": 0.974609375}, {"start": 1362.72, "end": 1363.18, "word": " 200", "probability": 0.84912109375}, {"start": 1363.18, "end": 1363.84, "word": " students", "probability": 0.97705078125}, {"start": 1363.84, "end": 1364.14, "word": " is", "probability": 0.61083984375}, {"start": 1364.14, "end": 1364.5, "word": " shown", "probability": 0.9072265625}, {"start": 1364.5, "end": 1364.82, "word": " in", "probability": 0.826171875}, {"start": 1364.82, "end": 1365.02, "word": " this", "probability": 0.94580078125}, {"start": 1365.02, "end": 1365.4, "word": " table.", "probability": 0.9296875}, {"start": 1366.16, "end": 1366.46, "word": " So", "probability": 0.9150390625}, {"start": 1366.46, "end": 1366.7, "word": " there", "probability": 0.72412109375}, {"start": 1366.7, "end": 1366.98, "word": " are", "probability": 0.93798828125}, {"start": 1366.98, "end": 1367.28, "word": " two", "probability": 0.8779296875}, {"start": 1367.28, "end": 1367.78, "word": " variables", "probability": 0.94873046875}, {"start": 1367.78, "end": 1368.02, "word": " of", "probability": 0.9658203125}, {"start": 1368.02, "end": 1368.46, "word": " interest.", "probability": 0.91845703125}, {"start": 1369.78, "end": 1370.08, "word": " The", "probability": 0.88623046875}, {"start": 1370.08, "end": 1370.36, "word": " first", "probability": 0.888671875}, {"start": 1370.36, "end": 1370.62, "word": " one", "probability": 0.923828125}, {"start": 1370.62, "end": 1370.96, "word": " is", "probability": 0.947265625}, {"start": 1370.96, "end": 1371.36, "word": " number", "probability": 0.892578125}, {"start": 1371.36, "end": 1371.58, "word": " of", "probability": 0.9716796875}, {"start": 1371.58, "end": 1371.94, "word": " meals", "probability": 0.9453125}, {"start": 1371.94, "end": 1373.12, "word": " per", "probability": 0.94580078125}, {"start": 1373.12, "end": 1373.5, "word": " week.", "probability": 0.94921875}], "temperature": 1.0}, {"id": 52, "seek": 140393, "start": 1374.57, "end": 1403.93, "text": " And there are three types of number of meals, either 20 meals per week, or 10 meals per week, or none. So that's, so number of meals is classified into three groups. So three columns, 20 per week, 10 per week, or none. Class standing, students are classified into four levels.", "tokens": [400, 456, 366, 1045, 3467, 295, 1230, 295, 12832, 11, 2139, 945, 12832, 680, 1243, 11, 420, 1266, 12832, 680, 1243, 11, 420, 6022, 13, 407, 300, 311, 11, 370, 1230, 295, 12832, 307, 20627, 666, 1045, 3935, 13, 407, 1045, 13766, 11, 945, 680, 1243, 11, 1266, 680, 1243, 11, 420, 6022, 13, 9471, 4877, 11, 1731, 366, 20627, 666, 1451, 4358, 13], "avg_logprob": -0.17139423076923077, "compression_ratio": 1.7531645569620253, "no_speech_prob": 0.0, "words": [{"start": 1374.57, "end": 1374.97, "word": " And", "probability": 0.68505859375}, {"start": 1374.97, "end": 1375.73, "word": " there", "probability": 0.8056640625}, {"start": 1375.73, "end": 1375.93, "word": " are", "probability": 0.94482421875}, {"start": 1375.93, "end": 1376.23, "word": " three", "probability": 0.8623046875}, {"start": 1376.23, "end": 1376.79, "word": " types", "probability": 0.81591796875}, {"start": 1376.79, "end": 1377.05, "word": " of", "probability": 0.95947265625}, {"start": 1377.05, "end": 1377.47, "word": " number", "probability": 0.900390625}, {"start": 1377.47, "end": 1377.69, "word": " of", "probability": 0.9697265625}, {"start": 1377.69, "end": 1377.95, "word": " meals,", "probability": 0.94921875}, {"start": 1378.33, "end": 1378.59, "word": " either", "probability": 0.912109375}, {"start": 1378.59, "end": 1379.89, "word": " 20", "probability": 0.7099609375}, {"start": 1379.89, "end": 1380.23, "word": " meals", "probability": 0.953125}, {"start": 1380.23, "end": 1380.55, "word": " per", "probability": 0.96533203125}, {"start": 1380.55, "end": 1380.89, "word": " week,", "probability": 0.95458984375}, {"start": 1381.43, "end": 1383.49, "word": " or", "probability": 0.9326171875}, {"start": 1383.49, "end": 1383.85, "word": " 10", "probability": 0.8876953125}, {"start": 1383.85, "end": 1384.27, "word": " meals", "probability": 0.955078125}, {"start": 1384.27, "end": 1384.49, "word": " per", "probability": 0.95751953125}, {"start": 1384.49, "end": 1384.87, "word": " week,", "probability": 0.947265625}, {"start": 1385.37, "end": 1385.65, "word": " or", "probability": 0.9638671875}, {"start": 1385.65, "end": 1385.89, "word": " none.", "probability": 0.919921875}, {"start": 1386.91, "end": 1387.15, "word": " So", "probability": 0.9091796875}, {"start": 1387.15, "end": 1387.55, "word": " that's,", "probability": 0.7978515625}, {"start": 1387.87, "end": 1387.87, "word": " so", "probability": 0.85400390625}, {"start": 1387.87, "end": 1388.57, "word": " number", "probability": 0.72119140625}, {"start": 1388.57, "end": 1388.81, "word": " of", "probability": 0.97119140625}, {"start": 1388.81, "end": 1389.15, "word": " meals", "probability": 0.9462890625}, {"start": 1389.15, "end": 1389.91, "word": " is", "probability": 0.92822265625}, {"start": 1389.91, "end": 1390.53, "word": " classified", "probability": 0.9443359375}, {"start": 1390.53, "end": 1391.21, "word": " into", "probability": 0.8447265625}, {"start": 1391.21, "end": 1391.63, "word": " three", "probability": 0.92431640625}, {"start": 1391.63, "end": 1392.15, "word": " groups.", "probability": 0.94677734375}, {"start": 1393.21, "end": 1393.47, "word": " So", "probability": 0.958984375}, {"start": 1393.47, "end": 1393.87, "word": " three", "probability": 0.85498046875}, {"start": 1393.87, "end": 1394.65, "word": " columns,", "probability": 0.9501953125}, {"start": 1395.37, "end": 1395.77, "word": " 20", "probability": 0.94482421875}, {"start": 1395.77, "end": 1396.13, "word": " per", "probability": 0.9091796875}, {"start": 1396.13, "end": 1396.41, "word": " week,", "probability": 0.95556640625}, {"start": 1396.71, "end": 1396.97, "word": " 10", "probability": 0.95654296875}, {"start": 1396.97, "end": 1397.19, "word": " per", "probability": 0.95166015625}, {"start": 1397.19, "end": 1397.43, "word": " week,", "probability": 0.9541015625}, {"start": 1397.49, "end": 1397.65, "word": " or", "probability": 0.962890625}, {"start": 1397.65, "end": 1397.89, "word": " none.", "probability": 0.931640625}, {"start": 1399.83, "end": 1400.35, "word": " Class", "probability": 0.6396484375}, {"start": 1400.35, "end": 1400.89, "word": " standing,", "probability": 0.8544921875}, {"start": 1401.49, "end": 1401.95, "word": " students", "probability": 0.6796875}, {"start": 1401.95, "end": 1402.31, "word": " are", "probability": 0.9306640625}, {"start": 1402.31, "end": 1402.81, "word": " classified", "probability": 0.94482421875}, {"start": 1402.81, "end": 1403.27, "word": " into", "probability": 0.8486328125}, {"start": 1403.27, "end": 1403.53, "word": " four", "probability": 0.9375}, {"start": 1403.53, "end": 1403.93, "word": " levels.", "probability": 0.91552734375}], "temperature": 1.0}, {"id": 53, "seek": 142858, "start": 1405.7, "end": 1428.58, "text": " A freshman, it means students like you, first year. Sophomore, it means second year. Junior, third level. Senior, fourth level. So that means first, second, third, and fourth level. And we have this number, these numbers for, I mean, there are 24", "tokens": [316, 22154, 11, 309, 1355, 1731, 411, 291, 11, 700, 1064, 13, 18921, 298, 418, 11, 309, 1355, 1150, 1064, 13, 21954, 11, 2636, 1496, 13, 18370, 11, 6409, 1496, 13, 407, 300, 1355, 700, 11, 1150, 11, 2636, 11, 293, 6409, 1496, 13, 400, 321, 362, 341, 1230, 11, 613, 3547, 337, 11, 286, 914, 11, 456, 366, 4022], "avg_logprob": -0.20696720627487683, "compression_ratio": 1.6466666666666667, "no_speech_prob": 0.0, "words": [{"start": 1405.7, "end": 1405.96, "word": " A", "probability": 0.55224609375}, {"start": 1405.96, "end": 1406.32, "word": " freshman,", "probability": 0.67236328125}, {"start": 1406.72, "end": 1407.04, "word": " it", "probability": 0.419677734375}, {"start": 1407.04, "end": 1407.42, "word": " means", "probability": 0.9287109375}, {"start": 1407.42, "end": 1408.18, "word": " students", "probability": 0.958984375}, {"start": 1408.18, "end": 1408.86, "word": " like", "probability": 0.93408203125}, {"start": 1408.86, "end": 1409.12, "word": " you,", "probability": 0.96337890625}, {"start": 1409.44, "end": 1409.86, "word": " first", "probability": 0.8701171875}, {"start": 1409.86, "end": 1410.18, "word": " year.", "probability": 0.9013671875}, {"start": 1411.02, "end": 1411.54, "word": " Sophomore,", "probability": 0.9178059895833334}, {"start": 1411.7, "end": 1411.96, "word": " it", "probability": 0.83447265625}, {"start": 1411.96, "end": 1412.4, "word": " means", "probability": 0.931640625}, {"start": 1412.4, "end": 1413.2, "word": " second", "probability": 0.89794921875}, {"start": 1413.2, "end": 1413.62, "word": " year.", "probability": 0.9072265625}, {"start": 1414.44, "end": 1414.74, "word": " Junior,", "probability": 0.93310546875}, {"start": 1415.1, "end": 1415.56, "word": " third", "probability": 0.91748046875}, {"start": 1415.56, "end": 1415.94, "word": " level.", "probability": 0.91845703125}, {"start": 1416.48, "end": 1416.72, "word": " Senior,", "probability": 0.94384765625}, {"start": 1417.04, "end": 1417.32, "word": " fourth", "probability": 0.92578125}, {"start": 1417.32, "end": 1417.64, "word": " level.", "probability": 0.93994140625}, {"start": 1418.06, "end": 1418.2, "word": " So", "probability": 0.9560546875}, {"start": 1418.2, "end": 1418.4, "word": " that", "probability": 0.751953125}, {"start": 1418.4, "end": 1418.66, "word": " means", "probability": 0.80322265625}, {"start": 1418.66, "end": 1418.98, "word": " first,", "probability": 0.85888671875}, {"start": 1419.14, "end": 1419.4, "word": " second,", "probability": 0.91845703125}, {"start": 1419.54, "end": 1419.82, "word": " third,", "probability": 0.94775390625}, {"start": 1420.0, "end": 1420.34, "word": " and", "probability": 0.93408203125}, {"start": 1420.34, "end": 1420.72, "word": " fourth", "probability": 0.93115234375}, {"start": 1420.72, "end": 1421.04, "word": " level.", "probability": 0.943359375}, {"start": 1421.86, "end": 1422.1, "word": " And", "probability": 0.943359375}, {"start": 1422.1, "end": 1422.24, "word": " we", "probability": 0.9501953125}, {"start": 1422.24, "end": 1422.38, "word": " have", "probability": 0.94482421875}, {"start": 1422.38, "end": 1422.64, "word": " this", "probability": 0.79736328125}, {"start": 1422.64, "end": 1423.06, "word": " number,", "probability": 0.89453125}, {"start": 1424.16, "end": 1424.46, "word": " these", "probability": 0.52880859375}, {"start": 1424.46, "end": 1424.96, "word": " numbers", "probability": 0.90576171875}, {"start": 1424.96, "end": 1425.36, "word": " for,", "probability": 0.8349609375}, {"start": 1425.68, "end": 1425.92, "word": " I", "probability": 0.9609375}, {"start": 1425.92, "end": 1426.14, "word": " mean,", "probability": 0.96435546875}, {"start": 1427.04, "end": 1427.36, "word": " there", "probability": 0.91064453125}, {"start": 1427.36, "end": 1427.78, "word": " are", "probability": 0.9462890625}, {"start": 1427.78, "end": 1428.58, "word": " 24", "probability": 0.95361328125}], "temperature": 1.0}, {"id": 54, "seek": 145420, "start": 1429.06, "end": 1454.2, "text": " A freshman who have meals for 20 per week. So there are 24 freshmen have 20 meals per week. 22 sophomores, the same, 10 for junior and 14 for senior. And the question is just to see if number of meals per week is independent of class standing.", "tokens": [316, 22154, 567, 362, 12832, 337, 945, 680, 1243, 13, 407, 456, 366, 4022, 43694, 362, 945, 12832, 680, 1243, 13, 5853, 32931, 2706, 11, 264, 912, 11, 1266, 337, 16195, 293, 3499, 337, 7965, 13, 400, 264, 1168, 307, 445, 281, 536, 498, 1230, 295, 12832, 680, 1243, 307, 6695, 295, 1508, 4877, 13], "avg_logprob": -0.18261718164597238, "compression_ratio": 1.5443037974683544, "no_speech_prob": 0.0, "words": [{"start": 1429.06, "end": 1429.3, "word": " A", "probability": 0.1630859375}, {"start": 1429.3, "end": 1429.7, "word": " freshman", "probability": 0.72265625}, {"start": 1429.7, "end": 1430.6, "word": " who", "probability": 0.85009765625}, {"start": 1430.6, "end": 1431.02, "word": " have", "probability": 0.7666015625}, {"start": 1431.02, "end": 1432.22, "word": " meals", "probability": 0.94091796875}, {"start": 1432.22, "end": 1432.72, "word": " for", "probability": 0.9365234375}, {"start": 1432.72, "end": 1433.12, "word": " 20", "probability": 0.79736328125}, {"start": 1433.12, "end": 1433.66, "word": " per", "probability": 0.88525390625}, {"start": 1433.66, "end": 1433.98, "word": " week.", "probability": 0.95263671875}, {"start": 1434.62, "end": 1434.78, "word": " So", "probability": 0.943359375}, {"start": 1434.78, "end": 1434.94, "word": " there", "probability": 0.783203125}, {"start": 1434.94, "end": 1435.1, "word": " are", "probability": 0.94775390625}, {"start": 1435.1, "end": 1436.46, "word": " 24", "probability": 0.94287109375}, {"start": 1436.46, "end": 1437.26, "word": " freshmen", "probability": 0.63427734375}, {"start": 1437.26, "end": 1438.84, "word": " have", "probability": 0.71875}, {"start": 1438.84, "end": 1439.24, "word": " 20", "probability": 0.947265625}, {"start": 1439.24, "end": 1439.6, "word": " meals", "probability": 0.94873046875}, {"start": 1439.6, "end": 1439.88, "word": " per", "probability": 0.95068359375}, {"start": 1439.88, "end": 1440.22, "word": " week.", "probability": 0.9443359375}, {"start": 1441.0, "end": 1441.4, "word": " 22", "probability": 0.65673828125}, {"start": 1441.4, "end": 1442.14, "word": " sophomores,", "probability": 0.84326171875}, {"start": 1442.28, "end": 1442.42, "word": " the", "probability": 0.84814453125}, {"start": 1442.42, "end": 1442.68, "word": " same,", "probability": 0.900390625}, {"start": 1442.92, "end": 1443.32, "word": " 10", "probability": 0.9228515625}, {"start": 1443.32, "end": 1443.64, "word": " for", "probability": 0.9443359375}, {"start": 1443.64, "end": 1443.9, "word": " junior", "probability": 0.92724609375}, {"start": 1443.9, "end": 1444.16, "word": " and", "probability": 0.75390625}, {"start": 1444.16, "end": 1444.64, "word": " 14", "probability": 0.962890625}, {"start": 1444.64, "end": 1445.52, "word": " for", "probability": 0.947265625}, {"start": 1445.52, "end": 1445.88, "word": " senior.", "probability": 0.92822265625}, {"start": 1446.22, "end": 1446.38, "word": " And", "probability": 0.93896484375}, {"start": 1446.38, "end": 1446.52, "word": " the", "probability": 0.9208984375}, {"start": 1446.52, "end": 1446.82, "word": " question", "probability": 0.923828125}, {"start": 1446.82, "end": 1447.84, "word": " is", "probability": 0.93310546875}, {"start": 1447.84, "end": 1448.66, "word": " just", "probability": 0.33935546875}, {"start": 1448.66, "end": 1448.86, "word": " to", "probability": 0.96923828125}, {"start": 1448.86, "end": 1449.16, "word": " see", "probability": 0.87451171875}, {"start": 1449.16, "end": 1450.22, "word": " if", "probability": 0.91845703125}, {"start": 1450.22, "end": 1450.6, "word": " number", "probability": 0.8974609375}, {"start": 1450.6, "end": 1450.86, "word": " of", "probability": 0.96826171875}, {"start": 1450.86, "end": 1451.18, "word": " meals", "probability": 0.943359375}, {"start": 1451.18, "end": 1451.44, "word": " per", "probability": 0.94921875}, {"start": 1451.44, "end": 1451.76, "word": " week", "probability": 0.94921875}, {"start": 1451.76, "end": 1452.4, "word": " is", "probability": 0.9384765625}, {"start": 1452.4, "end": 1452.92, "word": " independent", "probability": 0.8427734375}, {"start": 1452.92, "end": 1453.38, "word": " of", "probability": 0.9638671875}, {"start": 1453.38, "end": 1453.74, "word": " class", "probability": 0.84228515625}, {"start": 1453.74, "end": 1454.2, "word": " standing.", "probability": 0.8173828125}], "temperature": 1.0}, {"id": 55, "seek": 147559, "start": 1455.77, "end": 1475.59, "text": " to see if there is a relationship between these two variables. In this case, there are four rows because the class standing is classified into four groups. So there are four rows and three columns. So this table actually is four by three.", "tokens": [281, 536, 498, 456, 307, 257, 2480, 1296, 613, 732, 9102, 13, 682, 341, 1389, 11, 456, 366, 1451, 13241, 570, 264, 1508, 4877, 307, 20627, 666, 1451, 3935, 13, 407, 456, 366, 1451, 13241, 293, 1045, 13766, 13, 407, 341, 3199, 767, 307, 1451, 538, 1045, 13], "avg_logprob": -0.16757015792690977, "compression_ratio": 1.5827814569536425, "no_speech_prob": 0.0, "words": [{"start": 1455.77, "end": 1455.97, "word": " to", "probability": 0.4423828125}, {"start": 1455.97, "end": 1456.19, "word": " see", "probability": 0.92333984375}, {"start": 1456.19, "end": 1456.33, "word": " if", "probability": 0.94873046875}, {"start": 1456.33, "end": 1456.47, "word": " there", "probability": 0.91357421875}, {"start": 1456.47, "end": 1456.61, "word": " is", "probability": 0.90185546875}, {"start": 1456.61, "end": 1456.73, "word": " a", "probability": 0.9873046875}, {"start": 1456.73, "end": 1457.27, "word": " relationship", "probability": 0.921875}, {"start": 1457.27, "end": 1458.43, "word": " between", "probability": 0.86962890625}, {"start": 1458.43, "end": 1458.97, "word": " these", "probability": 0.85693359375}, {"start": 1458.97, "end": 1459.93, "word": " two", "probability": 0.9140625}, {"start": 1459.93, "end": 1460.43, "word": " variables.", "probability": 0.939453125}, {"start": 1460.75, "end": 1461.05, "word": " In", "probability": 0.95751953125}, {"start": 1461.05, "end": 1461.31, "word": " this", "probability": 0.9462890625}, {"start": 1461.31, "end": 1461.61, "word": " case,", "probability": 0.91259765625}, {"start": 1461.69, "end": 1461.89, "word": " there", "probability": 0.90869140625}, {"start": 1461.89, "end": 1462.19, "word": " are", "probability": 0.9423828125}, {"start": 1462.19, "end": 1462.69, "word": " four", "probability": 0.876953125}, {"start": 1462.69, "end": 1464.33, "word": " rows", "probability": 0.88427734375}, {"start": 1464.33, "end": 1465.17, "word": " because", "probability": 0.5791015625}, {"start": 1465.17, "end": 1465.87, "word": " the", "probability": 0.409912109375}, {"start": 1465.87, "end": 1466.13, "word": " class", "probability": 0.82373046875}, {"start": 1466.13, "end": 1466.61, "word": " standing", "probability": 0.85595703125}, {"start": 1466.61, "end": 1466.85, "word": " is", "probability": 0.87255859375}, {"start": 