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So B dash is called the bold estimate for the overall proportion. 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{"id": 7, "seek": 16452, "start": 138.98, "end": 164.52, "text": " So this is your Z statistic. The critical regions. I'm sorry, first, the appropriate null and alternative hypothesis are given by three cases we have. Either two-tailed test or one-tailed and it has either upper or lower tail. 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So if this is one by one smaller than by two, so the opposite by one is greater than or equal to two. Similarly, but the opposite side here, we are talking about the upper tail of probability. So under the alternative hypothesis, by one is greater than by two. 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Difference means either greater than or smaller than. So we have this not equal sign. So by one does not equal by two. Or it could be written as by one minus by two is not equal to zero. It's the same as the one we have discussed when we are talking about comparison of two population means. We just replaced these by's by mus. 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We reject the null hypothesis if the value of the test statistic fall in the rejection region, which is in the left side. So that means we reject zero if this statistic is smaller than negative zero. That's for lower tail test.", "tokens": [1045, 819, 17767, 510, 337, 264, 3126, 6838, 1500, 13, 492, 8248, 264, 18184, 17291, 498, 264, 2158, 295, 264, 1500, 29588, 2100, 294, 264, 26044, 4458, 11, 597, 307, 294, 264, 1411, 1252, 13, 407, 300, 1355, 321, 8248, 4018, 498, 341, 29588, 307, 4356, 813, 3671, 4018, 13, 663, 311, 337, 3126, 6838, 1500, 13], "avg_logprob": -0.2490570992231369, "compression_ratio": 1.6726190476190477, "no_speech_prob": 0.0, "words": [{"start": 265.9, "end": 266.32, "word": " three", "probability": 0.2379150390625}, {"start": 266.32, "end": 266.88, "word": " different", "probability": 0.8701171875}, {"start": 266.88, "end": 267.58, "word": " charts", "probability": 0.8623046875}, {"start": 267.58, "end": 267.98, "word": " here", "probability": 0.83544921875}, {"start": 267.98, "end": 269.08, "word": " for", "probability": 0.498291015625}, {"start": 269.08, "end": 269.36, "word": " the", "probability": 0.91796875}, {"start": 269.36, "end": 269.76, "word": " lower", "probability": 0.74462890625}, {"start": 269.76, "end": 270.0, "word": " tail", "probability": 0.412109375}, {"start": 270.0, "end": 271.24, "word": " test.", "probability": 0.537109375}, {"start": 272.26, "end": 272.9, "word": " We", "probability": 0.94384765625}, {"start": 272.9, "end": 273.3, "word": " reject", "probability": 0.8740234375}, {"start": 273.3, "end": 273.46, "word": " the", "probability": 0.7421875}, {"start": 273.46, "end": 273.58, "word": " null", "probability": 0.962890625}, {"start": 273.58, "end": 274.02, "word": " hypothesis", "probability": 0.9501953125}, {"start": 274.02, "end": 275.06, "word": " if", "probability": 0.88720703125}, {"start": 275.06, "end": 275.22, "word": " the", "probability": 0.9150390625}, {"start": 275.22, "end": 275.5, "word": " value", "probability": 0.9501953125}, {"start": 275.5, "end": 275.62, "word": " of", "probability": 0.94140625}, {"start": 275.62, "end": 275.76, "word": " the", "probability": 0.84228515625}, {"start": 275.76, "end": 275.96, "word": " test", "probability": 0.77294921875}, {"start": 275.96, "end": 276.4, "word": " statistic", "probability": 0.8603515625}, {"start": 276.4, "end": 