1466.85, "end": 1467.29, "word": " classified", "probability": 0.91162109375}, {"start": 1467.29, "end": 1467.61, "word": " into", "probability": 0.84423828125}, {"start": 1467.61, "end": 1467.91, "word": " four", "probability": 0.93798828125}, {"start": 1467.91, "end": 1468.29, "word": " groups.", "probability": 0.94970703125}, {"start": 1468.43, "end": 1468.59, "word": " So", "probability": 0.95166015625}, {"start": 1468.59, "end": 1468.77, "word": " there", "probability": 0.693359375}, {"start": 1468.77, "end": 1468.95, "word": " are", "probability": 0.94140625}, {"start": 1468.95, "end": 1469.19, "word": " four", "probability": 0.9462890625}, {"start": 1469.19, "end": 1469.57, "word": " rows", "probability": 0.89111328125}, {"start": 1469.57, "end": 1470.49, "word": " and", "probability": 0.900390625}, {"start": 1470.49, "end": 1471.33, "word": " three", "probability": 0.91357421875}, {"start": 1471.33, "end": 1471.87, "word": " columns.", "probability": 0.94287109375}, {"start": 1472.37, "end": 1472.53, "word": " So", "probability": 0.95556640625}, {"start": 1472.53, "end": 1472.81, "word": " this", "probability": 0.890625}, {"start": 1472.81, "end": 1473.21, "word": " table", "probability": 0.896484375}, {"start": 1473.21, "end": 1473.93, "word": " actually", "probability": 0.833984375}, {"start": 1473.93, "end": 1474.23, "word": " is", "probability": 0.939453125}, {"start": 1474.23, "end": 1474.53, "word": " four", "probability": 0.486572265625}, {"start": 1474.53, "end": 1474.85, "word": " by", "probability": 0.96435546875}, {"start": 1474.85, "end": 1475.59, "word": " three.", "probability": 0.9375}], "temperature": 1.0}, {"id": 56, "seek": 150152, "start": 1476.7, "end": 1501.52, "text": " And there are twelve cells in this case. Now it takes time to compute the expected frequencies because in this case we have to compute the expected frequency for each cell. And we are going to use this formula for only six of them.", "tokens": [400, 456, 366, 14390, 5438, 294, 341, 1389, 13, 823, 309, 2516, 565, 281, 14722, 264, 5176, 20250, 570, 294, 341, 1389, 321, 362, 281, 14722, 264, 5176, 7893, 337, 1184, 2815, 13, 400, 321, 366, 516, 281, 764, 341, 8513, 337, 787, 2309, 295, 552, 13], "avg_logprob": -0.20117187655220428, "compression_ratio": 1.6571428571428573, "no_speech_prob": 0.0, "words": [{"start": 1476.7, "end": 1477.18, "word": " And", "probability": 0.3984375}, {"start": 1477.18, "end": 1477.66, "word": " there", "probability": 0.59033203125}, {"start": 1477.66, "end": 1478.22, "word": " are", "probability": 0.94287109375}, {"start": 1478.22, "end": 1478.84, "word": " twelve", "probability": 0.4501953125}, {"start": 1478.84, "end": 1479.76, "word": " cells", "probability": 0.89697265625}, {"start": 1479.76, "end": 1480.0, "word": " in", "probability": 0.90380859375}, {"start": 1480.0, "end": 1480.2, "word": " this", "probability": 0.93798828125}, {"start": 1480.2, "end": 1480.54, "word": " case.", "probability": 0.9052734375}, {"start": 1481.02, "end": 1481.2, "word": " Now", "probability": 0.80322265625}, {"start": 1481.2, "end": 1481.54, "word": " it", "probability": 0.65576171875}, {"start": 1481.54, "end": 1482.98, "word": " takes", "probability": 0.45458984375}, {"start": 1482.98, "end": 1484.62, "word": " time", "probability": 0.66357421875}, {"start": 1484.62, "end": 1485.74, "word": " to", "probability": 0.89599609375}, {"start": 1485.74, "end": 1486.12, "word": " compute", "probability": 0.90869140625}, {"start": 1486.12, "end": 1486.32, "word": " the", "probability": 0.48828125}, {"start": 1486.32, "end": 1486.66, "word": " expected", "probability": 0.9287109375}, {"start": 1486.66, "end": 1487.22, "word": " frequencies", "probability": 0.67431640625}, {"start": 1487.22, "end": 1487.66, "word": " because", "probability": 0.57568359375}, {"start": 1487.66, "end": 1487.84, "word": " in", "probability": 0.880859375}, {"start": 1487.84, "end": 1488.08, "word": " this", "probability": 0.94775390625}, {"start": 1488.08, "end": 1488.46, "word": " case", "probability": 0.9150390625}, {"start": 1488.46, "end": 1489.36, "word": " we", "probability": 0.6357421875}, {"start": 1489.36, "end": 1489.56, "word": " have", "probability": 0.9443359375}, {"start": 1489.56, "end": 1489.76, "word": " to", "probability": 0.97021484375}, {"start": 1489.76, "end": 1490.14, "word": " compute", "probability": 0.9248046875}, {"start": 1490.14, "end": 1490.46, "word": " the", "probability": 0.8056640625}, {"start": 1490.46, "end": 1490.84, "word": " expected", "probability": 0.923828125}, {"start": 1490.84, "end": 1491.46, "word": " frequency", "probability": 0.88427734375}, {"start": 1491.46, "end": 1491.8, "word": " for", "probability": 0.93798828125}, {"start": 1491.8, "end": 1492.36, "word": " each", "probability": 0.94287109375}, {"start": 1492.36, "end": 1493.96, "word": " cell.", "probability": 0.88037109375}, {"start": 1494.82, "end": 1495.12, "word": " And", "probability": 0.89892578125}, {"start": 1495.12, "end": 1495.26, "word": " we", "probability": 0.94921875}, {"start": 1495.26, "end": 1495.4, "word": " are", "probability": 0.91259765625}, {"start": 1495.4, "end": 1495.7, "word": " going", "probability": 0.94482421875}, {"start": 1495.7, "end": 1495.88, "word": " to", "probability": 0.9609375}, {"start": 1495.88, "end": 1496.14, "word": " use", "probability": 0.880859375}, {"start": 1496.14, "end": 1496.8, "word": " this", "probability": 0.9453125}, {"start": 1496.8, "end": 1499.64, "word": " formula", "probability": 0.88427734375}, {"start": 1499.64, "end": 1500.1, "word": " for", "probability": 0.9423828125}, {"start": 1500.1, "end": 1500.58, "word": " only", "probability": 0.92041015625}, {"start": 1500.58, "end": 1501.12, "word": " six", "probability": 0.88720703125}, {"start": 1501.12, "end": 1501.32, "word": " of", "probability": 0.9716796875}, {"start": 1501.32, "end": 1501.52, "word": " them.", "probability": 0.88330078125}], "temperature": 1.0}, {"id": 57, "seek": 153178, "start": 1503.26, "end": 1531.78, "text": " I mean, we can apply this formula for only six of them. And the others can be computed by the complement by using either column total or row total. So because degrees of freedom is six, that means you may use this rule six times only. The others can be computed by using the complement. So here again, the hypothesis to be tested is,", "tokens": [286, 914, 11, 321, 393, 3079, 341, 8513, 337, 787, 2309, 295, 552, 13, 400, 264, 2357, 393, 312, 40610, 538, 264, 17103, 538, 1228, 2139, 7738, 3217, 420, 5386, 3217, 13, 407, 570, 5310, 295, 5645, 307, 2309, 11, 300, 1355, 291, 815, 764, 341, 4978, 2309, 1413, 787, 13, 440, 2357, 393, 312, 40610, 538, 1228, 264, 17103, 13, 407, 510, 797, 11, 264, 17291, 281, 312, 8246, 307, 11], "avg_logprob": -0.1642765427288944, "compression_ratio": 1.7395833333333333, "no_speech_prob": 0.0, "words": [{"start": 1503.26, "end": 1503.48, "word": " I", "probability": 0.861328125}, {"start": 1503.48, "end": 1503.62, "word": " mean,", "probability": 0.96142578125}, {"start": 1503.66, "end": 1503.78, "word": " we", "probability": 0.9423828125}, {"start": 1503.78, "end": 1504.06, "word": " can", "probability": 0.9482421875}, {"start": 1504.06, "end": 1504.48, "word": " apply", "probability": 0.92529296875}, {"start": 1504.48, "end": 1504.86, "word": " this", "probability": 0.9423828125}, {"start": 1504.86, "end": 1505.54, "word": " formula", "probability": 0.93310546875}, {"start": 1505.54, "end": 1505.92, "word": " for", "probability": 0.90185546875}, {"start": 1505.92, "end": 1506.26, "word": " only", "probability": 0.80810546875}, {"start": 1506.26, "end": 1506.62, "word": " six", "probability": 0.77587890625}, {"start": 1506.62, "end": 1506.82, "word": " of", "probability": 0.97021484375}, {"start": 1506.82, "end": 1507.06, "word": " them.", "probability": 0.8935546875}, {"start": 1507.48, "end": 1507.94, "word": " And", "probability": 0.94677734375}, {"start": 1507.94, "end": 1508.08, "word": " the", "probability": 0.81982421875}, {"start": 1508.08, "end": 1508.38, "word": " others", "probability": 0.91162109375}, {"start": 1508.38, "end": 1508.68, "word": " can", "probability": 0.9462890625}, {"start": 1508.68, "end": 1508.9, "word": " be", "probability": 0.9541015625}, {"start": 1508.9, "end": 1509.38, "word": " computed", "probability": 0.9306640625}, {"start": 1509.38, "end": 1509.66, "word": " by", "probability": 0.966796875}, {"start": 1509.66, "end": 1509.88, "word": " the", "probability": 0.91015625}, {"start": 1509.88, "end": 1510.2, "word": " complement", "probability": 0.84912109375}, {"start": 1510.2, "end": 1511.5, "word": " by", "probability": 0.51611328125}, {"start": 1511.5, "end": 1511.94, "word": " using", "probability": 0.93701171875}, {"start": 1511.94, "end": 1512.7, "word": " either", "probability": 0.93212890625}, {"start": 1512.7, "end": 1513.22, "word": " column", "probability": 0.845703125}, {"start": 1513.22, "end": 1513.6, "word": " total", "probability": 0.80126953125}, {"start": 1513.6, "end": 1514.08, "word": " or", "probability": 0.9453125}, {"start": 1514.08, "end": 1514.3, "word": " row", "probability": 0.86572265625}, {"start": 1514.3, "end": 1514.6, "word": " total.", "probability": 0.6728515625}, {"start": 1516.24, "end": 1516.92, "word": " So", "probability": 0.63232421875}, {"start": 1516.92, "end": 1517.28, "word": " because", "probability": 0.76123046875}, {"start": 1517.28, "end": 1517.74, "word": " degrees", "probability": 0.64013671875}, {"start": 1517.74, "end": 1517.92, "word": " of", "probability": 0.94921875}, {"start": 1517.92, "end": 1518.16, "word": " freedom", "probability": 0.93359375}, {"start": 1518.16, "end": 1518.42, "word": " is", "probability": 0.7080078125}, {"start": 1518.42, "end": 1518.74, "word": " six,", "probability": 0.83251953125}, {"start": 1519.6, "end": 1519.94, "word": " that", "probability": 0.927734375}, {"start": 1519.94, "end": 1520.28, "word": " means", "probability": 0.93505859375}, {"start": 1520.28, "end": 1520.92, "word": " you", "probability": 0.93798828125}, {"start": 1520.92, "end": 1521.22, "word": " may", "probability": 0.931640625}, {"start": 1521.22, "end": 1521.58, "word": " use", "probability": 0.87548828125}, {"start": 1521.58, "end": 1521.86, "word": " this", "probability": 0.94140625}, {"start": 1521.86, "end": 1522.08, "word": " rule", "probability": 0.875}, {"start": 1522.08, "end": 1522.4, "word": " six", "probability": 0.9365234375}, {"start": 1522.4, "end": 1522.82, "word": " times", "probability": 0.9267578125}, {"start": 1522.82, "end": 1523.26, "word": " only.", "probability": 0.89111328125}, {"start": 1523.76, "end": 1523.88, "word": " The", "probability": 0.86474609375}, {"start": 1523.88, "end": 1524.18, "word": " others", "probability": 0.904296875}, {"start": 1524.18, "end": 1524.44, "word": " can", "probability": 0.943359375}, {"start": 1524.44, "end": 1524.62, "word": " be", "probability": 0.9560546875}, {"start": 1524.62, "end": 1525.06, "word": " computed", "probability": 0.943359375}, {"start": 1525.06, "end": 1525.46, "word": " by", "probability": 0.95556640625}, {"start": 1525.46, "end": 1526.04, "word": " using", "probability": 0.9267578125}, {"start": 1526.04, "end": 1526.28, "word": " the", "probability": 0.90576171875}, {"start": 1526.28, "end": 1526.6, "word": " complement.", "probability": 0.63330078125}, {"start": 1527.74, "end": 1528.42, "word": " So", "probability": 0.95458984375}, {"start": 1528.42, "end": 1528.64, "word": " here", "probability": 0.78759765625}, {"start": 1528.64, "end": 1528.98, "word": " again,", "probability": 0.771484375}, {"start": 1529.68, "end": 1529.92, "word": " the", "probability": 0.896484375}, {"start": 1529.92, "end": 1530.38, "word": " hypothesis", "probability": 0.81005859375}, {"start": 1530.38, "end": 1530.78, "word": " to", "probability": 0.9677734375}, {"start": 1530.78, "end": 1530.96, "word": " be", "probability": 0.95166015625}, {"start": 1530.96, "end": 1531.34, "word": " tested", "probability": 0.8818359375}, {"start": 1531.34, "end": 1531.78, "word": " is,", "probability": 0.94140625}], "temperature": 1.0}, {"id": 58, "seek": 156047, "start": 1533.75, "end": 1560.47, "text": " Mean plan and class standing are independent, that means there is no relationship between them. Against alternative hypothesis, mean plan and class standing are dependent, that means there exists significant relationship between them. Now let's see how can we compute the expected cell, the expected frequency for each cell. For example,", "tokens": [12302, 1393, 293, 1508, 4877, 366, 6695, 11, 300, 1355, 456, 307, 572, 2480, 1296, 552, 13, 29995, 8535, 17291, 11, 914, 1393, 293, 1508, 4877, 366, 12334, 11, 300, 1355, 456, 8198, 4776, 2480, 1296, 552, 13, 823, 718, 311, 536, 577, 393, 321, 14722, 264, 5176, 2815, 11, 264, 5176, 7893, 337, 1184, 2815, 13, 1171, 1365, 11], "avg_logprob": -0.20005122559969543, "compression_ratio": 1.8777777777777778, "no_speech_prob": 0.0, "words": [{"start": 1533.75, "end": 1534.07, "word": " Mean", "probability": 0.180908203125}, {"start": 1534.07, "end": 1534.31, "word": " plan", "probability": 0.68603515625}, {"start": 1534.31, "end": 1534.61, "word": " and", "probability": 0.93359375}, {"start": 1534.61, "end": 1534.91, "word": " class", "probability": 0.54296875}, {"start": 1534.91, "end": 1535.27, "word": " standing", "probability": 0.82763671875}, {"start": 1535.27, "end": 1535.49, "word": " are", "probability": 0.92236328125}, {"start": 1535.49, "end": 1535.89, "word": " independent,", "probability": 0.8544921875}, {"start": 1536.29, "end": 1536.55, "word": " that", "probability": 0.79931640625}, {"start": 1536.55, "end": 1536.85, "word": " means", "probability": 0.921875}, {"start": 1536.85, "end": 1537.09, "word": " there", "probability": 0.84130859375}, {"start": 1537.09, "end": 1537.29, "word": " is", "probability": 0.9169921875}, {"start": 1537.29, "end": 1537.47, "word": " no", "probability": 0.93310546875}, {"start": 1537.47, "end": 1537.99, "word": " relationship", "probability": 0.89306640625}, {"start": 1537.99, "end": 1538.37, "word": " between", "probability": 0.876953125}, {"start": 1538.37, "end": 1538.67, "word": " them.", "probability": 0.90478515625}, {"start": 1539.15, "end": 1539.59, "word": " Against", "probability": 0.86572265625}, {"start": 1539.59, "end": 1540.23, "word": " alternative", "probability": 0.68017578125}, {"start": 1540.23, "end": 1540.73, "word": " hypothesis,", "probability": 0.685546875}, {"start": 1540.91, "end": 1541.05, "word": " mean", "probability": 0.89501953125}, {"start": 1541.05, "end": 1541.35, "word": " plan", "probability": 0.95849609375}, {"start": 1541.35, "end": 1541.65, "word": " and", "probability": 0.93701171875}, {"start": 1541.65, "end": 1541.93, "word": " class", "probability": 0.9365234375}, {"start": 1541.93, "end": 1542.29, "word": " standing", "probability": 0.8779296875}, {"start": 1542.29, "end": 1542.77, "word": " are", "probability": 0.9423828125}, {"start": 1542.77, "end": 1543.71, "word": " dependent,", "probability": 0.83837890625}, {"start": 1543.99, "end": 1544.15, "word": " that", "probability": 0.93212890625}, {"start": 1544.15, "end": 1544.43, "word": " means", "probability": 0.935546875}, {"start": 1544.43, "end": 1544.63, "word": " there", "probability": 0.8623046875}, {"start": 1544.63, "end": 1544.99, "word": " exists", "probability": 0.76708984375}, {"start": 1544.99, "end": 1545.83, "word": " significant", "probability": 0.84326171875}, {"start": 1545.83, "end": 1547.03, "word": " relationship", "probability": 0.91162109375}, {"start": 1547.03, "end": 1547.61, "word": " between", "probability": 0.857421875}, {"start": 1547.61, "end": 1548.81, "word": " them.", "probability": 0.89208984375}, {"start": 1549.73, "end": 1549.95, "word": " Now", "probability": 0.955078125}, {"start": 1549.95, "end": 1550.21, "word": " let's", "probability": 0.8212890625}, {"start": 1550.21, "end": 1550.33, "word": " see", "probability": 0.92041015625}, {"start": 1550.33, "end": 1550.43, "word": " how", "probability": 0.9169921875}, {"start": 1550.43, "end": 1550.65, "word": " can", "probability": 0.81689453125}, {"start": 1550.65, "end": 1550.81, "word": " we", "probability": 0.95166015625}, {"start": 1550.81, "end": 1551.39, "word": " compute", "probability": 0.91943359375}, {"start": 1551.39, "end": 1552.41, "word": " the", "probability": 0.8486328125}, {"start": 1552.41, "end": 1552.97, "word": " expected", "probability": 0.91357421875}, {"start": 1552.97, "end": 1554.39, "word": " cell,", "probability": 0.82568359375}, {"start": 1555.99, "end": 1556.21, "word": " the", "probability": 0.8984375}, {"start": 1556.21, "end": 1556.53, "word": " expected", "probability": 0.9208984375}, {"start": 1556.53, "end": 1557.09, "word": " frequency", "probability": 0.96435546875}, {"start": 1557.09, "end": 1557.39, "word": " for", "probability": 0.9384765625}, {"start": 1557.39, "end": 1557.63, "word": " each", "probability": 0.91064453125}, {"start": 1557.63, "end": 1557.89, "word": " cell.", "probability": 0.90478515625}, {"start": 1559.51, "end": 1560.11, "word": " For", "probability": 0.96533203125}, {"start": 1560.11, "end": 1560.47, "word": " example,", "probability": 0.97607421875}], "temperature": 1.0}, {"id": 59, "seek": 159121, "start": 1562.25, "end": 1591.21, "text": " The first observed frequency is 24. Now the expected should be 70 times 70 divided by 200. So for cell 11, the first cell. If expected, we can use this notation, 11. Means first row.", "tokens": [440, 700, 13095, 7893, 307, 4022, 13, 823, 264, 5176, 820, 312, 5285, 1413, 5285, 6666, 538, 2331, 13, 407, 337, 2815, 2975, 11, 264, 700, 2815, 13, 759, 5176, 11, 321, 393, 764, 341, 24657, 11, 2975, 13, 40290, 700, 5386, 13], "avg_logprob": -0.29456675255840475, "compression_ratio": 1.297872340425532, "no_speech_prob": 0.0, "words": [{"start": 1562.25, "end": 1563.15, "word": " The", "probability": 0.398193359375}, {"start": 1563.15, "end": 1563.53, "word": " first", "probability": 0.8642578125}, {"start": 1563.53, "end": 1564.29, "word": " observed", "probability": 0.8076171875}, {"start": 1564.29, "end": 1565.23, "word": " frequency", "probability": 0.9482421875}, {"start": 1565.23, "end": 1565.51, "word": " is", "probability": 0.93115234375}, {"start": 1565.51, "end": 1566.03, "word": " 24.", "probability": 0.93505859375}, {"start": 1567.39, "end": 1567.61, "word": " Now", "probability": 0.92138671875}, {"start": 1567.61, "end": 1567.79, "word": " the", "probability": 0.5556640625}, {"start": 1567.79, "end": 1568.25, "word": " expected", "probability": 0.91650390625}, {"start": 1568.25, "end": 1569.43, "word": " should", "probability": 0.94384765625}, {"start": 1569.43, "end": 1569.89, "word": " be", "probability": 0.95654296875}, {"start": 1569.89, "end": 1571.43, "word": " 70", "probability": 0.91796875}, {"start": 1571.43, "end": 1572.75, "word": " times", "probability": 0.697265625}, {"start": 1572.75, "end": 1573.43, "word": " 70", "probability": 0.95849609375}, {"start": 1573.43, "end": 1574.21, "word": " divided", "probability": 0.7041015625}, {"start": 1574.21, "end": 1574.51, "word": " by", "probability": 0.97314453125}, {"start": 1574.51, "end": 1575.01, "word": " 200.", "probability": 0.92236328125}, {"start": 1575.71, "end": 1575.99, "word": " So", "probability": 0.92041015625}, {"start": 1575.99, "end": 1576.57, "word": " for", "probability": 0.63671875}, {"start": 1576.57, "end": 1576.79, "word": " cell", "probability": 0.884765625}, {"start": 1576.79, "end": 1577.19, "word": " 11,", "probability": 0.71435546875}, {"start": 1578.93, "end": 1579.93, "word": " the", "probability": 0.8203125}, {"start": 1579.93, "end": 1580.29, "word": " first", "probability": 0.888671875}, {"start": 1580.29, "end": 1580.73, "word": " cell.", "probability": 0.76318359375}, {"start": 1582.37, "end": 1582.75, "word": " If", "probability": 0.256591796875}, {"start": 1582.75, "end": 1583.37, "word": " expected,", "probability": 0.90380859375}, {"start": 1584.55, "end": 1584.89, "word": " we", "probability": 0.8974609375}, {"start": 1584.89, "end": 1585.05, "word": " can", "probability": 0.9267578125}, {"start": 1585.05, "end": 1585.21, "word": " use", "probability": 0.8857421875}, {"start": 1585.21, "end": 1585.41, "word": " this", "probability": 0.82470703125}, {"start": 1585.41, "end": 1585.77, "word": " notation,", "probability": 0.98974609375}, {"start": 1585.93, "end": 1586.15, "word": " 11.", "probability": 0.89404296875}, {"start": 1588.03, "end": 1588.79, "word": " Means", "probability": 0.61083984375}, {"start": 1588.79, "end": 1590.83, "word": " first", "probability": 0.2177734375}, {"start": 1590.83, "end": 1591.21, "word": " row.", "probability": 0.50927734375}], "temperature": 1.0}, {"id": 60, "seek": 162009, "start": 1592.05, "end": 1620.09, "text": " First column. That should be 70. It is 70. Multiplied by column totals. Again, in this case, 70. Multiplied by 200. That will give 24.5. Similarly, for the second cell, for 32. 70 times 88 divided by 200.", "tokens": [2386, 7738, 13, 663, 820, 312, 5285, 13, 467, 307, 5285, 13, 29238, 564, 1091, 538, 7738, 1993, 1124, 13, 3764, 11, 294, 341, 1389, 11, 5285, 13, 29238, 564, 1091, 538, 2331, 13, 663, 486, 976, 4022, 13, 20, 13, 13157, 11, 337, 264, 1150, 2815, 11, 337, 8858, 13, 5285, 1413, 24587, 6666, 538, 2331, 13], "avg_logprob": -0.2738347599061869, "compression_ratio": 1.3945578231292517, "no_speech_prob": 0.0, "words": [{"start": 1592.05, "end": 1592.45, "word": " First", "probability": 0.130859375}, {"start": 1592.45, "end": 1593.59, "word": " column.", "probability": 0.89697265625}, {"start": 1594.31, "end": 1594.69, "word": " That", "probability": 0.62451171875}, {"start": 1594.69, "end": 1595.37, "word": " should", "probability": 0.95556640625}, {"start": 1595.37, "end": 1595.61, "word": " be", "probability": 0.9541015625}, {"start": 1595.61, "end": 1596.23, "word": " 70.", "probability": 0.798828125}, {"start": 1596.73, "end": 1596.85, "word": " It", "probability": 0.2578125}, {"start": 1596.85, "end": 1596.97, "word": " is", "probability": 0.93603515625}, {"start": 1596.97, "end": 1597.41, "word": " 70.", "probability": 0.95654296875}, {"start": 1598.95, "end": 1599.75, "word": " Multiplied", "probability": 0.8234049479166666}, {"start": 1599.75, "end": 1600.11, "word": " by", "probability": 0.9658203125}, {"start": 1600.11, "end": 1600.61, "word": " column", "probability": 0.74755859375}, {"start": 1600.61, "end": 1601.29, "word": " totals.", "probability": 0.908203125}, {"start": 1601.65, "end": 1601.97, "word": " Again,", "probability": 0.91162109375}, {"start": 1602.17, "end": 1602.31, "word": " in", "probability": 0.76806640625}, {"start": 1602.31, "end": 1602.49, "word": " this", "probability": 0.94921875}, {"start": 1602.49, "end": 1602.73, "word": " case,", "probability": 0.91650390625}, {"start": 1602.77, "end": 1603.23, "word": " 70.", "probability": 0.9169921875}, {"start": 1603.49, "end": 1603.99, "word": " Multiplied", "probability": 0.7411295572916666}, {"start": 1603.99, "end": 1604.29, "word": " by", "probability": 0.97412109375}, {"start": 1604.29, "end": 1604.59, "word": " 200.", "probability": 0.73193359375}, {"start": 1605.17, "end": 1605.57, "word": " That", "probability": 0.8857421875}, {"start": 1605.57, "end": 1605.83, "word": " will", "probability": 0.8486328125}, {"start": 1605.83, "end": 1606.09, "word": " give", "probability": 0.79541015625}, {"start": 1606.09, "end": 1606.61, "word": " 24", "probability": 0.71435546875}, {"start": 1606.61, "end": 1607.27, "word": ".5.", "probability": 0.98779296875}, {"start": 1610.15, "end": 1610.95, "word": " Similarly,", "probability": 0.79833984375}, {"start": 1611.23, "end": 1611.41, "word": " for", "probability": 0.94921875}, {"start": 1611.41, "end": 1611.77, "word": " the", "probability": 0.91943359375}, {"start": 1611.77, "end": 1612.33, "word": " second", "probability": 0.8916015625}, {"start": 1612.33, "end": 1612.69, "word": " cell,", "probability": 0.912109375}, {"start": 1612.85, "end": 1613.03, "word": " for", "probability": 0.80224609375}, {"start": 1613.03, "end": 1613.73, "word": " 32.", "probability": 0.87939453125}, {"start": 1616.35, "end": 1617.15, "word": " 70", "probability": 0.89990234375}, {"start": 1617.15, "end": 1617.83, "word": " times", "probability": 0.90185546875}, {"start": 1617.83, "end": 1618.61, "word": " 88", "probability": 0.810546875}, {"start": 1618.61, "end": 1619.47, "word": " divided", "probability": 0.68115234375}, {"start": 1619.47, "end": 1619.69, "word": " by", "probability": 0.97216796875}, {"start": 1619.69, "end": 1620.09, "word": " 200.", "probability": 0.9248046875}], "temperature": 1.0}, {"id": 61, "seek": 164942, "start": 1622.82, "end": 1649.42, "text": " So for F22, again it's 70 times 88 divided by 200, that will get 30.8. So 70 times 88, that will give 30.8. 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the third one now either you can use the same equation which is 70 times 42 so you can use 70 times 42 divided by 200 that will give 14.7 or it's just the complement which is 70 minus", "tokens": [20293, 502, 1150, 472, 264, 2636, 472, 586, 2139, 291, 393, 764, 264, 912, 5367, 597, 307, 5285, 1413, 14034, 370, 291, 393, 764, 5285, 1413, 14034, 6666, 538, 2331, 300, 486, 976, 3499, 13, 22, 420, 309, 311, 445, 264, 17103, 597, 307, 5285, 3175], "avg_logprob": -0.23154919705492386, "compression_ratio": 1.5112781954887218, "no_speech_prob": 0.0, "words": [{"start": 1650.64, "end": 1651.02, "word": " rho", "probability": 0.07763671875}, {"start": 1651.02, "end": 1651.36, "word": " 1", "probability": 0.57421875}, {"start": 1651.36, "end": 1652.78, "word": " second", "probability": 0.454345703125}, {"start": 1652.78, "end": 1653.2, "word": " one", "probability": 0.587890625}, {"start": 1653.2, "end": 1654.58, "word": " the", "probability": 0.322998046875}, {"start": 1654.58, "end": 1654.94, 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So either use 70 multiplied by 40 divided by 200 or just the complement, 70 minus.", "tokens": [4022, 13, 20, 1804, 2217, 13, 23, 13, 407, 2139, 764, 5285, 17207, 538, 3356, 6666, 538, 2331, 420, 445, 264, 17103, 11, 5285, 3175, 13], "avg_logprob": -0.3136573985770897, "compression_ratio": 1.1, "no_speech_prob": 0.0, "words": [{"start": 1683.3899999999999, "end": 1684.29, "word": " 24", "probability": 0.188232421875}, {"start": 1684.29, "end": 1685.19, "word": ".5", "probability": 0.90869140625}, {"start": 1685.19, "end": 1686.31, "word": " plus", "probability": 0.35888671875}, {"start": 1686.31, "end": 1686.71, "word": " 30", "probability": 0.9404296875}, {"start": 1686.71, "end": 1687.35, "word": ".8.", "probability": 0.974609375}, {"start": 1688.63, "end": 1689.29, "word": " So", "probability": 0.818359375}, {"start": 1689.29, "end": 1689.59, "word": " either", "probability": 0.82470703125}, {"start": 1689.59, "end": 1690.07, "word": " use", "probability": 0.58349609375}, {"start": 1690.07, "end": 1691.51, "word": " 70", "probability": 0.87646484375}, {"start": 1691.51, "end": 1693.15, "word": " multiplied", "probability": 0.57666015625}, {"start": 1693.15, "end": 1693.47, "word": " by", "probability": 0.97021484375}, {"start": 1693.47, "end": 1694.51, "word": " 40", "probability": 0.89404296875}, {"start": 1694.51, "end": 1694.83, "word": " divided", "probability": 0.6982421875}, {"start": 1694.83, "end": 1695.05, "word": " by", "probability": 0.96630859375}, {"start": 1695.05, "end": 1695.41, "word": " 200", "probability": 0.9189453125}, {"start": 1695.41, "end": 1696.19, "word": " or", "probability": 0.64990234375}, {"start": 1696.19, "end": 1696.55, "word": " just", "probability": 0.9130859375}, {"start": 1696.55, "end": 1696.81, "word": " the", "probability": 0.57373046875}, {"start": 1696.81, "end": 1697.15, "word": " complement,", "probability": 0.8046875}, {"start": 1697.57, "end": 1698.11, "word": " 70", "probability": 0.85009765625}, {"start": 1698.11, "end": 1699.39, "word": " minus.", "probability": 0.96533203125}], "temperature": 1.0}, {"id": 64, "seek": 172256, "start": 1700.8, "end": 1722.56, "text": " 24.5 plus 30.8 will give the same value. So I just compute the expected cell for 1 and 2, and the third one is just the complement. Similarly, for the second row, I mean cell 21, then 22, and 23.", "tokens": [4022, 13, 20, 1804, 2217, 13, 23, 486, 976, 264, 912, 2158, 13, 407, 286, 445, 14722, 264, 5176, 2815, 337, 502, 293, 568, 11, 293, 264, 2636, 472, 307, 445, 264, 17103, 13, 13157, 11, 337, 264, 1150, 5386, 11, 286, 914, 2815, 5080, 11, 550, 5853, 11, 293, 6673, 13], "avg_logprob": -0.18160377920798534, "compression_ratio": 1.3611111111111112, "no_speech_prob": 0.0, "words": [{"start": 1700.8, "end": 1701.22, "word": " 24", "probability": 0.6689453125}, {"start": 1701.22, "end": 1702.02, "word": ".5", "probability": 0.979248046875}, {"start": 1702.02, "end": 1703.1, "word": " plus", "probability": 0.72900390625}, {"start": 1703.1, "end": 1703.54, "word": " 30", "probability": 0.92236328125}, {"start": 1703.54, "end": 1704.12, "word": ".8", "probability": 0.99365234375}, {"start": 1704.12, "end": 1704.36, "word": " will", "probability": 0.83984375}, {"start": 1704.36, "end": 1704.58, "word": " give", "probability": 0.88232421875}, {"start": 1704.58, "end": 1704.76, "word": " the", "probability": 0.89453125}, {"start": 1704.76, "end": 1705.08, "word": " same", "probability": 0.91552734375}, {"start": 1705.08, "end": 1706.08, "word": " value.", "probability": 0.9697265625}, {"start": 1707.38, "end": 1707.84, "word": " So", "probability": 0.88916015625}, {"start": 1707.84, "end": 1707.98, "word": " I", "probability": 0.74462890625}, {"start": 1707.98, "end": 1708.4, "word": " just", "probability": 0.88037109375}, {"start": 1708.4, "end": 1708.96, "word": " compute", "probability": 0.8740234375}, {"start": 1708.96, "end": 1709.26, "word": " the", "probability": 0.89794921875}, {"start": 1709.26, "end": 1709.78, "word": " expected", "probability": 0.9033203125}, {"start": 1709.78, "end": 1710.06, "word": " cell", "probability": 0.8232421875}, {"start": 1710.06, "end": 1710.46, "word": " for", "probability": 0.88134765625}, {"start": 1710.46, "end": 1711.7, "word": " 1", "probability": 0.71484375}, {"start": 1711.7, "end": 1711.84, "word": " and", "probability": 0.916015625}, {"start": 1711.84, "end": 1712.12, "word": " 2,", "probability": 0.99658203125}, {"start": 1712.32, "end": 1712.58, "word": " and", "probability": 0.93310546875}, {"start": 1712.58, "end": 1712.74, "word": " the", "probability": 0.9150390625}, {"start": 1712.74, "end": 1712.98, "word": " third", "probability": 0.89990234375}, {"start": 1712.98, "end": 1713.26, "word": " one", "probability": 0.9248046875}, {"start": 1713.26, "end": 1713.54, "word": " is", "probability": 0.94775390625}, {"start": 1713.54, "end": 1713.86, "word": " just", "probability": 0.91748046875}, {"start": 1713.86, "end": 1714.04, "word": " the", "probability": 0.366943359375}, {"start": 1714.04, "end": 1714.28, "word": " complement.", "probability": 0.67626953125}, {"start": 1715.18, "end": 1715.68, "word": " Similarly,", "probability": 0.80224609375}, {"start": 1715.88, "end": 1716.12, "word": " for", "probability": 0.951171875}, {"start": 1716.12, "end": 1716.3, "word": " the", "probability": 0.91796875}, {"start": 1716.3, "end": 1716.6, "word": " second", "probability": 0.8984375}, {"start": 1716.6, "end": 1716.94, "word": " row,", "probability": 0.91455078125}, {"start": 1717.78, "end": 1718.1, "word": " I", "probability": 0.99462890625}, {"start": 1718.1, "end": 1718.32, "word": " mean", "probability": 0.96044921875}, {"start": 1718.32, "end": 1718.76, "word": " cell", "probability": 0.79443359375}, {"start": 1718.76, "end": 1719.24, "word": " 21,", "probability": 0.44482421875}, {"start": 1720.66, "end": 1721.06, "word": " then", "probability": 0.84619140625}, {"start": 1721.06, "end": 1721.58, "word": " 22,", "probability": 0.97265625}, {"start": 1721.92, "end": 1722.16, "word": " and", "probability": 0.876953125}, {"start": 1722.16, "end": 1722.56, "word": " 23.", "probability": 0.9423828125}], "temperature": 1.0}, {"id": 65, "seek": 174430, "start": 1723.68, "end": 1744.3, "text": " By using the same method, he will get these two values, and the other one is the complement, which is 60 minus these, the sum of these two values, will give 12. Similarly, for the third cell, I'm sorry, the third row, for this value,", "tokens": [3146, 1228, 264, 912, 3170, 11, 415, 486, 483, 613, 732, 4190, 11, 293, 264, 661, 472, 307, 264, 17103, 11, 597, 307, 4060, 3175, 613, 11, 264, 2408, 295, 613, 732, 4190, 11, 486, 976, 2272, 13, 13157, 11, 337, 264, 2636, 2815, 11, 286, 478, 2597, 11, 264, 2636, 5386, 11, 337, 341, 2158, 11], "avg_logprob": -0.2408405210951279, "compression_ratio": 1.5194805194805194, "no_speech_prob": 0.0, "words": [{"start": 1723.68, "end": 1723.94, "word": " By", "probability": 0.40234375}, {"start": 1723.94, "end": 1724.22, "word": " using", "probability": 0.93359375}, {"start": 1724.22, "end": 1724.44, "word": " the", "probability": 0.892578125}, {"start": 1724.44, "end": 1724.68, "word": " same", "probability": 0.916015625}, {"start": 1724.68, "end": 1725.08, "word": " method,", "probability": 0.88427734375}, {"start": 1726.18, "end": 1726.32, "word": " he", "probability": 0.414306640625}, {"start": 1726.32, "end": 1726.44, "word": " will", "probability": 0.83837890625}, {"start": 1726.44, "end": 1726.64, "word": " get", "probability": 0.9326171875}, {"start": 1726.64, "end": 1727.56, "word": " these", "probability": 0.85498046875}, {"start": 1727.56, "end": 1727.94, "word": " two", "probability": 0.892578125}, {"start": 1727.94, "end": 1729.02, "word": " values,", "probability": 0.96142578125}, {"start": 1729.78, "end": 1730.24, "word": " and", "probability": 0.931640625}, {"start": 1730.24, "end": 1730.36, "word": " the", "probability": 0.8388671875}, {"start": 1730.36, "end": 1730.58, "word": " other", "probability": 0.89794921875}, {"start": 1730.58, "end": 1730.78, "word": " one", "probability": 0.919921875}, {"start": 1730.78, "end": 1730.94, "word": " is", "probability": 0.9482421875}, {"start": 1730.94, "end": 1731.1, "word": " the", "probability": 0.90625}, {"start": 1731.1, "end": 1731.48, "word": " complement,", "probability": 0.79052734375}, {"start": 1731.72, "end": 1731.88, "word": " which", "probability": 0.95068359375}, {"start": 1731.88, "end": 1732.1, "word": " is", "probability": 0.94287109375}, {"start": 1732.1, "end": 1732.54, "word": " 60", "probability": 0.87353515625}, {"start": 1732.54, "end": 1732.96, "word": " minus", "probability": 0.97802734375}, {"start": 1732.96, "end": 1733.4, "word": " these,", "probability": 0.46142578125}, {"start": 1733.6, "end": 1733.76, "word": " the", "probability": 0.88671875}, {"start": 1733.76, "end": 1734.0, "word": " sum", "probability": 0.943359375}, {"start": 1734.0, "end": 1734.16, "word": " of", "probability": 0.96630859375}, {"start": 1734.16, "end": 1734.36, "word": " these", "probability": 0.8525390625}, {"start": 1734.36, "end": 1734.56, "word": " two", "probability": 0.77001953125}, {"start": 1734.56, "end": 1734.88, "word": " values,", "probability": 0.8642578125}, {"start": 1735.3, "end": 1735.44, "word": " will", "probability": 0.84423828125}, {"start": 1735.44, "end": 1735.64, "word": " give", "probability": 0.8935546875}, {"start": 1735.64, "end": 1735.96, "word": " 12.", "probability": 0.78271484375}, {"start": 1738.72, "end": 1739.2, "word": " Similarly,", "probability": 0.462646484375}, {"start": 1739.56, "end": 1739.72, "word": " for", "probability": 0.9306640625}, {"start": 1739.72, "end": 1739.88, "word": " the", "probability": 0.9130859375}, {"start": 1739.88, "end": 1740.18, "word": " third", "probability": 0.9208984375}, {"start": 1740.18, "end": 1740.52, "word": " cell,", "probability": 0.86376953125}, {"start": 1741.12, "end": 1741.3, "word": " I'm", "probability": 0.899169921875}, {"start": 1741.3, "end": 1741.52, "word": " sorry,", "probability": 0.85302734375}, {"start": 1741.74, "end": 1741.92, "word": " the", "probability": 0.56787109375}, {"start": 1741.92, "end": 1742.16, "word": " third", "probability": 0.93994140625}, {"start": 1742.16, "end": 1742.44, "word": " row,", "probability": 0.94189453125}, {"start": 1743.38, "end": 1743.7, "word": " for", "probability": 0.95068359375}, {"start": 1743.7, "end": 1743.92, "word": " this", "probability": 0.94775390625}, {"start": 1743.92, "end": 1744.3, "word": " value,", "probability": 0.97802734375}], "temperature": 1.0}, {"id": 66, "seek": 177330, "start": 1745.72, "end": 1773.3, "text": " For 10, it's 30 times 70 divided by 200 will give this result. And the other one is just 30 multiplied by 88 divided by 200. The other one is just the complement, 30 minus the sum of these. Now, for the last column, either 70 multiplied by 70 divided by 