276.86, "word": " fall", "probability": 0.673828125}, {"start": 276.86, "end": 277.04, "word": " in", "probability": 0.90869140625}, {"start": 277.04, "end": 277.14, "word": " the", "probability": 0.91845703125}, {"start": 277.14, "end": 277.5, "word": " rejection", "probability": 0.96142578125}, {"start": 277.5, "end": 277.96, "word": " region,", "probability": 0.9208984375}, {"start": 278.26, "end": 278.68, "word": " which", "probability": 0.9228515625}, {"start": 278.68, "end": 278.82, "word": " is", "probability": 0.94091796875}, {"start": 278.82, "end": 278.94, "word": " in", "probability": 0.477783203125}, {"start": 278.94, "end": 279.04, "word": " the", "probability": 0.9130859375}, {"start": 279.04, "end": 279.28, "word": " left", "probability": 0.95361328125}, {"start": 279.28, "end": 279.74, "word": " side.", "probability": 0.8544921875}, {"start": 280.22, "end": 280.42, "word": " So", "probability": 0.9404296875}, {"start": 280.42, "end": 280.62, "word": " that", "probability": 0.857421875}, {"start": 280.62, "end": 280.94, "word": " means", "probability": 0.939453125}, {"start": 280.94, "end": 281.1, "word": " we", "probability": 0.8779296875}, {"start": 281.1, "end": 281.42, "word": " reject", "probability": 0.78369140625}, {"start": 281.42, "end": 281.88, "word": " zero", "probability": 0.461181640625}, {"start": 281.88, "end": 282.56, "word": " if", "probability": 0.837890625}, {"start": 282.56, "end": 282.72, "word": " this", "probability": 0.50732421875}, {"start": 282.72, "end": 283.14, "word": " statistic", "probability": 0.873046875}, {"start": 283.14, "end": 283.46, "word": " is", "probability": 0.94482421875}, {"start": 283.46, "end": 283.78, "word": " smaller", "probability": 0.869140625}, {"start": 283.78, "end": 284.04, "word": " than", "probability": 0.93994140625}, {"start": 284.04, "end": 284.4, "word": " negative", "probability": 0.8232421875}, {"start": 284.4, "end": 284.62, "word": " zero.", "probability": 0.2783203125}, {"start": 285.36, "end": 286.0, "word": " That's", "probability": 0.935791015625}, {"start": 286.0, "end": 286.38, "word": " for", "probability": 0.93310546875}, {"start": 286.38, "end": 286.98, "word": " lower", "probability": 0.81005859375}, {"start": 286.98, "end": 287.3, "word": " tail", "probability": 0.52197265625}, {"start": 287.3, "end": 287.62, "word": " test.", "probability": 0.77001953125}], "temperature": 1.0}, {"id": 13, "seek": 31744, "start": 289.08, "end": 317.44, "text": " On the other hand, for other tailed tests, your rejection region is the right side, so you reject the null hypothesis if this statistic is greater than Z alpha. In addition, for two-tailed tests, there are two rejection regions. One is on the right side, the other on the left side. Here, alpha is split into two halves, alpha over two to the right, similarly alpha over two to the left side. Here, we reject the null hypothesis if your Z statistic", "tokens": [1282, 264, 661, 1011, 11, 337, 661, 6838, 292, 6921, 11, 428, 26044, 4458, 307, 264, 558, 1252, 11, 370, 291, 8248, 264, 18184, 17291, 498, 341, 29588, 307, 5044, 813, 1176, 8961, 13, 682, 4500, 11, 337, 732, 12, 14430, 292, 6921, 11, 456, 366, 732, 26044, 10682, 13, 1485, 307, 322, 264, 558, 1252, 11, 264, 661, 322, 264, 1411, 1252, 13, 1692, 11, 8961, 307, 7472, 666, 732, 38490, 11, 8961, 670, 732, 281, 264, 558, 11, 14138, 8961, 670, 732, 281, 264, 1411, 1252, 13, 1692, 11, 321, 8248, 264, 18184, 17291, 498, 428, 1176, 29588], "avg_logprob": -0.23174504242321053, "compression_ratio": 2.1179245283018866, "no_speech_prob": 0.0, "words": [{"start": 289.08, "end": 289.32, "word": " On", "probability": 0.875}, {"start": 289.32, "end": 289.44, "word": " the", "probability": 0.9189453125}, {"start": 289.44, "end": 289.62, "word": " other", "probability": 0.8896484375}, {"start": 289.62, "end": 289.94, "word": " hand,", 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Now this one, I mean the rejection regions are the same for either one sample t-test or two sample t-test, either for the population proportion or the population mean. We have the same", "tokens": [8804, 294, 264, 26044, 4458, 510, 11, 300, 1355, 710, 307, 4356, 813, 3671, 710, 8961, 670, 568, 420, 710, 307, 5044, 813, 710, 8961, 670, 568, 13, 823, 341, 472, 11, 286, 914, 264, 26044, 10682, 366, 264, 912, 337, 2139, 472, 6889, 256, 12, 31636, 420, 732, 6889, 256, 12, 31636, 11, 2139, 337, 264, 4415, 16068, 420, 264, 4415, 914, 13, 492, 362, 264, 912], "avg_logprob": -0.2259963794031005, "compression_ratio": 1.8734939759036144, "no_speech_prob": 0.0, "words": [{"start": 318.16, "end": 318.6, "word": " falls", "probability": 0.1778564453125}, {"start": 318.6, "end": 318.88, "word": " in", "probability": 0.865234375}, {"start": 318.88, "end": 319.02, "word": " the", "probability": 0.8798828125}, {"start": 319.02, "end": 319.32, "word": " rejection", "probability": 0.92919921875}, {"start": 319.32, "end": 319.74, "word": " region", "probability": 0.9150390625}, {"start": 319.74, "end": 320.06, "word": " here,", "probability": 0.80859375}, {"start": 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Sometimes we replace z by t. It depends if we are talking about small samples and sigmas unknown. So that's the basic concepts about testing or hypothesis testing for the comparison between two population proportions. And we stopped at this point. I will give three examples, three examples for testing about two population proportions. The first one is given here.", "tokens": [26044, 10682, 13, 4803, 321, 7406, 710, 538, 256, 13, 467, 5946, 498, 321, 366, 1417, 466, 1359, 10938, 293, 4556, 3799, 9841, 13, 407, 300, 311, 264, 3875, 10392, 466, 4997, 420, 17291, 4997, 337, 264, 9660, 1296, 732, 4415, 32482, 13, 400, 321, 5936, 412, 341, 935, 13, 286, 486, 976, 1045, 5110, 11, 1045, 5110, 337, 4997, 466, 732, 4415, 32482, 13, 440, 700, 472, 307, 2212, 510, 13], "avg_logprob": -0.18161387149601765, "compression_ratio": 1.7035398230088497, "no_speech_prob": 0.0, "words": [{"start": 343.96, "end": 344.5, "word": " rejection", "probability": 0.351318359375}, {"start": 344.5, "end": 345.1, "word": " regions.", "probability": 0.9404296875}, {"start": 345.42, "end": 345.9, "word": " Sometimes", "probability": 0.91552734375}, {"start": 345.9, "end": 346.12, "word": " we", "probability": 0.77978515625}, {"start": 346.12, "end": 346.52, "word": " replace", "probability": 0.89404296875}, {"start": 346.52, "end": 346.76, "word": " z", "probability": 0.580078125}, {"start": 346.76, "end": 346.98, "word": " by", "probability": 0.96142578125}, {"start": 346.98, "end": 347.24, "word": " t.", "probability": 0.8828125}, {"start": 347.68, "end": 347.88, "word": " It", "probability": 0.94873046875}, {"start": 347.88, "end": 348.32, "word": " depends", "probability": 0.916015625}, {"start": 348.32, "end": 348.84, "word": " if", "probability": 0.89794921875}, {"start": 348.84, "end": 348.96, "word": " we", "probability": 0.94677734375}, {"start": 348.96, "end": 349.08, "word": " are", "probability": 0.9326171875}, {"start": 349.08, "end": 349.38, "word": " talking", "probability": 0.83154296875}, {"start": 349.38, "end": 349.8, "word": " about", "probability": 