200, or", "tokens": [1171, 1266, 11, 309, 311, 2217, 1413, 5285, 6666, 538, 2331, 486, 976, 341, 1874, 13, 400, 264, 661, 472, 307, 445, 2217, 17207, 538, 24587, 6666, 538, 2331, 13, 440, 661, 472, 307, 445, 264, 17103, 11, 2217, 3175, 264, 2408, 295, 613, 13, 823, 11, 337, 264, 1036, 7738, 11, 2139, 5285, 17207, 538, 5285, 6666, 538, 2331, 11, 420], "avg_logprob": -0.22730654714599488, "compression_ratio": 1.6477987421383649, "no_speech_prob": 0.0, "words": [{"start": 1745.72, "end": 1746.0, "word": " For", "probability": 0.33251953125}, {"start": 1746.0, "end": 1746.26, "word": " 10,", "probability": 0.70458984375}, {"start": 1746.52, "end": 1746.76, "word": " it's", "probability": 0.746337890625}, {"start": 1746.76, "end": 1747.14, "word": " 30", "probability": 0.95361328125}, {"start": 1747.14, "end": 1747.46, "word": " times", "probability": 0.73828125}, {"start": 1747.46, "end": 1748.08, "word": " 70", "probability": 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"end": 1758.64, "word": " just", "probability": 0.919921875}, {"start": 1758.64, "end": 1758.84, "word": " the", "probability": 0.501953125}, {"start": 1758.84, "end": 1759.18, "word": " complement,", "probability": 0.76904296875}, {"start": 1759.86, "end": 1760.2, "word": " 30", "probability": 0.9609375}, {"start": 1760.2, "end": 1760.48, "word": " minus", "probability": 0.986328125}, {"start": 1760.48, "end": 1760.7, "word": " the", "probability": 0.91015625}, {"start": 1760.7, "end": 1760.9, "word": " sum", "probability": 0.9443359375}, {"start": 1760.9, "end": 1761.08, "word": " of", "probability": 0.96826171875}, {"start": 1761.08, "end": 1761.26, "word": " these.", "probability": 0.744140625}, {"start": 1762.96, "end": 1763.6, "word": " Now,", "probability": 0.93359375}, {"start": 1763.66, "end": 1763.8, "word": " for", "probability": 0.9541015625}, {"start": 1763.8, "end": 1764.16, "word": " the", "probability": 0.9189453125}, {"start": 1764.16, "end": 1764.7, "word": " last", "probability": 0.88525390625}, {"start": 1764.7, "end": 1765.18, "word": " column,", "probability": 0.83251953125}, {"start": 1766.66, "end": 1768.3, "word": " either", "probability": 0.93701171875}, {"start": 1768.3, "end": 1770.34, "word": " 70", "probability": 0.9609375}, {"start": 1770.34, "end": 1770.74, "word": " multiplied", "probability": 0.7255859375}, {"start": 1770.74, "end": 1771.04, "word": " by", "probability": 0.97314453125}, {"start": 1771.04, "end": 1771.42, "word": " 70", "probability": 0.95703125}, {"start": 1771.42, "end": 1771.74, "word": " divided", "probability": 0.8369140625}, {"start": 1771.74, "end": 1771.94, "word": " by", "probability": 0.96923828125}, {"start": 1771.94, "end": 1772.32, "word": " 200,", "probability": 0.92529296875}, {"start": 1772.76, "end": 1773.3, "word": " or", "probability": 0.96630859375}], "temperature": 1.0}, {"id": 67, "seek": 180112, "start": 1774.56, "end": 1801.12, "text": " 70 this 70 minus the sum of these. 70 this one equals 70 minus the sum of 24 plus 21 plus 10. That will give 14. 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Now for the last one, last one is either by 42 minus the sum of these three, or 40 minus the sum of 14 plus 6, 17.6. 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For this reason, degrees of freedom is six. The other six are computed by the complement as we mentioned. So these are the expected frequencies. It takes time to compute these.", "tokens": [407, 718, 311, 584, 321, 764, 300, 8513, 2309, 1413, 13, 1171, 341, 1778, 11, 5310, 295, 5645, 307, 2309, 13, 440, 661, 2309, 366, 40610, 538, 264, 17103, 382, 321, 2835, 13, 407, 613, 366, 264, 5176, 20250, 13, 467, 2516, 565, 281, 14722, 613, 13], "avg_logprob": -0.21647135571887097, "compression_ratio": 1.4539473684210527, "no_speech_prob": 0.0, "words": [{"start": 1827.04, "end": 1827.38, "word": " So", "probability": 0.87353515625}, {"start": 1827.38, "end": 1827.94, "word": " let's", "probability": 0.7646484375}, {"start": 1827.94, "end": 1828.14, "word": " say", "probability": 0.57763671875}, {"start": 1828.14, "end": 1828.82, "word": " we", "probability": 0.7265625}, {"start": 1828.82, "end": 1829.26, "word": " use", "probability": 0.673828125}, {"start": 1829.26, "end": 1830.1, "word": " that", "probability": 0.9150390625}, {"start": 1830.1, "end": 1831.24, "word": " formula", "probability": 0.8310546875}, {"start": 1831.24, "end": 1832.28, "word": " six", "probability": 0.71337890625}, {"start": 1832.28, "end": 1832.86, "word": " times.", "probability": 0.92626953125}, {"start": 1834.36, "end": 1834.94, "word": " For", "probability": 0.53515625}, {"start": 1834.94, "end": 1835.18, "word": " this", "probability": 0.89404296875}, {"start": 1835.18, "end": 1835.44, "word": " reason,", "probability": 0.9375}, {"start": 1835.76, "end": 1836.18, "word": " degrees", "probability": 0.61376953125}, {"start": 1836.18, "end": 1836.36, "word": " of", "probability": 0.93505859375}, {"start": 1836.36, "end": 1836.54, "word": " freedom", "probability": 0.94677734375}, {"start": 1836.54, "end": 1836.9, "word": " is", "probability": 0.8115234375}, {"start": 1836.9, "end": 1837.46, "word": " six.", "probability": 0.654296875}, {"start": 1838.04, "end": 1838.3, "word": " The", "probability": 0.89599609375}, {"start": 1838.3, "end": 1838.6, "word": " other", "probability": 0.896484375}, {"start": 1838.6, "end": 1839.1, "word": " six", "probability": 0.92724609375}, {"start": 1839.1, "end": 1841.34, "word": " are", "probability": 0.9189453125}, {"start": 1841.34, "end": 1841.86, "word": " computed", "probability": 0.9384765625}, {"start": 1841.86, "end": 1842.78, "word": " by", "probability": 0.96484375}, {"start": 1842.78, "end": 1843.16, "word": " the", "probability": 0.9091796875}, {"start": 1843.16, "end": 1843.56, "word": " complement", "probability": 0.80078125}, {"start": 1843.56, "end": 1845.36, "word": " as", "probability": 0.53662109375}, {"start": 1845.36, "end": 1845.48, "word": " we", "probability": 0.8603515625}, {"start": 1845.48, "end": 1845.76, "word": " mentioned.", "probability": 0.83349609375}, {"start": 1846.24, "end": 1846.48, "word": " So", "probability": 0.93603515625}, {"start": 1846.48, "end": 1846.96, "word": " these", "probability": 0.7705078125}, {"start": 1846.96, "end": 1847.24, "word": " are", "probability": 0.9404296875}, {"start": 1847.24, "end": 1847.38, "word": " the", "probability": 0.9072265625}, {"start": 1847.38, "end": 1847.86, "word": " expected", "probability": 0.90771484375}, {"start": 1847.86, "end": 1849.0, "word": " frequencies.", "probability": 0.78125}, {"start": 1849.5, "end": 1849.64, "word": " It", "probability": 0.9599609375}, {"start": 1849.64, "end": 1849.9, "word": " takes", "probability": 0.79443359375}, {"start": 1849.9, "end": 1850.24, "word": " time", "probability": 0.8955078125}, {"start": 1850.24, "end": 1850.54, "word": " to", "probability": 0.96923828125}, {"start": 1850.54, "end": 1851.06, "word": " compute", "probability": 0.89404296875}, {"start": 1851.06, "end": 1851.48, "word": " these.", "probability": 0.49462890625}], "temperature": 1.0}, {"id": 70, "seek": 187813, "start": 1853.79, "end": 1878.13, "text": " But if you have only two by two table, it's easier. Now based on that, we can compute chi-square statistic value by using this equation for each cell. I mean, the first one, if you go back a little bit to the previous table, here, in order to compute chi-square,", "tokens": [583, 498, 291, 362, 787, 732, 538, 732, 3199, 11, 309, 311, 3571, 13, 823, 2361, 322, 300, 11, 321, 393, 14722, 13228, 12, 33292, 543, 29588, 2158, 538, 1228, 341, 5367, 337, 1184, 2815, 13, 286, 914, 11, 264, 700, 472, 11, 498, 291, 352, 646, 257, 707, 857, 281, 264, 3894, 3199, 11, 510, 11, 294, 1668, 281, 14722, 13228, 12, 33292, 543, 11], "avg_logprob": -0.2150186571612287, "compression_ratio": 1.5380116959064327, "no_speech_prob": 0.0, "words": [{"start": 1853.7900000000002, "end": 1854.39, "word": " But", "probability": 0.271728515625}, {"start": 1854.39, "end": 1854.89, "word": " if", "probability": 0.8515625}, {"start": 1854.89, "end": 1855.01, "word": " you", "probability": 0.96142578125}, {"start": 1855.01, "end": 1855.21, "word": " have", "probability": 0.9150390625}, {"start": 1855.21, "end": 1855.51, "word": " only", "probability": 0.900390625}, 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But again, for two by two, it's straightforward. Anyway, now if you compare the expected and observed cells, you can have an idea either to reject or fail to reject without computing the value itself. Now, 24, 24.5. 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So the difference between observed and expected looks small. In this case, chi-square value is close to zero. So it's 709. Now, without looking at the table we have, we have to don't reject. 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That's for one degrees of freedom and the alpha is 25%. So I expect my decision is don't reject the null hypothesis. 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Now the minimum value of Chi-square is 7.84. I mean critical value. But under 5% is 12.59. So this value is 12.59.", "tokens": [823, 5310, 295, 5645, 1386, 13, 823, 264, 7285, 2158, 295, 17730, 12, 33292, 543, 307, 1614, 13, 25494, 13, 286, 914, 4924, 2158, 13, 583, 833, 1025, 4, 307, 2272, 13, 19600, 13, 407, 341, 2158, 307, 2272, 13, 19600, 13], "avg_logprob": -0.19531249722769095, "compression_ratio": 1.194915254237288, "no_speech_prob": 0.0, "words": [{"start": 2010.2, "end": 2010.5, "word": " Now", "probability": 0.7607421875}, {"start": 2010.5, "end": 2010.76, "word": " degrees", "probability": 0.859375}, {"start": 2010.76, "end": 2010.96, "word": " of", "probability": 0.951171875}, {"start": 2010.96, "end": 2011.14, "word": " freedom", "probability": 0.935546875}, {"start": 2011.14, "end": 2011.64, "word": " 6.", "probability": 0.447998046875}, {"start": 2014.02, "end": 2014.34, "word": " Now", "probability": 0.88134765625}, {"start": 2014.34, "end": 2014.7, "word": " the", "probability": 0.6748046875}, {"start": 2014.7, "end": 2015.08, "word": " minimum", "probability": 0.96484375}, {"start": 2015.08, "end": 2016.04, "word": " value", "probability": 0.9716796875}, {"start": 2016.04, "end": 2016.26, "word": " of", "probability": 0.96337890625}, {"start": 2016.26, "end": 2016.48, "word": " Chi", "probability": 0.468017578125}, {"start": 2016.48, "end": 2016.86, "word": "-square", "probability": 0.7256673177083334}, {"start": 2016.86, "end": 2017.04, "word": " is", "probability": 0.921875}, {"start": 2017.04, "end": 2017.3, "word": " 7", "probability": 0.97021484375}, {"start": 2017.3, "end": 2018.04, "word": ".84.", "probability": 0.98974609375}, {"start": 2018.46, "end": 2018.64, "word": " I", "probability": 0.94091796875}, {"start": 2018.64, "end": 2018.74, "word": " mean", "probability": 0.95849609375}, {"start": 2018.74, "end": 2019.1, "word": " critical", "probability": 0.83251953125}, {"start": 2019.1, "end": 2019.52, "word": " value.", "probability": 0.97607421875}, {"start": 2020.12, "end": 2020.52, "word": " But", "probability": 0.92236328125}, {"start": 2020.52, "end": 2020.92, "word": " under", "probability": 0.85205078125}, {"start": 2020.92, "end": 2021.32, "word": " 5", "probability": 0.88671875}, {"start": 2021.32, "end": 2021.6, "word": "%", "probability": 0.5576171875}, {"start": 2021.6, "end": 2021.98, "word": " is", "probability": 0.81689453125}, {"start": 2021.98, "end": 2022.4, "word": " 12", "probability": 0.9619140625}, {"start": 2022.4, "end": 2023.38, "word": ".59.", "probability": 0.991943359375}, {"start": 2024.2, "end": 2024.52, "word": " So", "probability": 0.755859375}, {"start": 2024.52, "end": 2024.74, "word": " this", "probability": 0.86474609375}, {"start": 2024.74, "end": 2025.1, "word": " value", "probability": 0.97119140625}, {"start": 2025.1, "end": 2025.28, "word": " is", "probability": 0.93798828125}, {"start": 2025.28, "end": 2025.66, "word": " 12", "probability": 0.9306640625}, {"start": 2025.66, "end": 2026.36, "word": ".59.", "probability": 0.843017578125}], "temperature": 1.0}, {"id": 77, "seek": 205548, "start": 2027.97, "end": 2055.49, "text": " So critical value is 12.59. So my rejection region is above this value. Now, my chi-square value falls in the non-rejection regions. It's very small value. So chi-square statistic is 0.709. It's much smaller.", "tokens": [407, 4924, 2158, 307, 2272, 13, 19600, 13, 407, 452, 26044, 4458, 307, 3673, 341, 2158, 13, 823, 11, 452, 13228, 12, 33292, 543, 2158, 8804, 294, 264, 2107, 12, 265, 1020, 313, 10682, 13, 467, 311, 588, 1359, 2158, 13, 407, 13228, 12, 33292, 543, 29588, 307, 1958, 13, 5867, 24, 13, 467, 311, 709, 4356, 13], "avg_logprob": -0.17677435784016626, "compression_ratio": 1.4413793103448276, "no_speech_prob": 0.0, "words": [{"start": 2027.97, "end": 2028.29, "word": " So", "probability": 0.693359375}, {"start": 2028.29, "end": 2028.69, "word": " critical", "probability": 0.7138671875}, {"start": 2028.69, "end": 2029.17, "word": " value", "probability": 0.97265625}, {"start": 2029.17, "end": 2030.29, "word": " is", "probability": 0.8740234375}, {"start": 2030.29, "end": 2030.71, "word": " 12", "probability": 0.89697265625}, {"start": 2030.71, "end": 2031.71, "word": ".59.", "probability": 0.964111328125}, {"start": 2032.13, "end": 2032.85, "word": " So", 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So conclusion, there is not sufficient evidence that Mealy Plan, which was classified into three groups, 20 per week or 10 per week or none, and class standing.", "tokens": [407, 452, 3537, 307, 11, 500, 380, 8248, 264, 18184, 17291, 13, 407, 10063, 11, 456, 307, 406, 11563, 4467, 300, 1923, 5222, 8112, 11, 597, 390, 20627, 666, 1045, 3935, 11, 945, 680, 1243, 420, 1266, 680, 1243, 420, 6022, 11, 293, 1508, 4877, 13], "avg_logprob": -0.17785904572365133, "compression_ratio": 1.3986928104575163, "no_speech_prob": 0.0, "words": [{"start": 2069.11, "end": 2069.47, "word": " So", "probability": 0.84326171875}, {"start": 2069.47, "end": 2069.67, "word": " my", "probability": 0.76171875}, {"start": 2069.67, "end": 2070.07, "word": " decision", "probability": 0.93896484375}, {"start": 2070.07, "end": 2070.59, "word": " is,", "probability": 0.94140625}, {"start": 2071.77, "end": 2072.01, "word": " don't", "probability": 0.9111328125}, {"start": 2072.01, "end": 2072.53, "word": " reject", "probability": 0.9140625}, {"start": 2072.53, "end": 2073.17, "word": " the", "probability": 0.888671875}, {"start": 2073.17, "end": 2073.33, "word": " null", "probability": 0.93115234375}, {"start": 2073.33, "end": 2073.85, "word": " hypothesis.", "probability": 0.849609375}, {"start": 2074.77, "end": 2074.89, "word": " So", "probability": 0.88720703125}, {"start": 2074.89, "end": 2075.41, "word": " conclusion,", "probability": 0.74560546875}, {"start": 2076.17, "end": 2076.35, "word": " there", "probability": 0.90234375}, {"start": 2076.35, "end": 2076.51, "word": " is", "probability": 0.9267578125}, {"start": 2076.51, "end": 2076.69, "word": " not", "probability": 0.9345703125}, {"start": 2076.69, "end": 2077.17, "word": " sufficient", "probability": 0.90380859375}, {"start": 2077.17, "end": 2077.59, "word": " evidence", "probability": 0.955078125}, {"start": 2077.59, "end": 2078.27, "word": " that", "probability": 0.9306640625}, {"start": 2078.27, "end": 2079.63, "word": " Mealy", "probability": 0.688232421875}, {"start": 2079.63, "end": 2079.99, "word": " Plan,", "probability": 0.69482421875}, {"start": 2080.69, "end": 2081.15, "word": " which", "probability": 0.9501953125}, {"start": 2081.15, "end": 2081.41, "word": " was", "probability": 0.95458984375}, {"start": 2081.41, "end": 2081.87, "word": " classified", "probability": 0.9384765625}, {"start": 2081.87, "end": 2082.27, "word": " into", "probability": 0.84619140625}, {"start": 2082.27, "end": 2082.57, "word": " three", "probability": 0.87841796875}, {"start": 2082.57, "end": 2083.05, "word": " groups,", "probability": 0.9404296875}, {"start": 2083.77, "end": 2084.17, "word": " 20", "probability": 0.54248046875}, {"start": 2084.17, "end": 2084.43, "word": " per", "probability": 0.7861328125}, {"start": 2084.43, "end": 2084.75, "word": " week", "probability": 0.96240234375}, {"start": 2084.75, "end": 2085.31, "word": " or", "probability": 0.69287109375}, {"start": 2085.31, "end": 2085.65, "word": " 10", "probability": 0.92138671875}, {"start": 2085.65, "end": 2086.09, "word": " per", "probability": 0.93017578125}, {"start": 2086.09, "end": 2086.31, "word": " week", "probability": 0.94921875}, {"start": 2086.31, "end": 2086.55, "word": " or", "probability": 0.91796875}, {"start": 2086.55, "end": 2086.79, "word": " none,", "probability": 0.86376953125}, {"start": 2087.59, "end": 2087.89, "word": " and", "probability": 0.92724609375}, {"start": 2087.89, "end": 2088.27, "word": " class", "probability": 0.8076171875}, {"start": 2088.27, "end": 2088.79, "word": " standing.", "probability": 0.8095703125}], "temperature": 1.0}, {"id": 80, "seek": 211359, "start": 2089.65, "end": 2113.59, "text": " which is classified into four groups, freshman, sophomore, junior, and senior are related. So you don't have sufficient evidence that they are related. It means they are independent. So the two variables in this case are independent.", "tokens": [597, 307, 20627, 666, 1451, 3935, 11, 22154, 11, 35798, 11, 16195, 11, 293, 7965, 366, 4077, 13, 407, 291, 500, 380, 362, 11563, 4467, 300, 436, 366, 4077, 13, 467, 1355, 436, 366, 6695, 13, 407, 264, 732, 9102, 294, 341, 1389, 366, 6695, 13], "avg_logprob": -0.20611702317887165, "compression_ratio": 1.5294117647058822, "no_speech_prob": 0.0, "words": [{"start": 2089.65, "end": 2090.05, "word": " which", "probability": 0.2379150390625}, {"start": 2090.05, "end": 2090.31, "word": " is", "probability": 0.84228515625}, {"start": 2090.31, "end": 2090.77, "word": " classified", "probability": 0.958984375}, {"start": 2090.77, "end": 2091.11, "word": " into", "probability": 0.83642578125}, {"start": 2091.11, "end": 2091.57, "word": " four", "probability": 0.83203125}, {"start": 2091.57, "end": 2092.29, "word": " groups,", "probability": 0.94140625}, {"start": 2093.29, "end": 2093.81, "word": " freshman,", "probability": 0.29443359375}, {"start": 2094.45, "end": 2094.75, "word": " sophomore,", "probability": 0.765625}, {"start": 2095.01, "end": 2095.25, "word": " junior,", "probability": 0.96728515625}, {"start": 2095.49, "end": 2095.69, "word": " and", "probability": 0.9365234375}, {"start": 2095.69, "end": 2095.99, "word": " senior", "probability": 0.93310546875}, {"start": 2095.99, "end": 2096.73, "word": " are", "probability": 0.51171875}, {"start": 2096.73, "end": 2097.27, "word": " related.", "probability": 0.966796875}, {"start": 2097.39, "end": 2097.51, "word": " So", "probability": 0.94384765625}, {"start": 2097.51, "end": 2097.65, "word": " you", "probability": 0.68505859375}, {"start": 2097.65, "end": 2097.81, "word": " don't", "probability": 0.971435546875}, {"start": 2097.81, "end": 2098.03, "word": " have", "probability": 0.94287109375}, {"start": 2098.03, "end": 2098.45, "word": " sufficient", "probability": 0.93505859375}, {"start": 2098.45, "end": 2098.89, "word": " evidence", "probability": 0.953125}, {"start": 2098.89, "end": 2099.53, "word": " that", "probability": 0.9296875}, {"start": 2099.53, "end": 2099.75, "word": " they", "probability": 0.8896484375}, {"start": 2099.75, "end": 2099.97, "word": " are", "probability": 0.93994140625}, {"start": 2099.97, "end": 2100.49, "word": " related.", "probability": 0.97119140625}, {"start": 2100.59, "end": 2100.69, "word": " It", "probability": 0.90576171875}, {"start": 2100.69, "end": 2100.93, "word": " means", "probability": 0.93359375}, {"start": 2100.93, "end": 2101.15, "word": " they", "probability": 0.8623046875}, {"start": 2101.15, "end": 2101.55, "word": " are", "probability": 0.94140625}, {"start": 2101.55, "end": 2102.73, "word": " independent.", "probability": 0.90869140625}, {"start": 2103.55, "end": 2104.11, "word": " So", "probability": 0.95361328125}, {"start": 2104.11, "end": 2104.73, "word": " the", "probability": 0.7783203125}, {"start": 2104.73, "end": 2104.97, "word": " two", "probability": 0.87353515625}, {"start": 2104.97, "end": 2105.63, "word": " variables", "probability": 0.9453125}, {"start": 2105.63, "end": 2108.59, "word": " in", "probability": 0.5576171875}, {"start": 2108.59, "end": 2108.87, "word": " this", "probability": 0.9462890625}, {"start": 2108.87, "end": 2109.41, "word": " case", "probability": 0.90087890625}, {"start": 2109.41, "end": 2112.19, "word": " are", "probability": 0.908203125}, {"start": 2112.19, "end": 2113.59, "word": " independent.", "probability": 0.88330078125}], "temperature": 1.0}, {"id": 81, "seek": 214726, "start": 2118.42, "end": 2147.26, "text": " It means there is no relationship between number of meals and class standing. It means the proportions are equal. So this means pi 1 equals pi 2 equals pi 3. So the three proportions are equal. Pi 1 for 20 meals per week is the same as 10 or none according to class standing. Any question?", "tokens": [467, 1355, 456, 307, 572, 2480, 1296, 1230, 295, 12832, 293, 1508, 4877, 13, 467, 1355, 264, 32482, 366, 2681, 13, 407, 341, 1355, 3895, 502, 6915, 3895, 568, 6915, 3895, 805, 13, 407, 264, 1045, 32482, 366, 2681, 13, 17741, 502, 337, 945, 12832, 680, 1243, 307, 264, 912, 382, 1266, 420, 6022, 4650, 281, 1508, 4877, 13, 2639, 1168, 30], "avg_logprob": -0.14880952854005117, "compression_ratio": 1.7159763313609468, "no_speech_prob": 0.0, "words": [{"start": 2118.42, "end": 2118.66, "word": " It", "probability": 0.75341796875}, {"start": 2118.66, "end": 2118.92, "word": " means", "probability": 0.921875}, {"start": 2118.92, "end": 2119.12, "word": " there", "probability": 0.8447265625}, {"start": 2119.12, "end": 2119.32, "word": " is", "probability": 0.9267578125}, {"start": 2119.32, "end": 2119.56, "word": " no", "probability": 0.94775390625}, {"start": 2119.56, "end": 2120.12, "word": " relationship", "probability": 0.90673828125}, {"start": 2120.12, "end": 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{"start": 2146.96, "end": 2147.26, "word": " question?", "probability": 0.57763671875}], "temperature": 1.0}, {"id": 82, "seek": 216988, "start": 2148.88, "end": 2169.88, "text": " I think it's straightforward test, maybe even easier than using a T statistic. And that's all for this chapter. Any questions? I will do some practice problems for chapter 11.", "tokens": [286, 519, 309, 311, 15325, 1500, 11, 1310, 754, 3571, 813, 1228, 257, 314, 29588, 13, 400, 300, 311, 439, 337, 341, 7187, 13, 2639, 1651, 30, 286, 486, 360, 512, 3124, 2740, 337, 7187, 2975, 13], "avg_logprob": -0.21504933543895421, "compression_ratio": 1.3037037037037038, "no_speech_prob": 0.0, "words": [{"start": 2148.88, "end": 2149.12, "word": " I", "probability": 0.94140625}, {"start": 2149.12, "end": 2149.3, "word": " think", "probability": 0.912109375}, {"start": 2149.3, "end": 2149.48, "word": " it's", "probability": 0.6895751953125}, {"start": 2149.48, "end": 2150.04, "word": " straightforward", "probability": 0.77197265625}, {"start": 2150.04, "end": 2151.66, "word": " test,", "probability": 0.6142578125}, {"start": 2152.36, "end": 2152.6, "word": " maybe", "probability": 0.90380859375}, {"start": 2152.6, "end": 2153.3, "word": " even", "probability": 0.765625}, {"start": 2153.3, "end": 2153.82, "word": " easier", "probability": 0.98388671875}, {"start": 2153.82, "end": 2154.26, "word": " than", "probability": 0.9375}, {"start": 2154.26, "end": 2155.66, "word": " using", "probability": 0.91162109375}, {"start": 2155.66, "end": 2156.34, "word": " a", "probability": 0.5400390625}, {"start": 2156.34, "end": 2156.6, "word": " T", "probability": 0.54052734375}, {"start": 2156.6, "end": 2157.72, "word": " statistic.", "probability": 0.8525390625}, {"start": 2158.62, "end": 2158.74, "word": " And", "probability": 0.86474609375}, {"start": 2158.74, "end": 2159.14, "word": " that's", "probability": 0.964599609375}, {"start": 2159.14, "end": 2159.6, "word": " all", "probability": 0.953125}, {"start": 2159.6, "end": 2160.56, "word": " for", "probability": 0.94384765625}, {"start": 2160.56, "end": 2161.3, "word": " this", "probability": 0.9326171875}, {"start": 2161.3, "end": 2161.72, "word": " chapter.", "probability": 0.9013671875}, {"start": 2162.78, "end": 2163.16, "word": " Any", "probability": 0.9072265625}, {"start": 2163.16, "end": 2163.44, "word": " questions?", "probability": 0.5234375}, {"start": 2164.46, "end": 2165.5, "word": " I", "probability": 0.9765625}, {"start": 2165.5, "end": 2165.66, "word": " will", "probability": 0.8896484375}, {"start": 2165.66, "end": 2165.84, "word": " do", "probability": 0.9580078125}, {"start": 2165.84, "end": 2166.26, "word": " some", "probability": 0.9111328125}, {"start": 2166.26, "end": 2167.4, "word": " practice", "probability": 0.9248046875}, {"start": 2167.4, "end": 2168.42, "word": " problems", "probability": 0.876953125}, {"start": 2168.42, "end": 2168.92, "word": " for", "probability": 0.94482421875}, {"start": 2168.92, "end": 2169.34, "word": " chapter", "probability": 0.62255859375}, {"start": 2169.34, "end": 2169.88, "word": " 11.", "probability": 0.7646484375}], "temperature": 1.0}, {"id": 83, "seek": 219169, "start": 2171.76, "end": 2191.7, "text": " These problems will be posted in the course website this week, sometime this week, maybe tomorrow or after tomorrow. So Monday or Tuesday I'm going to post the practice problems and solutions for chapter 11. So let's do some of these problems.", "tokens": [1981, 2740, 486, 312, 9437, 294, 264, 1164, 3144, 341, 1243, 11, 15053, 341, 1243, 11, 1310, 4153, 420, 934, 4153, 13, 407, 8138, 420, 10017, 286, 478, 516, 281, 2183, 264, 3124, 2740, 293, 6547, 337, 7187, 2975, 13, 407, 718, 311, 360, 512, 295, 613, 2740, 13], "avg_logprob": -0.1859375062584877, "compression_ratio": 1.525, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2171.76, "end": 2172.36, "word": " These", "probability": 0.52978515625}, {"start": 2172.36, "end": 2172.78, "word": " problems", "probability": 0.83251953125}, {"start": 2172.78, "end": 2173.0, "word": " will", "probability": 0.8857421875}, {"start": 2173.0, "end": 2173.14, "word": " be", "probability": 0.90478515625}, {"start": 2173.14, "end": 2173.48, "word": " posted", "probability": 0.93994140625}, {"start": 2173.48, "end": 2173.72, "word": " in", "probability": 0.6533203125}, {"start": 2173.72, "end": 2173.86, "word": " the", "probability": 0.8857421875}, {"start": 2173.86, "end": 2174.08, "word": " course", "probability": 0.96728515625}, {"start": 2174.08, "end": 2174.58, "word": " website", "probability": 0.87841796875}, {"start": 2174.58, "end": 2176.16, "word": " this", "probability": 0.56396484375}, {"start": 2176.16, "end": 2176.48, "word": " week,", "probability": 0.9267578125}, {"start": 2176.6, "end": 2176.88, "word": " sometime", "probability": 0.92578125}, {"start": 2176.88, "end": 2177.24, "word": " this", "probability": 0.9375}, {"start": 2177.24, "end": 2177.48, "word": " week,", "probability": 0.93896484375}, {"start": 2177.62, "end": 2177.76, "word": " maybe", "probability": 0.9208984375}, {"start": 2177.76, "end": 2178.3, "word": " tomorrow", "probability": 0.87109375}, {"start": 2178.3, "end": 2178.88, "word": " or", "probability": 0.86865234375}, {"start": 2178.88, "end": 2179.22, "word": " after", "probability": 0.78515625}, {"start": 2179.22, "end": 2179.66, "word": " tomorrow.", "probability": 0.904296875}, {"start": 2180.38, "end": 2180.6, "word": " So", "probability": 0.87890625}, {"start": 2180.6, "end": 2180.96, "word": " Monday", "probability": 0.67138671875}, {"start": 2180.96, "end": 2181.32, "word": " or", "probability": 0.93408203125}, {"start": 2181.32, "end": 2181.68, "word": " Tuesday", "probability": 0.8798828125}, {"start": 2181.68, "end": 2181.98, "word": " I'm", "probability": 0.7529296875}, {"start": 2181.98, "end": 2182.22, "word": " going", "probability": 0.9453125}, {"start": 2182.22, "end": 2182.42, "word": " to", "probability": 0.96337890625}, {"start": 2182.42, "end": 2182.84, "word": " post", "probability": 0.8984375}, {"start": 2182.84, "end": 2184.34, "word": " the", "probability": 0.89306640625}, {"start": 2184.34, "end": 2184.96, "word": " practice", "probability": 0.92578125}, {"start": 2184.96, "end": 2185.56, "word": " problems", "probability": 0.83642578125}, {"start": 2185.56, "end": 2185.92, "word": " and", "probability": 0.93994140625}, {"start": 2185.92, "end": 2186.58, "word": " solutions", "probability": 0.9345703125}, {"start": 2186.58, "end": 2186.92, "word": " for", "probability": 0.939453125}, {"start": 2186.92, "end": 2187.28, "word": " chapter", "probability": 0.4912109375}, {"start": 2187.28, "end": 2187.7, "word": " 11.", "probability": 0.7548828125}, {"start": 2188.58, "end": 2188.84, "word": " So", "probability": 0.953125}, {"start": 2188.84, "end": 2189.1, "word": " let's", "probability": 0.947021484375}, {"start": 2189.1, "end": 2189.26, "word": " do", "probability": 0.92626953125}, {"start": 2189.26, "end": 2189.64, "word": " some", "probability": 0.90673828125}, {"start": 2189.64, "end": 2190.1, "word": " of", "probability": 0.96826171875}, {"start": 2190.1, "end": 2190.54, "word": " these", "probability": 0.83203125}, {"start": 2190.54, "end": 2191.7, "word": " problems.", "probability": 0.8251953125}], "temperature": 1.0}, {"id": 84, "seek": 222564, "start": 2200.16, "end": 2225.64, "text": " Let's do some of multiple choice problems. When testing for independence in contingency table with three rows and four columns.", "tokens": [961, 311, 360, 512, 295, 3866, 3922, 2740, 13, 1133, 4997, 337, 14640, 294, 27820, 3020, 3199, 365, 1045, 13241, 293, 1451, 13766, 13], "avg_logprob": -0.18078124523162842, "compression_ratio": 1.2190476190476192, "no_speech_prob": 0.0, "words": [{"start": 2200.16, "end": 2201.04, "word": " Let's", "probability": 0.890380859375}, {"start": 2201.04, "end": 2201.34, "word": " do", "probability": 0.95556640625}, {"start": 2201.34, "end": 2201.74, "word": " some", "probability": 0.8935546875}, {"start": 2201.74, "end": 2202.1, "word": " of", "probability": 0.449951171875}, {"start": 2202.1, "end": 2202.46, "word": " multiple", "probability": 0.90283203125}, {"start": 2202.46, "end": 2202.84, "word": " choice", "probability": 0.64208984375}, {"start": 2202.84, "end": 2203.26, "word": " problems.", "probability": 0.8369140625}, {"start": 2215.0, "end": 2215.88, "word": " When", "probability": 0.875}, {"start": 2215.88, "end": 2216.24, "word": " testing", "probability": 0.88623046875}, {"start": 2216.24, "end": 2216.7, "word": " for", "probability": 0.90625}, {"start": 2216.7, "end": 2217.3, "word": " independence", "probability": 0.79150390625}, {"start": 2217.3, "end": 2218.4, "word": " in", "probability": 0.7705078125}, {"start": 2218.4, "end": 2219.08, "word": " contingency", "probability": 0.843994140625}, {"start": 2219.08, "end": 2219.42, "word": " table", "probability": 0.8125}, {"start": 2219.42, "end": 2219.64, "word": " with", "probability": 0.8603515625}, {"start": 2219.64, "end": 2219.9, "word": " three", "probability": 0.8125}, {"start": 2219.9, "end": 2220.36, "word": " rows", "probability": 0.8759765625}, {"start": 2220.36, "end": 2223.84, "word": " and", "probability": 0.72509765625}, {"start": 2223.84, "end": 2225.22, "word": " four", "probability": 0.95068359375}, {"start": 2225.22, "end": 2225.64, "word": " columns.", "probability": 0.9521484375}], "temperature": 1.0}, {"id": 85, "seek": 225213, "start": 2227.73, "end": 2252.13, "text": " So there are three rows, four columns. There are degrees of freedom. So degrees of freedom. R minus one multiplied by C minus one. Two times three is six. So there are six degrees of freedom. Second question.", "tokens": [407, 456, 366, 1045, 13241, 11, 1451, 13766, 13, 821, 366, 5310, 295, 5645, 13, 407, 5310, 295, 5645, 13, 497, 3175, 472, 17207, 538, 383, 3175, 472, 13, 4453, 1413, 1045, 307, 2309, 13, 407, 456, 366, 2309, 5310, 295, 5645, 13, 5736, 1168, 13], "avg_logprob": -0.19082446998738228, "compression_ratio": 1.6587301587301588, "no_speech_prob": 0.0, "words": [{"start": 2227.73, "end": 2227.97, "word": " So", "probability": 0.6845703125}, {"start": 2227.97, "end": 2228.17, "word": " there", "probability": 0.69873046875}, {"start": 2228.17, "end": 2228.35, "word": " are", "probability": 0.93505859375}, {"start": 2228.35, "end": 2228.87, "word": " three", "probability": 0.65478515625}, {"start": 2228.87, "end": 2229.81, "word": " rows,", "probability": 0.91064453125}, {"start": 2230.05, "end": 2230.25, "word": " four", "probability": 0.92333984375}, {"start": 2230.25, "end": 2230.71, "word": " columns.", "probability": 0.931640625}, {"start": 2231.89, "end": 2232.45, "word": " There", "probability": 0.71484375}, {"start": 2232.45, "end": 2233.73, "word": " are", "probability": 0.9462890625}, {"start": 2233.73, "end": 2235.43, "word": " degrees", "probability": 0.89599609375}, {"start": 2235.43, "end": 2235.63, "word": " of", "probability": 0.9619140625}, {"start": 2235.63, "end": 2235.89, "word": " freedom.", "probability": 0.93017578125}, {"start": 2237.09, "end": 2237.79, "word": " So", "probability": 0.583984375}, {"start": 2237.79, "end": 2238.15, "word": " degrees", "probability": 0.8583984375}, {"start": 2238.15, "end": 2238.39, "word": " of", "probability": 0.966796875}, {"start": 2238.39, "end": 2238.71, "word": " freedom.", "probability": 0.9296875}, {"start": 2239.77, "end": 2240.47, "word": " R", "probability": 0.8271484375}, {"start": 2240.47, "end": 2240.77, "word": " minus", "probability": 0.90771484375}, {"start": 2240.77, "end": 2241.11, "word": " one", "probability": 0.5693359375}, {"start": 2241.11, "end": 2242.13, "word": " multiplied", "probability": 0.57275390625}, {"start": 2242.13, "end": 2242.49, "word": " by", "probability": 0.9716796875}, {"start": 2242.49, "end": 2242.69, "word": " C", "probability": 0.646484375}, {"start": 2242.69, "end": 2243.01, "word": " minus", "probability": 0.98486328125}, {"start": 2243.01, "end": 2243.31, "word": " one.", "probability": 0.92626953125}, {"start": 2244.09, "end": 2244.43, "word": " Two", "probability": 0.54736328125}, {"start": 2244.43, "end": 2244.87, "word": " times", "probability": 0.9189453125}, {"start": 2244.87, "end": 2245.47, "word": " three", "probability": 0.91943359375}, {"start": 2245.47, "end": 2246.33, "word": " is", "probability": 0.8955078125}, {"start": 2246.33, "end": 2246.59, "word": " six.", "probability": 0.9404296875}, {"start": 2246.91, "end": 2247.19, "word": " So", "probability": 0.9482421875}, {"start": 2247.19, "end": 2247.37, "word": " there", "probability": 0.8974609375}, {"start": 2247.37, "end": 2247.57, "word": " are", "probability": 0.93896484375}, {"start": 2247.57, "end": 2247.99, "word": " six", "probability": 0.93359375}, {"start": 2247.99, "end": 2248.63, "word": " degrees", "probability": 0.939453125}, {"start": 2248.63, "end": 2249.45, "word": " of", "probability": 0.96630859375}, {"start": 2249.45, "end": 2249.93, "word": " freedom.", "probability": 0.94140625}, {"start": 2251.25, "end": 2251.71, "word": " Second", "probability": 0.79443359375}, {"start": 2251.71, "end": 2252.13, "word": " question.", "probability": 0.90283203125}], "temperature": 1.0}, {"id": 86, "seek": 227489, "start": 2256.71, "end": 2274.89, "text": " If we wish to determine whether there is evidence that the proportion of items of interest is the same in group 1 as in group 2, the appropriate test to use is. So here we are testing", "tokens": [759, 321, 3172, 281, 6997, 1968, 456, 307, 4467, 300, 264, 16068, 295, 4754, 295, 1179, 307, 264, 912, 294, 1594, 502, 382, 294, 1594, 568, 11, 264, 6854, 1500, 281, 764, 307, 13, 407, 510, 321, 366, 4997], "avg_logprob": -0.16474608778953553, "compression_ratio": 1.4488188976377954, "no_speech_prob": 0.0, "words": [{"start": 2256.71, "end": 2257.05, "word": " If", "probability": 0.76220703125}, {"start": 2257.05, "end": 2257.23, "word": " we", "probability": 0.955078125}, {"start": 2257.23, "end": 2257.67, "word": " wish", "probability": 0.88525390625}, {"start": 2257.67, "end": 2259.73, "word": " to", "probability": 0.939453125}, {"start": 2259.73, "end": 2260.33, "word": " determine", "probability": 0.9150390625}, {"start": 2260.33, "end": 2261.85, "word": " whether", "probability": 0.91943359375}, {"start": 2261.85, "end": 2262.21, "word": " there", "probability": 0.9169921875}, {"start": 2262.21, "end": 2262.47, "word": " is", "probability": 0.93017578125}, {"start": 2262.47, "end": 2263.15, "word": " evidence", "probability": 0.95361328125}, {"start": 2263.15, "end": 2263.65, "word": " that", "probability": 0.9248046875}, {"start": 2263.65, "end": 2263.85, "word": " the", "probability": 0.89208984375}, {"start": 