0.89697265625}, {"start": 349.8, "end": 350.48, "word": " small", "probability": 0.8701171875}, {"start": 350.48, "end": 350.9, "word": " samples", "probability": 0.334716796875}, {"start": 350.9, "end": 351.22, "word": " and", "probability": 0.880859375}, {"start": 351.22, "end": 351.7, "word": " sigmas", "probability": 0.7032470703125}, {"start": 351.7, "end": 352.5, "word": " unknown.", "probability": 0.70703125}, {"start": 354.06, "end": 354.38, "word": " So", "probability": 0.9345703125}, {"start": 354.38, "end": 354.64, "word": " that's", "probability": 0.903564453125}, {"start": 354.64, "end": 354.76, "word": " the", "probability": 0.91796875}, {"start": 354.76, "end": 355.02, "word": " basic", "probability": 0.9658203125}, {"start": 355.02, "end": 355.64, "word": " concepts", "probability": 0.75244140625}, {"start": 355.64, "end": 356.2, "word": " about", "probability": 0.9072265625}, {"start": 356.2, "end": 356.94, "word": " testing", "probability": 0.75732421875}, {"start": 356.94, "end": 357.24, "word": " or", "probability": 0.6533203125}, {"start": 357.24, "end": 357.7, "word": " hypothesis", "probability": 0.86474609375}, {"start": 357.7, "end": 358.16, "word": " testing", "probability": 0.857421875}, {"start": 358.16, "end": 358.54, 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"probability": 0.91845703125}, {"start": 364.84, "end": 365.02, "word": " I", "probability": 0.9970703125}, {"start": 365.02, "end": 365.14, "word": " will", "probability": 0.88671875}, {"start": 365.14, "end": 365.36, "word": " give", "probability": 0.87841796875}, {"start": 365.36, "end": 365.6, "word": " three", "probability": 0.91162109375}, {"start": 365.6, "end": 366.16, "word": " examples,", "probability": 0.84521484375}, {"start": 366.3, "end": 366.6, "word": " three", "probability": 0.90869140625}, {"start": 366.6, "end": 367.04, "word": " examples", "probability": 0.85546875}, {"start": 367.04, "end": 367.5, "word": " for", "probability": 0.85205078125}, {"start": 367.5, "end": 368.78, "word": " testing", "probability": 0.82275390625}, {"start": 368.78, "end": 369.26, "word": " about", "probability": 0.9052734375}, {"start": 369.26, "end": 369.64, "word": " two", "probability": 0.91943359375}, {"start": 369.64, "end": 370.14, "word": " population", "probability": 0.85693359375}, {"start": 370.14, "end": 370.7, "word": " proportions.", "probability": 0.74169921875}, {"start": 370.92, "end": 371.06, "word": " The", "probability": 0.87060546875}, {"start": 371.06, "end": 371.34, "word": " first", "probability": 0.88525390625}, {"start": 371.34, "end": 371.52, "word": " one", "probability": 0.9248046875}, {"start": 371.52, "end": 371.66, "word": " is", "probability": 0.9443359375}, {"start": 371.66, "end": 371.9, "word": " given", "probability": 0.88427734375}, {"start": 371.9, "end": 372.26, "word": " here.", "probability": 0.85595703125}], "temperature": 1.0}, {"id": 16, "seek": 38463, "start": 373.09, "end": 384.63, "text": " It says that, is there a significant difference between the proportion of men and the proportion of women who will vote yes on a proposition?", "tokens": [467, 1619, 300, 11, 307, 456, 257, 4776, 2649, 1296, 264, 16068, 295, 1706, 293, 264, 16068, 295, 2266, 567, 486, 4740, 2086, 322, 257, 24830, 30], "avg_logprob": 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a", "probability": 0.76904296875}, {"start": 384.17, "end": 384.63, "word": " proposition?", "probability": 0.8837890625}], "temperature": 1.0}, {"id": 17, "seek": 41572, "start": 388.22, "end": 415.72, "text": " In this case, we are talking about a proportion. So this problem tests for a proportion. We have two proportions here because we have two samples for two population spheres, men and women. So there are two populations. So we are talking about two population proportions. Now, we have to state carefully now an alternative hypothesis. So for example, let's say that phi 1", "tokens": [682, 341, 1389, 11, 321, 366, 1417, 466, 257, 16068, 13, 407, 341, 1154, 6921, 337, 257, 16068, 13, 492, 362, 732, 32482, 510, 570, 321, 362, 732, 10938, 337, 732, 4415, 41225, 11, 1706, 293, 2266, 13, 407, 456, 366, 732, 12822, 13, 407, 321, 366, 1417, 466, 732, 4415, 32482, 13, 823, 11, 321, 362, 281, 1785, 7500, 586, 364, 8535, 17291, 13, 407, 337, 1365, 11, 718, 311, 584, 300, 13107, 502], "avg_logprob": -0.2002467107223837, "compression_ratio": 1.8366336633663367, "no_speech_prob": 0.0, "words": [{"start": 388.22, "end": 388.5, "word": " In", "probability": 0.87548828125}, {"start": 388.5, "end": 388.8, "word": " this", "probability": 0.94775390625}, {"start": 388.8, "end": 389.08, "word": " case,", "probability": 0.9169921875}, {"start": 389.14, "end": 389.22, "word": " we", "probability": 0.9599609375}, {"start": 389.22, "end": 389.34, "word": " are", "probability": 0.91748046875}, {"start": 389.34, "end": 389.66, "word": " 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{"start": 412.02, "end": 412.54, "word": " hypothesis.", "probability": 0.85009765625}, {"start": 413.02, "end": 413.22, "word": " So", "probability": 0.95751953125}, {"start": 413.22, "end": 413.44, "word": " for", "probability": 0.77685546875}, {"start": 413.44, "end": 413.78, "word": " example,", "probability": 0.97607421875}, {"start": 413.88, "end": 414.32, "word": " let's", "probability": 0.96728515625}, {"start": 414.32, "end": 414.7, "word": " say", "probability": 0.9033203125}, {"start": 414.7, "end": 415.08, "word": " that", "probability": 0.88134765625}, {"start": 415.08, "end": 415.44, "word": " phi", "probability": 0.65869140625}, {"start": 415.44, "end": 415.72, "word": " 1", "probability": 0.86083984375}], "temperature": 1.0}, {"id": 18, "seek": 43330, "start": 416.74, "end": 433.3, "text": " is the population proportion, proportion of men who will vote for a proposition A for example, for vote yes, for vote yes for proposition A.", "tokens": [307, 264, 4415, 16068, 11, 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So the first one for men and the other of women. 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Difference means two tails. So it should be pi 1 does not equal pi 2. Pi 1 does not equal pi 2. So there's still one state null and alternate hypothesis. 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So for example, if X1 represents number of men who would vote yes, that means X1 equals 36 in 172. So that's for men. Now for women.", "tokens": [400, 10353, 295, 2625, 2266, 16176, 436, 576, 4740, 2086, 13, 407, 337, 1365, 11, 498, 1783, 16, 8855, 1230, 295, 1706, 567, 576, 4740, 2086, 11, 300, 1355, 1783, 16, 6915, 8652, 294, 3282, 17, 13, 407, 300, 311, 337, 1706, 13, 823, 337, 2266, 13], "avg_logprob": -0.21435546781867743, "compression_ratio": 1.326086956521739, "no_speech_prob": 0.0, "words": [{"start": 506.06, "end": 506.42, "word": " And", "probability": 0.370849609375}, {"start": 506.42, "end": 506.9, "word": " 31", "probability": 0.6982421875}, {"start": 506.9, "end": 507.42, "word": " of", "probability": 0.6005859375}, {"start": 507.42, "end": 507.86, "word": " 50", "probability": 0.94580078125}, {"start": 507.86, "end": 508.22, "word": " women", "probability": 