2263.85, "end": 2264.29, "word": " proportion", "probability": 0.8388671875}, {"start": 2264.29, "end": 2264.53, "word": " of", "probability": 0.970703125}, {"start": 2264.53, "end": 2265.03, "word": " items", "probability": 0.78271484375}, {"start": 2265.03, "end": 2265.27, "word": " of", "probability": 0.96826171875}, {"start": 2265.27, "end": 2265.81, "word": " interest", "probability": 0.90087890625}, {"start": 2265.81, "end": 2266.67, "word": " is", "probability": 0.90283203125}, {"start": 2266.67, "end": 2266.89, "word": " the", "probability": 0.9228515625}, {"start": 2266.89, "end": 2267.17, "word": " same", "probability": 0.9130859375}, {"start": 2267.17, "end": 2267.29, "word": " in", "probability": 0.9326171875}, {"start": 2267.29, "end": 2267.55, "word": " group", "probability": 0.6328125}, {"start": 2267.55, "end": 2268.09, "word": " 1", "probability": 0.568359375}, {"start": 2268.09, "end": 2269.15, "word": " as", "probability": 0.9267578125}, {"start": 2269.15, "end": 2269.31, "word": " in", "probability": 0.8369140625}, {"start": 2269.31, "end": 2269.67, "word": " group", "probability": 0.9345703125}, {"start": 2269.67, "end": 2270.09, "word": " 2,", "probability": 0.98681640625}, {"start": 2270.95, "end": 2271.07, "word": " the", "probability": 0.87548828125}, {"start": 2271.07, "end": 2271.51, "word": " appropriate", "probability": 0.7890625}, {"start": 2271.51, "end": 2271.95, "word": " test", "probability": 0.84228515625}, {"start": 2271.95, "end": 2272.21, "word": " to", "probability": 0.95654296875}, {"start": 2272.21, "end": 2272.45, "word": " use", "probability": 0.8671875}, {"start": 2272.45, "end": 2272.75, "word": " is.", "probability": 0.92822265625}, {"start": 2273.31, "end": 2273.61, "word": " So", "probability": 0.93212890625}, {"start": 2273.61, "end": 2273.83, "word": " here", "probability": 0.6611328125}, {"start": 2273.83, "end": 2274.05, "word": " we", "probability": 0.734375}, {"start": 2274.05, "end": 2274.25, "word": " are", "probability": 0.9345703125}, {"start": 2274.25, "end": 2274.89, "word": " testing", "probability": 0.87109375}], "temperature": 1.0}, {"id": 87, "seek": 230376, "start": 2276.74, "end": 2303.76, "text": " Pi 1 equals Pi 2, so there are two populations. The answer is A. Z statistic, Z test, Chi squared, both A and B, neither A, neither of A nor B. Exactly, the answer is C because we can use either Z statistic or Chi squared. So Z or Chi.", "tokens": [17741, 502, 6915, 17741, 568, 11, 370, 456, 366, 732, 12822, 13, 440, 1867, 307, 316, 13, 1176, 29588, 11, 1176, 1500, 11, 17730, 8889, 11, 1293, 316, 293, 363, 11, 9662, 316, 11, 9662, 295, 316, 6051, 363, 13, 7587, 11, 264, 1867, 307, 383, 570, 321, 393, 764, 2139, 1176, 29588, 420, 17730, 8889, 13, 407, 1176, 420, 17730, 13], "avg_logprob": -0.29786706538427443, "compression_ratio": 1.5128205128205128, "no_speech_prob": 0.0, "words": [{"start": 2276.74, "end": 2277.0, "word": " Pi", "probability": 0.5556640625}, {"start": 2277.0, "end": 2277.28, "word": " 1", "probability": 0.63720703125}, {"start": 2277.28, "end": 2277.7, "word": " equals", "probability": 0.8193359375}, {"start": 2277.7, "end": 2277.92, "word": " Pi", "probability": 0.41552734375}, {"start": 2277.92, "end": 2278.16, "word": " 2,", "probability": 0.9873046875}, {"start": 2278.3, "end": 2278.44, "word": " so", "probability": 0.89453125}, {"start": 2278.44, "end": 2278.58, "word": " there", "probability": 0.5908203125}, {"start": 2278.58, "end": 2278.76, "word": " are", "probability": 0.93701171875}, {"start": 2278.76, "end": 2279.12, "word": " two", "probability": 0.87451171875}, {"start": 2279.12, "end": 2281.04, "word": " populations.", "probability": 0.20166015625}, {"start": 2282.48, "end": 2282.74, "word": " The", "probability": 0.4208984375}, {"start": 2282.74, "end": 2283.68, "word": " answer", "probability": 0.9658203125}, {"start": 2283.68, "end": 2284.84, "word": " is", "probability": 0.462890625}, {"start": 2284.84, "end": 2285.12, "word": " A.", "probability": 0.77490234375}, {"start": 2285.56, "end": 2285.76, "word": " Z", "probability": 0.465087890625}, {"start": 2285.76, "end": 2286.3, "word": " statistic,", "probability": 0.442626953125}, {"start": 2286.52, "end": 2286.66, "word": " Z", "probability": 0.5283203125}, {"start": 2286.66, "end": 2287.1, "word": " test,", "probability": 0.85400390625}, {"start": 2288.04, "end": 2288.24, "word": " Chi", "probability": 0.716796875}, {"start": 2288.24, "end": 2288.72, "word": " squared,", "probability": 0.51025390625}, {"start": 2289.74, "end": 2290.34, "word": " both", "probability": 0.84326171875}, {"start": 2290.34, "end": 2290.52, "word": " A", "probability": 0.9638671875}, {"start": 2290.52, "end": 2290.7, "word": " and", "probability": 0.94580078125}, {"start": 2290.7, "end": 2290.92, "word": " B,", "probability": 0.9970703125}, {"start": 2291.2, "end": 2291.46, "word": " neither", "probability": 0.9384765625}, {"start": 2291.46, "end": 2291.96, "word": " A,", "probability": 0.59375}, {"start": 2292.28, "end": 2292.62, "word": " neither", "probability": 0.91748046875}, {"start": 2292.62, "end": 2292.84, "word": " of", "probability": 0.9326171875}, {"start": 2292.84, "end": 2293.1, "word": " A", "probability": 0.9794921875}, {"start": 2293.1, "end": 2293.44, "word": " nor", "probability": 0.84130859375}, {"start": 2293.44, "end": 2293.84, "word": " B.", "probability": 0.923828125}, {"start": 2296.32, "end": 2296.86, "word": " Exactly,", "probability": 0.568359375}, {"start": 2297.04, "end": 2297.14, "word": " the", "probability": 0.9169921875}, {"start": 2297.14, "end": 2297.38, "word": " answer", "probability": 0.96240234375}, {"start": 2297.38, "end": 2297.6, "word": " is", "probability": 0.9482421875}, {"start": 2297.6, "end": 2297.74, "word": " C", "probability": 0.96337890625}, {"start": 2297.74, "end": 2298.16, "word": " because", "probability": 0.49365234375}, {"start": 2298.16, "end": 2298.66, "word": " we", "probability": 0.94189453125}, {"start": 2298.66, "end": 2298.94, "word": " can", "probability": 0.9453125}, {"start": 2298.94, "end": 2299.2, "word": " use", "probability": 0.82958984375}, {"start": 2299.2, "end": 2299.54, "word": " either", "probability": 0.94287109375}, {"start": 2299.54, "end": 2299.86, "word": " Z", "probability": 0.89111328125}, {"start": 2299.86, "end": 2300.4, "word": " statistic", "probability": 0.8935546875}, {"start": 2300.4, "end": 2300.82, "word": " or", "probability": 0.94970703125}, {"start": 2300.82, "end": 2301.12, "word": " Chi", "probability": 0.7041015625}, {"start": 2301.12, "end": 2301.48, "word": " squared.", "probability": 0.83837890625}, {"start": 2302.66, "end": 2302.92, "word": " So", "probability": 0.9326171875}, {"start": 2302.92, "end": 2303.16, "word": " Z", "probability": 0.64990234375}, {"start": 2303.16, "end": 2303.48, "word": " or", "probability": 0.9755859375}, {"start": 2303.48, "end": 2303.76, "word": " Chi.", "probability": 0.650390625}], "temperature": 1.0}, {"id": 88, "seek": 233038, "start": 2304.58, "end": 2330.38, "text": " can be used for testing difference between two population proportions. And again, chi-square can be extended to use for more than two. So in this case, the correct answer is C, because we can use either Z or chi-square test. Next, in testing,", "tokens": [393, 312, 1143, 337, 4997, 2649, 1296, 732, 4415, 32482, 13, 400, 797, 11, 13228, 12, 33292, 543, 393, 312, 10913, 281, 764, 337, 544, 813, 732, 13, 407, 294, 341, 1389, 11, 264, 3006, 1867, 307, 383, 11, 570, 321, 393, 764, 2139, 1176, 420, 13228, 12, 33292, 543, 1500, 13, 3087, 11, 294, 4997, 11], "avg_logprob": -0.2237338320962314, "compression_ratio": 1.5093167701863355, "no_speech_prob": 0.0, "words": [{"start": 2304.58, "end": 2304.88, "word": " can", "probability": 0.410888671875}, {"start": 2304.88, "end": 2305.08, "word": " be", "probability": 0.9501953125}, {"start": 2305.08, "end": 2305.54, "word": " used", "probability": 0.92041015625}, {"start": 2305.54, "end": 2306.1, "word": " for", "probability": 0.93505859375}, {"start": 2306.1, "end": 2306.78, "word": " testing", "probability": 0.84521484375}, {"start": 2306.78, "end": 2307.9, "word": " difference", "probability": 0.697265625}, {"start": 2307.9, "end": 2308.3, "word": " between", "probability": 0.876953125}, {"start": 2308.3, "end": 2308.52, "word": " two", "probability": 0.87890625}, {"start": 2308.52, "end": 2308.92, "word": " population", "probability": 0.8330078125}, {"start": 2308.92, "end": 2309.56, "word": " proportions.", "probability": 0.71142578125}, {"start": 2310.96, "end": 2311.1, "word": " And", "probability": 0.91162109375}, {"start": 2311.1, "end": 2311.4, "word": " again,", "probability": 0.923828125}, {"start": 2311.54, "end": 2311.66, "word": " chi", "probability": 0.404052734375}, {"start": 2311.66, "end": 2312.06, "word": "-square", "probability": 0.822265625}, {"start": 2312.06, "end": 2313.68, "word": " can", "probability": 0.9169921875}, {"start": 2313.68, "end": 2313.84, "word": " be", "probability": 0.94287109375}, {"start": 2313.84, "end": 2314.36, "word": " extended", "probability": 0.26025390625}, {"start": 2314.36, "end": 2314.56, "word": " to", "probability": 0.62353515625}, {"start": 2314.56, "end": 2314.92, "word": " use", "probability": 0.85546875}, {"start": 2314.92, "end": 2315.52, "word": " for", "probability": 0.9052734375}, {"start": 2315.52, "end": 2316.74, "word": " more", "probability": 0.62451171875}, {"start": 2316.74, "end": 2316.94, "word": " than", "probability": 0.935546875}, {"start": 2316.94, "end": 2317.18, "word": " two.", "probability": 0.82958984375}, {"start": 2318.32, "end": 2319.08, "word": " So", "probability": 0.89501953125}, {"start": 2319.08, "end": 2319.5, "word": " in", "probability": 0.6455078125}, {"start": 2319.5, "end": 2319.72, "word": " this", "probability": 0.947265625}, {"start": 2319.72, "end": 2319.94, "word": " case,", "probability": 0.91796875}, {"start": 2320.0, "end": 2320.14, "word": " the", "probability": 0.91455078125}, {"start": 2320.14, "end": 2320.5, "word": " correct", "probability": 0.90478515625}, {"start": 2320.5, "end": 2320.98, "word": " answer", "probability": 0.96142578125}, {"start": 2320.98, "end": 2321.24, "word": " is", "probability": 0.9404296875}, {"start": 2321.24, "end": 2321.46, "word": " C,", "probability": 0.76806640625}, {"start": 2321.6, "end": 2321.98, "word": " because", "probability": 0.896484375}, {"start": 2321.98, "end": 2322.16, "word": " we", "probability": 0.9560546875}, {"start": 2322.16, "end": 2322.38, "word": " can", "probability": 0.94482421875}, {"start": 2322.38, "end": 2322.6, "word": " use", "probability": 0.8408203125}, {"start": 2322.6, "end": 2322.84, "word": " either", "probability": 0.93701171875}, {"start": 2322.84, "end": 2323.22, "word": " Z", "probability": 0.77587890625}, {"start": 2323.22, "end": 2324.16, "word": " or", "probability": 0.8427734375}, {"start": 2324.16, "end": 2324.48, "word": " chi", "probability": 0.71728515625}, {"start": 2324.48, "end": 2324.88, "word": "-square", "probability": 0.94287109375}, {"start": 2324.88, "end": 2325.28, "word": " test.", "probability": 0.8115234375}, {"start": 2327.54, "end": 2328.3, "word": " Next,", "probability": 0.92138671875}, {"start": 2329.32, "end": 2329.9, "word": " in", "probability": 0.939453125}, {"start": 2329.9, "end": 2330.38, "word": " testing,", "probability": 0.8798828125}], "temperature": 1.0}, {"id": 89, "seek": 235921, "start": 2331.33, "end": 2359.21, "text": " hypothesis using chi-square test. The theoretical frequencies are based on null hypothesis, alternative, normal distribution, none of the above. Always when we are using chi-square test, we assume the null is true. So the theoretical frequencies are based on the null hypothesis. So always any statistic", "tokens": [17291, 1228, 13228, 12, 33292, 543, 1500, 13, 440, 20864, 20250, 366, 2361, 322, 18184, 17291, 11, 8535, 11, 2710, 7316, 11, 6022, 295, 264, 3673, 13, 11270, 562, 321, 366, 1228, 13228, 12, 33292, 543, 1500, 11, 321, 6552, 264, 18184, 307, 2074, 13, 407, 264, 20864, 20250, 366, 2361, 322, 264, 18184, 17291, 13, 407, 1009, 604, 29588], "avg_logprob": -0.21913421935722477, "compression_ratio": 1.8203592814371257, "no_speech_prob": 0.0, "words": [{"start": 2331.33, "end": 2332.09, "word": " hypothesis", "probability": 0.1282958984375}, {"start": 2332.09, "end": 2332.89, "word": " using", "probability": 0.8798828125}, {"start": 2332.89, "end": 2333.21, "word": " chi", "probability": 0.376220703125}, {"start": 2333.21, "end": 2333.51, "word": "-square", "probability": 0.8642578125}, {"start": 2333.51, "end": 2333.87, "word": " test.", "probability": 0.80029296875}, {"start": 2334.93, "end": 2335.31, "word": " The", "probability": 0.865234375}, {"start": 2335.31, "end": 2335.97, "word": " theoretical", "probability": 0.88916015625}, {"start": 2335.97, "end": 2338.35, "word": " frequencies", "probability": 0.79052734375}, {"start": 2338.35, "end": 2339.05, "word": " are", "probability": 0.9453125}, {"start": 2339.05, "end": 2339.43, "word": " based", "probability": 0.94482421875}, {"start": 2339.43, "end": 2339.89, "word": " on", "probability": 0.94970703125}, {"start": 2339.89, "end": 2341.05, "word": " null", "probability": 0.83837890625}, {"start": 2341.05, "end": 2341.59, "word": " hypothesis,", "probability": 0.61328125}, {"start": 2342.03, "end": 2342.43, "word": " alternative,", "probability": 0.44482421875}, {"start": 2342.91, "end": 2343.19, "word": " normal", "probability": 0.8193359375}, {"start": 2343.19, "end": 2343.71, "word": " distribution,", "probability": 0.8330078125}, {"start": 2343.87, "end": 2343.97, "word": " none", "probability": 0.91650390625}, {"start": 2343.97, "end": 2344.13, "word": " of", "probability": 0.974609375}, {"start": 2344.13, "end": 2344.21, "word": " the", "probability": 0.89697265625}, {"start": 2344.21, "end": 2344.53, "word": " above.", "probability": 0.978515625}, {"start": 2344.89, "end": 2345.49, "word": " Always", "probability": 0.78564453125}, {"start": 2345.49, "end": 2346.29, "word": " when", "probability": 0.61328125}, {"start": 2346.29, "end": 2346.49, "word": " we", "probability": 0.96337890625}, {"start": 2346.49, "end": 2346.67, "word": " are", "probability": 0.9404296875}, {"start": 2346.67, "end": 2346.99, "word": " using", "probability": 0.93505859375}, {"start": 2346.99, "end": 2347.27, "word": " chi", "probability": 0.81201171875}, {"start": 2347.27, "end": 2347.57, "word": "-square", "probability": 0.9471028645833334}, {"start": 2347.57, "end": 2347.93, "word": " test,", "probability": 0.78466796875}, {"start": 2348.03, "end": 2348.17, "word": " we", "probability": 0.9560546875}, {"start": 2348.17, "end": 2348.77, "word": " assume", "probability": 0.908203125}, {"start": 2348.77, "end": 2350.05, "word": " the", "probability": 0.7392578125}, {"start": 2350.05, "end": 2350.27, "word": " null", "probability": 0.91015625}, {"start": 2350.27, "end": 2350.45, "word": " is", "probability": 0.94287109375}, {"start": 2350.45, "end": 2350.85, "word": " true.", "probability": 0.94189453125}, {"start": 2351.47, "end": 2351.99, "word": " So", "probability": 0.95263671875}, {"start": 2351.99, "end": 2352.49, "word": " the", "probability": 0.64794921875}, {"start": 2352.49, "end": 2353.17, "word": " theoretical", "probability": 0.919921875}, {"start": 2353.17, "end": 2353.79, "word": " frequencies", "probability": 0.8388671875}, {"start": 2353.79, "end": 2354.09, "word": " are", "probability": 0.9453125}, {"start": 2354.09, "end": 2354.37, "word": " based", "probability": 0.94140625}, {"start": 2354.37, "end": 2354.63, "word": " on", "probability": 0.95068359375}, {"start": 2354.63, "end": 2354.79, "word": " the", "probability": 0.90087890625}, {"start": 2354.79, "end": 2354.95, "word": " null", "probability": 0.931640625}, {"start": 2354.95, "end": 2355.41, "word": " hypothesis.", "probability": 0.74853515625}, {"start": 2356.97, "end": 2357.29, "word": " So", "probability": 0.94921875}, {"start": 2357.29, "end": 2357.83, "word": " always", "probability": 0.818359375}, {"start": 2357.83, "end": 2358.43, "word": " any", "probability": 0.6845703125}, {"start": 2358.43, "end": 2359.21, "word": " statistic", "probability": 0.8037109375}], "temperature": 1.0}, {"id": 90, "seek": 237704, "start": 2359.76, "end": 2377.04, "text": " can be computed if we assume x0 is correct. So the correct answer is A. Let's look at table 11-2.", "tokens": [393, 312, 40610, 498, 321, 6552, 2031, 15, 307, 3006, 13, 407, 264, 3006, 1867, 307, 316, 13, 961, 311, 574, 412, 3199, 2975, 12, 17, 13], "avg_logprob": -0.20675223373941012, "compression_ratio": 1.0888888888888888, "no_speech_prob": 0.0, "words": [{"start": 2359.76, "end": 2360.06, "word": " can", "probability": 0.2220458984375}, {"start": 2360.06, "end": 2360.24, "word": " be", "probability": 0.9453125}, {"start": 2360.24, "end": 2360.74, "word": " computed", "probability": 0.9208984375}, {"start": 2360.74, "end": 2361.36, "word": " if", "probability": 0.9091796875}, {"start": 2361.36, "end": 2361.68, "word": " we", "probability": 0.9306640625}, {"start": 2361.68, "end": 2362.22, "word": " assume", "probability": 0.90673828125}, {"start": 2362.22, "end": 2363.46, "word": " x0", "probability": 0.5067138671875}, {"start": 2363.46, "end": 2363.78, "word": " is", "probability": 0.92236328125}, {"start": 2363.78, "end": 2364.14, "word": " correct.", "probability": 0.890625}, {"start": 2364.92, "end": 2365.16, "word": " So", "probability": 0.82177734375}, {"start": 2365.16, "end": 2365.3, "word": " the", "probability": 0.744140625}, {"start": 2365.3, "end": 2365.58, "word": " correct", "probability": 0.9072265625}, {"start": 2365.58, "end": 2365.9, "word": " answer", "probability": 0.962890625}, {"start": 2365.9, "end": 2366.12, "word": " is", "probability": 0.95263671875}, {"start": 2366.12, "end": 2366.4, "word": " A.", "probability": 0.70556640625}, {"start": 2374.06, "end": 2374.74, "word": " Let's", "probability": 0.935302734375}, {"start": 2374.74, "end": 2374.96, "word": " look", "probability": 0.96240234375}, {"start": 2374.96, "end": 2375.36, "word": " at", "probability": 0.96484375}, {"start": 2375.36, "end": 2376.12, "word": " table", "probability": 0.5703125}, {"start": 2376.12, "end": 2376.56, "word": " 11", "probability": 0.89306640625}, {"start": 2376.56, "end": 2377.04, "word": "-2.", "probability": 0.925537109375}], "temperature": 1.0}, {"id": 91, "seek": 