0.8974609375}, {"start": 508.22, "end": 508.88, "word": " indicated", "probability": 0.82666015625}, {"start": 508.88, "end": 509.16, "word": " they", "probability": 0.8427734375}, {"start": 509.16, "end": 509.36, "word": " would", "probability": 0.904296875}, {"start": 509.36, "end": 509.68, "word": " vote", "probability": 0.912109375}, {"start": 509.68, "end": 510.06, "word": " yes.", "probability": 0.5146484375}, {"start": 510.72, "end": 511.48, "word": " So", "probability": 0.7138671875}, {"start": 511.48, "end": 511.74, "word": " for", "probability": 0.64111328125}, {"start": 511.74, "end": 512.06, "word": " example,", "probability": 0.97705078125}, {"start": 512.16, "end": 512.3, "word": " if", "probability": 0.9423828125}, {"start": 512.3, "end": 513.38, "word": " X1", "probability": 0.719970703125}, {"start": 513.38, "end": 514.2, "word": " represents", "probability": 0.86474609375}, {"start": 514.2, "end": 514.64, "word": " number", "probability": 0.7421875}, {"start": 514.64, "end": 514.96, "word": " of", "probability": 0.97119140625}, {"start": 514.96, "end": 515.66, "word": " men", "probability": 0.7578125}, {"start": 515.66, "end": 516.94, "word": " who", "probability": 0.82763671875}, {"start": 516.94, "end": 517.8, "word": " would", "probability": 0.91162109375}, {"start": 517.8, "end": 518.1, "word": " vote", "probability": 0.90234375}, {"start": 518.1, "end": 518.54, "word": " yes,", "probability": 0.9453125}, {"start": 518.7, "end": 519.0, "word": " that", "probability": 0.91748046875}, {"start": 519.0, "end": 519.26, "word": " means", "probability": 0.93017578125}, {"start": 519.26, "end": 519.72, "word": " X1", "probability": 0.95947265625}, {"start": 519.72, "end": 520.22, "word": " equals", "probability": 0.84033203125}, {"start": 520.22, "end": 521.82, "word": " 36", "probability": 0.966796875}, {"start": 521.82, "end": 525.72, "word": " in", "probability": 0.471923828125}, {"start": 525.72, "end": 526.48, "word": " 172.", "probability": 0.911865234375}, {"start": 527.66, "end": 528.42, "word": " So", "probability": 0.94287109375}, {"start": 528.42, "end": 528.68, "word": " that's", "probability": 0.95361328125}, {"start": 528.68, "end": 528.84, "word": " for", "probability": 0.91552734375}, {"start": 528.84, "end": 529.08, "word": " men.", "probability": 0.94580078125}, {"start": 530.8, "end": 531.22, "word": " Now", "probability": 0.85205078125}, {"start": 531.22, "end": 531.46, "word": " for", "probability": 0.70703125}, {"start": 531.46, "end": 531.8, "word": " women.", "probability": 0.90869140625}], "temperature": 1.0}, {"id": 22, "seek": 56107, "start": 532.59, "end": 561.07, "text": " 31 out of 50. So 50 is the sample size for the second sample. Now it's ask about this test about the difference between the two population proportion at 5% level of significance. So alpha is given to be 5%. 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statement, we state null and alternative hypothesis. Now based on this information, we can solve the problem by using three different approaches. Critical value approach, B value, and confidence interval approach. Because we can use confidence interval approach because we are talking about two-tailed test. So let's start with the basic one, critical value approach. 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Or just if you remember that values from previous time. So the critical regions are above 196 or smaller than negative 196. I have to compute the Z statistic. Now Z statistic is given by this equation. 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This quantity divided by P dash 1 minus P dash multiplied by 1 over N1 plus 1 over N1. Here we have to find B1, B2. So B1 equals X1 over N1. 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Similarly, B2 is A equals X2 over into X to the third power over 50, so that's 60%. 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X1 and X2. 36 plus 31. Over 72 plus 7. 72 plus 7. So that means 67 over 152.549. 120.", "tokens": [708, 366, 264, 6889, 11602, 321, 362, 30, 1783, 16, 293, 1783, 17, 13, 8652, 1804, 10353, 13, 4886, 18731, 1804, 1614, 13, 18731, 1804, 1614, 13, 407, 300, 1355, 23879, 670, 2119, 17, 13, 20, 14938, 13, 10411, 13], "avg_logprob": -0.3313643176381181, "compression_ratio": 1.1308411214953271, "no_speech_prob": 0.0, "words": [{"start": 721.89, "end": 721.95, "word": " What", "probability": 0.08160400390625}, {"start": 721.95, "end": 722.09, "word": " are", "probability": 0.456787109375}, {"start": 722.09, "end": 722.19, "word": " the", "probability": 0.7021484375}, {"start": 722.19, "end": 722.39, "word": " sample", "probability": 0.88916015625}, {"start": 722.39, "end": 722.83, "word": " sizes", "probability": 0.8994140625}, {"start": 722.83, "end": 723.05, "word": " we", "probability": 0.85400390625}, {"start": 723.05, "end": 723.31, "word": " have?", "probability": 0.91796875}, {"start": 724.57, "end": 725.49, "word": " X1", "probability": 0.714599609375}, {"start": 725.49, "end": 725.67, "word": " and", "probability": 0.92626953125}, {"start": 725.67, "end": 726.13, "word": " X2.", "probability": 0.84619140625}, {"start": 726.21, "end": 727.13, "word": " 36", "probability": 0.7626953125}, {"start": 727.13, "end": 727.71, "word": " plus", "probability": 0.86328125}, {"start": 727.71, "end": 728.33, "word": " 31.", "probability": 0.9638671875}, {"start": 729.19, "end": 729.71, "word": " Over", "probability": 0.38720703125}, {"start": 729.71, "end": 730.23, "word": " 72", "probability": 0.64306640625}, {"start": 730.23, "end": 730.75, "word": " plus", "probability": 0.9228515625}, {"start": 730.75, "end": 731.11, "word": " 7.", "probability": 0.5576171875}, {"start": 731.41, "end": 731.99, "word": " 72", "probability": 0.74072265625}, {"start": 731.99, "end": 732.29, "word": " plus", "probability": 0.95263671875}, {"start": 732.29, "end": 732.73, "word": " 7.", "probability": 0.95556640625}, {"start": 733.49, "end": 734.13, "word": " So", "probability": 0.9169921875}, {"start": 734.13, "end": 734.35, "word": " that", "probability": 0.82763671875}, {"start": 734.35, "end": 734.55, "word": " means", "probability": 0.890625}, {"start": 734.55, "end": 735.21, "word": " 67", "probability": 0.85595703125}, {"start": 735.21, "end": 735.95, "word": " over", "probability": 0.90087890625}, {"start": 735.95, "end": 736.83, "word": " 152", "probability": 0.948974609375}, {"start": 736.83, "end": 742.31, "word": ".549.", "probability": 0.5545247395833334}, {"start": 744.69, "end": 745.61, "word": " 120.", "probability": 0.75634765625}], "temperature": 1.0}, {"id": 29, "seek": 77036, "start": 750.4, "end": 770.36, "text": " So simple calculations give B1 and B2, as well as B dash. Now, plug these values on the Z-state formula, we get the value that is this. So first, state null and alternative hypothesis, pi 1 minus pi 2 equals 0. 