240388, "start": 2384.28, "end": 2403.88, "text": " Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent.", "tokens": [5126, 3431, 764, 731, 12, 6861, 23200, 382, 25378, 21819, 892, 294, 641, 3558, 42897, 13, 316, 2979, 390, 13809, 281, 6997, 1968, 3360, 8888, 295, 6556, 3558, 8499, 293, 264, 7898, 295, 264, 45775, 366, 6695, 13], "avg_logprob": -0.15294471612343422, "compression_ratio": 1.4313725490196079, "no_speech_prob": 0.0, "words": [{"start": 2384.2799999999997, "end": 2385.2, "word": " Many", "probability": 0.79052734375}, {"start": 2385.2, "end": 2386.12, "word": " companies", "probability": 0.88916015625}, {"start": 2386.12, "end": 2387.06, "word": " use", "probability": 0.70263671875}, {"start": 2387.06, "end": 2387.38, "word": " well", "probability": 0.9248046875}, {"start": 2387.38, "end": 2387.64, "word": "-known", "probability": 0.872802734375}, {"start": 2387.64, "end": 2388.34, "word": " celebrities", "probability": 0.89599609375}, {"start": 2388.34, "end": 2389.0, "word": " as", "probability": 0.96826171875}, {"start": 2389.0, "end": 2390.68, "word": " spokespersons", "probability": 0.8916015625}, {"start": 2390.68, "end": 2390.9, "word": " in", "probability": 0.88037109375}, {"start": 2390.9, "end": 2391.12, "word": " their", "probability": 0.94775390625}, {"start": 2391.12, "end": 2391.46, "word": " TV", "probability": 0.96435546875}, {"start": 2391.46, "end": 2392.24, "word": " advertisements.", "probability": 0.560546875}, {"start": 2393.76, "end": 2394.06, "word": " A", "probability": 0.40869140625}, {"start": 2394.06, "end": 2394.42, "word": " study", "probability": 0.92822265625}, {"start": 2394.42, "end": 2394.68, "word": " was", "probability": 0.94140625}, {"start": 2394.68, "end": 2395.24, "word": " conducted", "probability": 0.8173828125}, {"start": 2395.24, "end": 2395.58, "word": " to", "probability": 0.953125}, {"start": 2395.58, "end": 2396.1, "word": " determine", "probability": 0.9052734375}, {"start": 2396.1, "end": 2396.56, "word": " whether", "probability": 0.92431640625}, {"start": 2396.56, "end": 2397.16, "word": " brand", "probability": 0.77783203125}, {"start": 2397.16, "end": 2397.76, "word": " awareness", "probability": 0.83935546875}, {"start": 2397.76, "end": 2398.16, "word": " of", "probability": 0.958984375}, {"start": 2398.16, "end": 2398.48, "word": " female", "probability": 0.865234375}, {"start": 2398.48, "end": 2398.86, "word": " TV", "probability": 0.955078125}, {"start": 2398.86, "end": 2400.08, "word": " viewers", "probability": 0.86474609375}, {"start": 2400.08, "end": 2400.96, "word": " and", "probability": 0.87109375}, {"start": 2400.96, "end": 2401.16, "word": " the", "probability": 0.89208984375}, {"start": 2401.16, "end": 2401.5, "word": " gender", "probability": 0.92626953125}, {"start": 2401.5, "end": 2401.92, "word": " of", "probability": 0.97216796875}, {"start": 2401.92, "end": 2402.14, "word": " the", "probability": 0.8564453125}, {"start": 2402.14, "end": 2402.7, "word": " spokesperson", "probability": 0.66650390625}, {"start": 2402.7, "end": 2403.48, "word": " are", "probability": 0.85693359375}, {"start": 2403.48, "end": 2403.88, "word": " independent.", "probability": 0.81103515625}], "temperature": 1.0}, {"id": 92, "seek": 243430, "start": 2404.96, "end": 2434.3, "text": " So there are two variables, whether a brand awareness of female TV and gender of the spokesperson are independent. Each and a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson, the gender of the spokesperson, and whether or not the viewer could identify the product was recorded.", "tokens": [407, 456, 366, 732, 9102, 11, 1968, 257, 3360, 8888, 295, 6556, 3558, 293, 7898, 295, 264, 45775, 366, 6695, 13, 6947, 293, 257, 6889, 295, 6641, 6556, 3558, 8499, 390, 2351, 281, 5876, 257, 1674, 42310, 538, 257, 18597, 45775, 11, 264, 7898, 295, 264, 45775, 11, 293, 1968, 420, 406, 264, 16767, 727, 5876, 264, 1674, 390, 8287, 13], "avg_logprob": -0.153981858203488, "compression_ratio": 1.7253886010362693, "no_speech_prob": 0.0, "words": [{"start": 2404.96, "end": 2405.24, "word": " So", "probability": 0.884765625}, {"start": 2405.24, "end": 2405.4, "word": " there", "probability": 0.751953125}, {"start": 2405.4, "end": 2405.56, "word": " are", "probability": 0.94140625}, {"start": 2405.56, "end": 2405.86, "word": " two", "probability": 0.90869140625}, {"start": 2405.86, "end": 2406.46, "word": " variables,", "probability": 0.97021484375}, {"start": 2407.62, "end": 2407.88, "word": " whether", "probability": 0.8505859375}, {"start": 2407.88, "end": 2408.3, "word": " a", "probability": 0.74755859375}, {"start": 2408.3, "end": 2408.6, "word": " brand", "probability": 0.89794921875}, {"start": 2408.6, "end": 2409.02, "word": " awareness", "probability": 0.87451171875}, {"start": 2409.02, "end": 2409.22, "word": " of", "probability": 0.912109375}, {"start": 2409.22, "end": 2409.5, "word": " female", "probability": 0.7978515625}, {"start": 2409.5, "end": 2409.82, "word": " TV", "probability": 0.96923828125}, {"start": 2409.82, "end": 2410.4, "word": " and", "probability": 0.875}, {"start": 2410.4, "end": 2410.78, "word": " gender", "probability": 0.908203125}, {"start": 2410.78, "end": 2412.1, "word": " of", "probability": 0.95703125}, {"start": 2412.1, "end": 2412.32, "word": " the", "probability": 0.88623046875}, {"start": 2412.32, "end": 2412.88, "word": " spokesperson", "probability": 0.90234375}, {"start": 2412.88, "end": 2413.34, "word": " are", "probability": 0.8974609375}, {"start": 2413.34, "end": 2413.74, "word": " independent.", "probability": 0.77587890625}, {"start": 2414.82, "end": 2415.2, "word": " Each", "probability": 0.91845703125}, {"start": 2415.2, "end": 2415.34, "word": " and", "probability": 0.44091796875}, {"start": 2415.34, "end": 2415.5, "word": " a", "probability": 0.517578125}, {"start": 2415.5, "end": 2415.72, "word": " sample", "probability": 0.86083984375}, {"start": 2415.72, "end": 2415.94, "word": " of", "probability": 0.97021484375}, {"start": 2415.94, "end": 2416.44, "word": " 300", "probability": 0.9453125}, {"start": 2416.44, "end": 2417.2, "word": " female", "probability": 0.8583984375}, {"start": 2417.2, "end": 2417.58, "word": " TV", "probability": 0.9755859375}, {"start": 2417.58, "end": 2418.22, "word": " viewers", "probability": 0.87841796875}, {"start": 2418.22, "end": 2419.54, "word": " was", "probability": 0.9052734375}, {"start": 2419.54, "end": 2419.98, "word": " asked", "probability": 0.8212890625}, {"start": 2419.98, "end": 2420.18, "word": " to", "probability": 0.9716796875}, {"start": 2420.18, "end": 2420.82, "word": " identify", "probability": 0.95263671875}, {"start": 2420.82, "end": 2421.9, "word": " a", "probability": 0.986328125}, {"start": 2421.9, "end": 2422.4, "word": " product", "probability": 0.919921875}, {"start": 2422.4, "end": 2423.28, "word": " advertised", "probability": 0.93017578125}, {"start": 2423.28, "end": 2423.68, "word": " by", "probability": 0.97216796875}, {"start": 2423.68, "end": 2424.0, "word": " a", "probability": 0.335693359375}, {"start": 2424.0, "end": 2424.28, "word": " celebrity", "probability": 0.7509765625}, {"start": 2424.28, "end": 2425.24, "word": " spokesperson,", "probability": 0.93310546875}, {"start": 2426.1, "end": 2426.26, "word": " the", "probability": 0.91796875}, {"start": 2426.26, "end": 2426.62, "word": " gender", "probability": 0.91357421875}, {"start": 2426.62, "end": 2426.86, "word": " of", "probability": 0.97021484375}, {"start": 2426.86, "end": 2427.0, "word": " the", "probability": 0.8447265625}, {"start": 2427.0, "end": 2428.36, "word": " spokesperson,", "probability": 0.9443359375}, {"start": 2429.3, "end": 2429.62, "word": " and", "probability": 0.9326171875}, {"start": 2429.62, "end": 2429.92, "word": " whether", "probability": 0.9150390625}, {"start": 2429.92, "end": 2430.18, "word": " or", "probability": 0.96337890625}, {"start": 2430.18, "end": 2430.56, "word": " not", "probability": 0.9462890625}, {"start": 2430.56, "end": 2431.52, "word": " the", "probability": 0.912109375}, {"start": 2431.52, "end": 2431.82, "word": " viewer", "probability": 0.89208984375}, {"start": 2431.82, "end": 2432.28, "word": " could", "probability": 0.884765625}, {"start": 2432.28, "end": 2432.9, "word": " identify", "probability": 0.93994140625}, {"start": 2432.9, "end": 2433.08, "word": " the", "probability": 0.89599609375}, {"start": 2433.08, "end": 2433.48, "word": " product", "probability": 0.91748046875}, {"start": 2433.48, "end": 2433.82, "word": " was", "probability": 0.94091796875}, {"start": 2433.82, "end": 2434.3, "word": " recorded.", "probability": 0.9404296875}], "temperature": 1.0}, {"id": 93, "seek": 246380, "start": 2435.38, "end": 2463.8, "text": " The number in each category are given below. Now, the questions are, number one, he asked about the calculated this statistic is. We have to find Chi-square statistic. It's two by two tables, easy one. So, for example, to find the F expected is, rho total is one over two.", "tokens": [440, 1230, 294, 1184, 7719, 366, 2212, 2507, 13, 823, 11, 264, 1651, 366, 11, 1230, 472, 11, 415, 2351, 466, 264, 15598, 341, 29588, 307, 13, 492, 362, 281, 915, 17730, 12, 33292, 543, 29588, 13, 467, 311, 732, 538, 732, 8020, 11, 1858, 472, 13, 407, 11, 337, 1365, 11, 281, 915, 264, 479, 5176, 307, 11, 20293, 3217, 307, 472, 670, 732, 13], "avg_logprob": -0.303404862311349, "compression_ratio": 1.4444444444444444, "no_speech_prob": 0.0, "words": [{"start": 2435.38, "end": 2435.64, "word": " The", "probability": 0.70068359375}, {"start": 2435.64, "end": 2436.02, "word": " number", "probability": 0.496337890625}, {"start": 2436.02, "end": 2436.46, "word": " in", "probability": 0.888671875}, {"start": 2436.46, "end": 2436.76, "word": " each", "probability": 0.9384765625}, {"start": 2436.76, "end": 2437.26, "word": " category", "probability": 0.9521484375}, {"start": 2437.26, "end": 2437.58, "word": " are", "probability": 0.8115234375}, {"start": 2437.58, "end": 2437.82, "word": " given", "probability": 0.8818359375}, {"start": 2437.82, "end": 2438.16, "word": " below.", "probability": 0.90380859375}, {"start": 2439.3, "end": 2439.54, "word": " Now,", "probability": 0.89404296875}, {"start": 2439.58, "end": 2439.68, "word": " the", "probability": 0.91552734375}, {"start": 2439.68, "end": 2440.08, "word": " questions", "probability": 0.92138671875}, {"start": 2440.08, "end": 2440.42, "word": " are,", "probability": 0.92578125}, {"start": 2441.46, "end": 2441.78, "word": " number", "probability": 0.810546875}, {"start": 2441.78, "end": 2442.1, "word": " one,", "probability": 0.7451171875}, {"start": 2443.44, "end": 2444.24, "word": " he", "probability": 0.7783203125}, {"start": 2444.24, "end": 2444.46, "word": " asked", "probability": 0.4384765625}, {"start": 2444.46, "end": 2444.8, "word": " about", "probability": 0.89599609375}, {"start": 2444.8, "end": 2445.02, "word": " the", "probability": 0.7353515625}, {"start": 2445.02, "end": 2445.52, "word": " calculated", "probability": 0.93212890625}, {"start": 2445.52, "end": 2445.94, "word": " this", "probability": 0.436767578125}, {"start": 2445.94, "end": 2446.46, "word": " statistic", "probability": 0.837890625}, {"start": 2446.46, "end": 2446.8, "word": " is.", "probability": 0.765625}, {"start": 2447.14, "end": 2447.44, "word": " We", "probability": 0.94873046875}, {"start": 2447.44, "end": 2447.64, "word": " have", "probability": 0.9501953125}, {"start": 2447.64, "end": 2447.88, "word": " to", "probability": 0.9697265625}, {"start": 2447.88, "end": 2448.44, "word": " find", "probability": 0.8916015625}, {"start": 2448.44, "end": 2448.72, "word": " Chi", "probability": 0.28515625}, {"start": 2448.72, "end": 2449.12, "word": "-square", "probability": 0.6865234375}, {"start": 2449.12, "end": 2449.64, "word": " statistic.", "probability": 0.78515625}, {"start": 2450.22, "end": 2450.56, "word": " It's", "probability": 0.95751953125}, {"start": 2450.56, "end": 2450.76, "word": " two", "probability": 0.765625}, {"start": 2450.76, "end": 2450.9, "word": " by", "probability": 0.92578125}, {"start": 2450.9, "end": 2451.08, "word": " two", "probability": 0.94140625}, {"start": 2451.08, "end": 2451.5, "word": " tables,", "probability": 0.82666015625}, {"start": 2451.74, "end": 2451.98, "word": " easy", "probability": 0.89599609375}, {"start": 2451.98, "end": 2452.24, "word": " one.", "probability": 0.93310546875}, {"start": 2453.58, "end": 2454.02, "word": " So,", "probability": 0.94091796875}, {"start": 2454.46, "end": 2454.74, "word": " for", "probability": 0.95703125}, {"start": 2454.74, "end": 2455.1, "word": " example,", "probability": 0.97998046875}, {"start": 2455.28, "end": 2455.38, "word": " to", "probability": 0.93359375}, {"start": 2455.38, "end": 2455.82, "word": " find", "probability": 0.89208984375}, {"start": 2455.82, "end": 2456.08, "word": " the", "probability": 0.8583984375}, {"start": 2456.08, "end": 2456.46, "word": " F", "probability": 0.76611328125}, {"start": 2456.46, "end": 2457.04, "word": " expected", "probability": 0.8857421875}, {"start": 2457.04, "end": 2459.46, "word": " is,", "probability": 0.63720703125}, {"start": 2460.42, "end": 2461.46, "word": " rho", "probability": 0.301025390625}, {"start": 2461.46, "end": 2461.78, "word": " total", "probability": 0.82958984375}, {"start": 2461.78, "end": 2462.3, "word": " is", "probability": 0.91650390625}, {"start": 2462.3, "end": 2462.64, "word": " one", "probability": 0.5986328125}, {"start": 2462.64, "end": 2463.5, "word": " over", "probability": 0.6318359375}, {"start": 2463.5, "end": 2463.8, "word": " two.", "probability": 0.92041015625}], "temperature": 1.0}, {"id": 94, "seek": 249101, "start": 2465.91, "end": 2491.01, "text": " And one line here. And this 150. And also 150. So the expected frequency for the first one is 102 times 150 divided by 300.", "tokens": [400, 472, 1622, 510, 13, 400, 341, 8451, 13, 400, 611, 8451, 13, 407, 264, 5176, 7893, 337, 264, 700, 472, 307, 45937, 1413, 8451, 6666, 538, 6641, 13], "avg_logprob": -0.28437501390775044, "compression_ratio": 1.24, "no_speech_prob": 0.0, "words": [{"start": 2465.91, "end": 2466.95, "word": " And", "probability": 0.58544921875}, {"start": 2466.95, "end": 2467.99, "word": " one", "probability": 0.462890625}, {"start": 2467.99, "end": 2470.89, "word": " line", "probability": 0.14453125}, {"start": 2470.89, "end": 2471.17, "word": " here.", "probability": 0.7021484375}, {"start": 2472.73, "end": 2473.13, "word": " And", "probability": 0.85400390625}, {"start": 2473.13, "end": 2473.29, "word": " this", "probability": 0.599609375}, {"start": 2473.29, "end": 2473.81, "word": " 150.", "probability": 0.62744140625}, {"start": 2476.43, "end": 2477.47, "word": " And", "probability": 0.912109375}, {"start": 2477.47, "end": 2478.01, "word": " also", "probability": 0.8544921875}, {"start": 2478.01, "end": 2478.91, "word": " 150.", "probability": 0.84326171875}, {"start": 2479.65, "end": 2480.43, "word": " So", "probability": 0.9345703125}, {"start": 2480.43, "end": 2481.09, "word": " the", "probability": 0.6962890625}, {"start": 2481.09, "end": 2481.55, "word": " expected", "probability": 0.89697265625}, {"start": 2481.55, "end": 2482.07, "word": " frequency", "probability": 0.896484375}, {"start": 2482.07, "end": 2482.35, "word": " for", "probability": 0.92626953125}, {"start": 2482.35, "end": 2482.51, "word": " the", "probability": 0.9189453125}, {"start": 2482.51, "end": 2482.75, "word": " first", "probability": 0.88916015625}, {"start": 2482.75, "end": 2482.97, "word": " one", "probability": 0.919921875}, {"start": 2482.97, "end": 2483.11, "word": " is", "probability": 0.93994140625}, {"start": 2483.11, "end": 2483.41, "word": " 102", "probability": 0.921875}, {"start": 2483.41, "end": 2485.45, "word": " times", "probability": 0.693359375}, {"start": 2485.45, "end": 2486.23, "word": " 150", "probability": 0.904296875}, {"start": 2486.23, "end": 2488.05, "word": " divided", "probability": 0.65087890625}, {"start": 2488.05, "end": 2488.53, "word": " by", "probability": 0.97607421875}, {"start": 2488.53, "end": 2491.01, "word": " 300.", "probability": 0.96630859375}], "temperature": 1.0}, {"id": 95, "seek": 252102, "start": 2495.68, "end": 2521.02, "text": " So the answer is 51. So the first expected is 51. The other one is just 102 minus 51 is also 51. Now here is 99.", "tokens": [407, 264, 1867, 307, 18485, 13, 407, 264, 700, 5176, 307, 18485, 13, 440, 661, 472, 307, 445, 45937, 3175, 18485, 307, 611, 18485, 13, 823, 510, 307, 11803, 13], "avg_logprob": -0.13104839190360038, "compression_ratio": 1.2282608695652173, "no_speech_prob": 0.0, "words": [{"start": 2495.68, "end": 2495.88, "word": " So", "probability": 0.58349609375}, {"start": 2495.88, "end": 2496.0, "word": " the", "probability": 0.734375}, {"start": 2496.0, "end": 2496.24, "word": " answer", "probability": 0.87646484375}, {"start": 2496.24, "end": 2496.7, "word": " is", "probability": 0.95458984375}, {"start": 2496.7, "end": 2499.64, "word": " 51.", "probability": 0.884765625}, {"start": 2502.88, "end": 2503.54, "word": " So", "probability": 0.87548828125}, {"start": 2503.54, "end": 2503.74, "word": " the", "probability": 0.83740234375}, {"start": 2503.74, "end": 2504.14, "word": " first", "probability": 0.865234375}, {"start": 2504.14, "end": 2505.0, "word": " expected", "probability": 0.8681640625}, {"start": 2505.0, "end": 2506.8, "word": " is", "probability": 0.82958984375}, {"start": 2506.8, "end": 2507.24, "word": " 51.", "probability": 0.9736328125}, {"start": 2509.58, "end": 2510.34, "word": " The", "probability": 0.87841796875}, {"start": 2510.34, "end": 2510.58, "word": " other", "probability": 0.890625}, {"start": 2510.58, "end": 2510.82, "word": " one", "probability": 0.91943359375}, {"start": 2510.82, "end": 2511.04, "word": " is", "probability": 0.93505859375}, {"start": 2511.04, "end": 2511.56, "word": " just", "probability": 0.8876953125}, {"start": 2511.56, "end": 2511.96, "word": " 102", "probability": 0.91796875}, {"start": 2511.96, "end": 2512.58, "word": " minus", "probability": 0.9453125}, {"start": 2512.58, "end": 2513.1, "word": " 51", "probability": 0.98095703125}, {"start": 2513.1, "end": 2513.36, "word": " is", "probability": 0.8994140625}, {"start": 2513.36, "end": 2513.78, "word": " also", "probability": 0.88671875}, {"start": 2513.78, "end": 2514.36, "word": " 51.", "probability": 0.9814453125}, {"start": 2517.32, "end": 2518.3, "word": " Now", "probability": 0.947265625}, {"start": 2518.3, "end": 2518.72, "word": " here", "probability": 0.63623046875}, {"start": 2518.72, "end": 2519.08, "word": " is", "probability": 0.9345703125}, {"start": 2519.08, "end": 2521.02, "word": " 99.", "probability": 0.8994140625}], "temperature": 1.0}, {"id": 96, "seek": 255288, "start": 2529.08, "end": 2552.88, "text": " So the second one are the expected frequencies. So my chi-square statistic is 41 minus 51 squared divided by 51 plus 61 minus 51 squared.", "tokens": [407, 264, 1150, 472, 366, 264, 5176, 20250, 13, 407, 452, 13228, 12, 33292, 543, 29588, 307, 18173, 3175, 18485, 8889, 6666, 538, 18485, 1804, 28294, 3175, 18485, 8889, 13], "avg_logprob": -0.2741935464643663, "compression_ratio": 1.3269230769230769, "no_speech_prob": 0.0, "words": [{"start": 2529.08, "end": 2530.16, "word": " So", "probability": 0.1375732421875}, {"start": 2530.16, "end": 2531.24, "word": " the", "probability": 0.286376953125}, {"start": 2531.24, "end": 2535.18, "word": " second", "probability": 0.8798828125}, {"start": 2535.18, "end": 2535.6, "word": " one", "probability": 0.8583984375}, {"start": 2535.6, "end": 2535.9, "word": " are", "probability": 0.78857421875}, {"start": 2535.9, "end": 2536.14, "word": " the", "probability": 0.8955078125}, {"start": 2536.14, "end": 2536.86, "word": " expected", "probability": 0.8896484375}, {"start": 2536.86, "end": 2537.38, "word": " frequencies.", "probability": 0.71142578125}, {"start": 2537.94, "end": 2538.1, "word": " So", "probability": 0.91357421875}, {"start": 2538.1, "end": 2538.34, "word": " my", "probability": 0.828125}, {"start": 2538.34, "end": 2538.52, "word": " chi", "probability": 0.6708984375}, {"start": 2538.52, "end": 2538.8, "word": "-square", "probability": 0.755859375}, {"start": 2538.8, "end": 2539.38, "word": " statistic", "probability": 0.62158203125}, {"start": 2539.38, "end": 2542.4, "word": " is", "probability": 0.87939453125}, {"start": 2542.4, "end": 2542.98, "word": " 41", "probability": 0.94287109375}, {"start": 2542.98, "end": 2544.62, "word": " minus", "probability": 0.9111328125}, {"start": 2544.62, "end": 2545.0, "word": " 51", "probability": 0.9775390625}, {"start": 2545.0, "end": 2545.52, "word": " squared", "probability": 0.857421875}, {"start": 2545.52, "end": 2547.48, "word": " divided", "probability": 0.52294921875}, {"start": 2547.48, "end": 2547.8, "word": " by", "probability": 0.97119140625}, {"start": 2547.8, "end": 2548.44, "word": " 51", "probability": 0.9814453125}, {"start": 2548.44, "end": 2549.46, "word": " plus", "probability": 0.85107421875}, {"start": 2549.46, "end": 2551.4, "word": " 61", "probability": 0.93798828125}, {"start": 2551.4, "end": 2551.82, "word": " minus", "probability": 0.986328125}, {"start": 2551.82, "end": 2552.26, "word": " 51", "probability": 0.98193359375}, {"start": 2552.26, "end": 2552.88, "word": " squared.", "probability": 0.8427734375}], "temperature": 1.0}, {"id": 97, "seek": 258176, "start": 2554.72, "end": 2581.76, "text": " 561 plus 109 minus 99 squared 99 plus 89 minus 99 squared. That will give 5 point. So the answer is 5.9418.", "tokens": [19687, 16, 1804, 1266, 24, 3175, 11803, 8889, 11803, 1804, 31877, 3175, 11803, 8889, 13, 663, 486, 976, 1025, 935, 13, 407, 264, 1867, 307, 1025, 13, 24, 19, 6494, 13], "avg_logprob": -0.2536621056497097, "compression_ratio": 1.2134831460674158, "no_speech_prob": 0.0, "words": [{"start": 2554.72, "end": 2555.5, "word": " 561", "probability": 0.6900634765625}, {"start": 2555.5, "end": 2556.0, "word": " plus", "probability": 0.73974609375}, {"start": 2556.0, "end": 2558.34, "word": " 109", "probability": 0.77978515625}, {"start": 2558.34, "end": 2558.74, "word": " minus", "probability": 0.96923828125}, {"start": 2558.74, "end": 2559.2, "word": " 99", "probability": 0.9462890625}, {"start": 2559.2, "end": 2560.86, "word": " squared", "probability": 0.810546875}, {"start": 2560.86, "end": 2561.48, "word": " 99", "probability": 0.6982421875}, {"start": 2561.48, "end": 2563.12, "word": " plus", "probability": 0.900390625}, {"start": 2563.12, "end": 2564.16, "word": " 89", "probability": 0.970703125}, {"start": 2564.16, "end": 2564.7, "word": " minus", "probability": 0.6640625}, {"start": 2564.7, "end": 2565.12, "word": " 99", "probability": 0.98974609375}, {"start": 2565.12, "end": 2567.04, "word": " squared.", "probability": 0.87939453125}, {"start": 2569.08, "end": 2570.24, "word": " That", "probability": 0.88427734375}, {"start": 2570.24, "end": 2570.44, "word": " will", "probability": 0.84619140625}, {"start": 2570.44, "end": 2570.84, "word": " give", "probability": 0.88720703125}, {"start": 2570.84, "end": 2572.72, "word": " 5", "probability": 0.83740234375}, {"start": 2572.72, "end": 2573.14, "word": " point.", "probability": 0.451904296875}, {"start": 2577.26, "end": 2578.42, "word": " So", "probability": 0.84716796875}, {"start": 2578.42, "end": 2578.58, "word": " the", "probability": 0.76220703125}, {"start": 2578.58, "end": 2578.86, "word": " answer", "probability": 0.95751953125}, {"start": 2578.86, "end": 2579.1, "word": " is", "probability": 0.9501953125}, {"start": 2579.1, "end": 2579.46, "word": " 5", "probability": 0.96484375}, {"start": 2579.46, "end": 2581.76, "word": ".9418.", "probability": 0.76666259765625}], "temperature": 1.0}, {"id": 98, "seek": 261161, "start": 2583.41, "end": 2611.61, "text": " So simple calculation will give this result. Now, next one, referring to the same information we have at 5% level of significance, the critical value of that statistic. In this case, we are talking about 2 by 2 table, and alpha is 5. So your critical value is 3 point. So chi squared alpha, 5% and 1 degrees of freedom.", "tokens": [407, 2199, 17108, 486, 976, 341, 1874, 13, 823, 11, 958, 472, 11, 13761, 281, 264, 912, 1589, 321, 362, 412, 1025, 4, 1496, 295, 17687, 11, 264, 4924, 2158, 295, 300, 29588, 13, 682, 341, 1389, 11, 321, 366, 1417, 466, 568, 538, 568, 3199, 11, 293, 8961, 307, 1025, 13, 407, 428, 4924, 2158, 307, 805, 935, 13, 407, 13228, 8889, 8961, 11, 1025, 4, 293, 502, 5310, 295, 5645, 13], "avg_logprob": -0.21568834499732867, "compression_ratio": 1.509433962264151, "no_speech_prob": 0.0, "words": [{"start": 2583.41, "end": 2583.65, "word": " So", "probability": 0.8779296875}, {"start": 2583.65, "end": 2583.93, "word": " simple", "probability": 0.77587890625}, {"start": 2583.93, "end": 2584.49, "word": " calculation", "probability": 0.8779296875}, {"start": 2584.49, "end": 2584.73, "word": " will", "probability": 0.875}, {"start": 2584.73, "end": 2584.93, "word": " give", "probability": 0.8837890625}, {"start": 2584.93, "end": 2585.13, 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Again, degrees of freedom of this statistic are 1, 2 by 2 is 1. Now at 5% level of significance, the conclusion is that", "tokens": [639, 307, 264, 16998, 2158, 562, 8961, 307, 1025, 8923, 370, 805, 13, 25494, 5211, 13, 3764, 11, 5310, 295, 5645, 295, 341, 29588, 366, 502, 11, 568, 538, 568, 307, 502, 13, 823, 412, 1025, 4, 1496, 295, 17687, 11, 264, 10063, 307, 300], "avg_logprob": -0.21705162751933801, "compression_ratio": 1.2571428571428571, "no_speech_prob": 0.0, "words": [{"start": 2615.0, "end": 2615.22, "word": " This", "probability": 0.6904296875}, {"start": 2615.22, "end": 2615.34, "word": " is", "probability": 0.9521484375}, {"start": 2615.34, "end": 2615.5, "word": " the", "probability": 0.91162109375}, {"start": 2615.5, "end": 2615.88, "word": " smallest", "probability": 0.9345703125}, {"start": 2615.88, "end": 2616.34, "word": " value", "probability": 0.97607421875}, {"start": 2616.34, "end": 2616.74, "word": " when", "probability": 0.89306640625}, {"start": 2616.74, "end": 2617.0, "word": " alpha", "probability": 0.6845703125}, {"start": 2617.0, "end": 2617.24, "word": " is", "probability": 0.955078125}, {"start": 2617.24, "end": 2617.92, "word": " 5%,", "probability": 0.4862060546875}, {"start": 2617.92, "end": 2618.9, "word": " so", "probability": 0.89501953125}, {"start": 2618.9, "end": 2619.22, "word": " 3", "probability": 0.93896484375}, {"start": 2619.22, "end": 2621.44, "word": ".8415.", "probability": 0.9324544270833334}, {"start": 2626.16, "end": 2626.88, "word": " Again,", "probability": 0.91064453125}, {"start": 2627.38, "end": 2627.64, "word": " degrees", "probability": 0.923828125}, {"start": 2627.64, "end": 2627.84, "word": " of", "probability": 0.96875}, {"start": 2627.84, "end": 2628.14, "word": " freedom", "probability": 0.9404296875}, {"start": 2628.14, "end": 2628.84, "word": " of", "probability": 0.95947265625}, {"start": 2628.84, "end": 2629.14, "word": " this", "probability": 0.4375}, {"start": 2629.14, "end": 2629.96, "word": " statistic", "probability": 0.8056640625}, {"start": 2629.96, "end": 2630.48, "word": " are", "probability": 0.92236328125}, {"start": 2630.48, "end": 2631.76, "word": " 1,", "probability": 0.6640625}, {"start": 2632.5, "end": 2632.84, "word": " 2", "probability": 0.9287109375}, {"start": 2632.84, "end": 2632.98, "word": " by", "probability": 0.76416015625}, {"start": 2632.98, "end": 2633.14, "word": " 2", "probability": 0.873046875}, {"start": 2633.14, "end": 2633.24, "word": " is", "probability": 0.456298828125}, {"start": 2633.24, "end": 2633.8, "word": " 1.", "probability": 0.69091796875}, {"start": 2636.38, "end": 2637.1, "word": " Now", "probability": 0.95263671875}, {"start": 2637.1, "end": 2637.42, "word": " at", "probability": 0.56884765625}, {"start": 2637.42, "end": 2637.74, "word": " 5", "probability": 0.93408203125}, {"start": 2637.74, "end": 2638.1, "word": "%", "probability": 0.94287109375}, {"start": 2638.1, "end": 2638.4, "word": " level", "probability": 0.92333984375}, {"start": 2638.4, "end": 2638.56, "word": " of", "probability": 0.9638671875}, {"start": 2638.56, "end": 2639.04, "word": " significance,", "probability": 0.96728515625}, {"start": 2640.48, "end": 2640.74, "word": " the", "probability": 0.90283203125}, {"start": 2640.74, "end": 2641.3, "word": " conclusion", "probability": 0.888671875}, {"start": 2641.3, "end": 2641.62, "word": " is", "probability": 0.943359375}, {"start": 2641.62, "end": 2641.98, "word": " that", "probability": 0.9345703125}], "temperature": 1.0}, {"id": 100, "seek": 266586, "start": 2646.84, "end": 2665.86, "text": " In this case, we reject H0. And H0 says the two variables are independent. X and Y are independent. We reject that they are independent.", "tokens": [682, 341, 1389, 11, 321, 8248, 389, 15, 13, 400, 389, 15, 1619, 264, 732, 9102, 366, 6695, 13, 1783, 293, 398, 366, 6695, 13, 492, 8248, 300, 436, 366, 6695, 13], "avg_logprob": -0.2011126893939394, "compression_ratio": 1.4421052631578948, "no_speech_prob": 0.0, "words": [{"start": 2646.8399999999997, "end": 2647.68, "word": " In", "probability": 0.27734375}, {"start": 2647.68, "end": 2648.52, "word": " this", "probability": 0.9072265625}, {"start": 2648.52, "end": 2648.84, "word": " case,", "probability": 0.9189453125}, {"start": 2649.0, "end": 2649.14, "word": " we", "probability": 0.9453125}, {"start": 2649.14, "end": 2651.9, "word": " reject", "probability": 0.8154296875}, {"start": 2651.9, "end": 2653.32, "word": " H0.", "probability": 0.794921875}, {"start": 2654.16, "end": 2654.42, "word": " And", "probability": 0.875}, {"start": 2654.42, "end": 2655.3, "word": " H0", "probability": 0.971435546875}, {"start": 2655.3, "end": 2655.78, "word": " says", "probability": 0.888671875}, {"start": 2655.78, "end": 2656.2, "word": " the", "probability": 0.689453125}, {"start": 2656.2, "end": 2656.38, "word": " two", "probability": 0.9248046875}, {"start": 2656.38, "end": 2656.84, "word": " variables", "probability": 0.95361328125}, {"start": 2656.84, "end": 2657.1, "word": " are", "probability": 0.9423828125}, {"start": 2657.1, "end": 2657.5, "word": " independent.", "probability": 0.89404296875}, {"start": 2658.56, "end": 2658.86, "word": " X", "probability": 0.9306640625}, {"start": 2658.86, "end": 2659.06, "word": " and", "probability": 0.9462890625}, {"start": 2659.06, "end": 2659.48, "word": " Y", "probability": 0.9443359375}, {"start": 2659.48, "end": 2660.8, "word": " are", "probability": 0.70654296875}, {"start": 2660.8, "end": 2660.8, "word": " independent.", "probability": 0.53759765625}, {"start": 2661.92, "end": 2662.0, "word": " We", "probability": 0.91845703125}, {"start": 2662.0, "end": 2662.4, "word": " reject", "probability": 0.9189453125}, {"start": 2662.4, "end": 2664.8, "word": " that", "probability": 0.67431640625}, {"start": 2664.8, "end": 2665.18, "word": " they", "probability": 0.8544921875}, {"start": 2665.18, "end": 2665.4, "word": " are", "probability": 0.93798828125}, {"start": 2665.4, "end": 2665.86, "word": " independent.", "probability": 0.90771484375}], "temperature": 1.0}, {"id": 101, "seek": 269438, "start": 2667.38, "end": 2694.38, "text": " That means they are dependent or related. So, A, brand awareness of female TV viewers and the gender of the spokesperson are independent. No, because we reject the null hypothesis. B, brand awareness of female TV viewers and the gender of spokesperson are not independent. Since we reject, then they are not.", "tokens": [663, 1355, 436, 366, 12334, 420, 4077, 13, 407, 11, 316, 11, 3360, 8888, 295, 6556, 3558, 8499, 293, 264, 7898, 295, 264, 45775, 366, 6695, 13, 883, 11, 570, 321, 8248, 264, 18184, 17291, 13, 363, 11, 3360, 8888, 295, 6556, 3558, 8499, 293, 264, 7898, 295, 45775, 366, 406, 6695, 13, 4162, 321, 8248, 11, 550, 436, 366, 406, 13], "avg_logprob": -0.19642857473994058, "compression_ratio": 1.9074074074074074, "no_speech_prob": 0.0, "words": [{"start": 2667.38, "end": 2667.8, "word": " That", "probability": 0.483154296875}, {"start": 2667.8, "end": 2668.1, "word": " means", "probability": 0.92236328125}, {"start": 2668.1, "end": 2668.3, "word": " they", "probability": 0.875}, {"start": 2668.3, "end": 2668.62, "word": " are", "probability": 0.92578125}, {"start": 2668.62, "end": 2669.82, "word": " dependent", "probability": 0.447265625}, {"start": 2669.82, "end": 2670.36, "word": " or", "probability": 0.91748046875}, {"start": 2670.36, "end": 2670.98, "word": " related.", "probability": 0.96728515625}, {"start": 2671.8, "end": 2672.0, "word": " So,", "probability": 0.84619140625}, {"start": 2672.94, "end": 2673.2, "word": " A,", "probability": 0.69384765625}, {"start": 2673.52, "end": 2674.04, "word": " brand", "probability": 0.76416015625}, {"start": 2674.04, "end": 2674.5, "word": " awareness", "probability": 0.85205078125}, {"start": 2674.5, "end": 2674.76, "word": " of", "probability": 0.9501953125}, {"start": 2674.76, "end": 2675.08, "word": " female", "probability": 0.8408203125}, {"start": 2675.08, "end": 2675.38, "word": " TV", "probability": 0.94384765625}, {"start": 2675.38, "end": 2676.0, "word": " viewers", "probability": 0.86865234375}, {"start": 2676.0, "end": 2676.48, "word": " and", "probability": 0.86181640625}, {"start": 2676.48, "end": 2676.68, "word": " the", "probability": 0.8544921875}, {"start": 2676.68, "end": 2677.0, "word": " gender", "probability": 0.896484375}, {"start": 2677.0, "end": 2677.24, "word": " of", "probability": 0.9677734375}, {"start": 2677.24, "end": 2677.42, "word": " the", "probability": 0.8916015625}, {"start": 2677.42, "end": 2678.04, "word": " spokesperson", "probability": 0.88427734375}, {"start": 2678.04, "end": 2679.22, "word": " are", "probability": 0.89013671875}, {"start": 2679.22, "end": 2679.68, "word": " independent.", "probability": 0.86767578125}, {"start": 2680.74, "end": 2681.38, "word": " No,", "probability": 0.921875}, {"start": 2681.58, "end": 2681.94, "word": " because", "probability": 0.900390625}, {"start": 2681.94, "end": 2682.2, "word": " we", "probability": 0.87841796875}, {"start": 2682.2, "end": 2682.98, "word": " reject", "probability": 0.85107421875}, {"start": 2682.98, "end": 2683.16, "word": " the", "probability": 0.313232421875}, {"start": 2683.16, "end": 2683.28, "word": " null", "probability": 0.95458984375}, {"start": 2683.28, "end": 2683.74, "word": " hypothesis.", "probability": 0.82861328125}, {"start": 2684.62, "end": 2684.78, "word": " B,", "probability": 0.9853515625}, {"start": 2684.88, "end": 2685.2, "word": " brand", "probability": 0.80126953125}, {"start": 2685.2, "end": 2685.76, "word": " awareness", "probability": 0.833984375}, {"start": 2685.76, "end": 2686.0, "word": " of", "probability": 0.94140625}, {"start": 2686.0, "end": 2686.44, "word": " female", "probability": 0.8720703125}, {"start": 2686.44, "end": 2686.92, "word": " TV", "probability": 0.9775390625}, {"start": 2686.92, "end": 2687.48, "word": " viewers", "probability": 0.859375}, {"start": 2687.48, "end": 2687.72, "word": " and", "probability": 0.9306640625}, {"start": 2687.72, "end": 2687.86, "word": " the", "probability": 0.89013671875}, {"start": 2687.86, "end": 2688.12, "word": " gender", "probability": 0.8876953125}, {"start": 2688.12, "end": 2688.34, "word": " of", "probability": 0.92138671875}, {"start": 2688.34, "end": 2689.0, "word": " spokesperson", "probability": 0.6181640625}, {"start": 2689.0, "end": 2689.9, "word": " are", "probability": 0.92431640625}, {"start": 2689.9, "end": 2690.2, "word": " not", "probability": 0.94482421875}, {"start": 2690.2, "end": 2690.74, "word": " independent.", "probability": 0.88037109375}, {"start": 2691.74, "end": 2692.36, "word": " Since", "probability": 0.798828125}, {"start": 2692.36, "end": 2692.58, "word": " we", "probability": 0.94384765625}, {"start": 2692.58, "end": 2693.14, "word": " reject,", "probability": 0.86376953125}, {"start": 2693.38, "end": 2693.62, "word": " then", "probability": 0.8271484375}, {"start": 2693.62, "end": 2693.8, "word": " they", "probability": 0.8779296875}, {"start": 2693.8, "end": 2694.0, "word": " are", "probability": 0.93896484375}, {"start": 2694.0, "end": 2694.38, "word": " not.", "probability": 0.94384765625}], "temperature": 1.0}, {"id": 102, "seek": 271595, "start": 2695.93, "end": 2715.95, "text": " Because it's a complement. So, B is the correct answer. Now, C. A brand awareness of female TV viewers and the gender of the spokesperson are related. The same meaning. 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D both B and C, so D is the correct answer. So again, if we reject the null hypothesis, it means the two variables either not independent or related or dependent. Any question? I will stop at this point. 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