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That means there is a significant difference between proportions. Now for men, we got proportion of 50%. That's for the similar proportion. And similar proportion for women who will vote yes for position A is 62%. The pooled estimate for the overall proportion equals 0.549.", "tokens": [492, 366, 516, 281, 1500, 341, 472, 1970, 17741, 502, 3175, 17741, 568, 307, 406, 4018, 13, 663, 1355, 456, 307, 257, 4776, 2649, 1296, 32482, 13, 823, 337, 1706, 11, 321, 658, 16068, 295, 2625, 6856, 663, 311, 337, 264, 2531, 16068, 13, 400, 2531, 16068, 337, 2266, 567, 486, 4740, 2086, 337, 2535, 316, 307, 24536, 6856, 440, 7005, 292, 12539, 337, 264, 4787, 16068, 6915, 1958, 13, 20, 14938, 13], "avg_logprob": -0.2106207820612031, "compression_ratio": 1.5981308411214954, "no_speech_prob": 0.0, "words": [{"start": 771.69, "end": 771.91, "word": " We", "probability": 0.7314453125}, {"start": 771.91, "end": 772.05, "word": " are", "probability": 0.900390625}, {"start": 772.05, "end": 772.27, "word": " going", "probability": 0.9443359375}, {"start": 772.27, "end": 772.47, "word": " to", "probability": 0.96435546875}, {"start": 772.47, "end": 772.79, "word": " test", "probability": 0.87548828125}, {"start": 772.79, 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Straightforward calculation, you will end with this result. So, Z start negative 1.31. So, we have to compute this one before either before using any of the approaches we have.", "tokens": [823, 11, 2361, 322, 341, 1589, 11, 321, 393, 8873, 264, 1176, 29588, 13, 26908, 13305, 17108, 11, 291, 486, 917, 365, 341, 1874, 13, 407, 11, 1176, 3543, 83, 3671, 502, 13, 12967, 13, 407, 11, 321, 362, 281, 14722, 341, 472, 949, 2139, 949, 1228, 604, 295, 264, 11587, 321, 362, 13], "avg_logprob": -0.30937499024651266, "compression_ratio": 1.5, "no_speech_prob": 0.0, "words": [{"start": 801.61, "end": 801.91, "word": " Now,", "probability": 0.51318359375}, {"start": 802.05, "end": 802.37, "word": " based", "probability": 0.90869140625}, {"start": 802.37, "end": 802.65, "word": " on", "probability": 0.95166015625}, {"start": 802.65, "end": 803.07, "word": " this", "probability": 0.93408203125}, {"start": 803.07, "end": 804.11, "word": " information,", "probability": 0.82666015625}, {"start": 804.23, "end": 804.35, "word": " we", "probability": 0.865234375}, {"start": 804.35, "end": 804.53, "word": " can", "probability": 0.9365234375}, {"start": 804.53, "end": 805.05, "word": " calculate", "probability": 0.90087890625}, {"start": 805.05, "end": 805.27, "word": " the", "probability": 0.63818359375}, {"start": 805.27, "end": 805.41, "word": " Z", "probability": 0.52001953125}, {"start": 805.41, "end": 806.01, "word": " statistic.", "probability": 0.6904296875}, {"start": 806.93, "end": 807.61, "word": " Straightforward", "probability": 0.620361328125}, {"start": 807.61, "end": 808.35, "word": " calculation,", "probability": 0.94189453125}, {"start": 809.59, "end": 809.93, "word": " you", "probability": 0.91357421875}, {"start": 809.93, "end": 810.11, "word": " will", "probability": 0.88818359375}, {"start": 810.11, "end": 810.43, "word": " end", "probability": 0.90380859375}, {"start": 810.43, "end": 810.97, "word": " with", "probability": 0.7216796875}, {"start": 810.97, "end": 811.29, "word": " this", "probability": 0.9453125}, {"start": 811.29, "end": 811.67, "word": " result.", "probability": 0.93017578125}, {"start": 812.85, "end": 813.23, "word": " So,", "probability": 0.92578125}, {"start": 813.41, "end": 813.47, "word": " Z", "probability": 0.7919921875}, {"start": 813.47, "end": 814.05, "word": " start", "probability": 0.29986572265625}, {"start": 814.05, "end": 816.57, "word": " negative", "probability": 0.46337890625}, {"start": 816.57, "end": 818.39, "word": " 1", "probability": 0.60009765625}, {"start": 818.39, "end": 819.35, "word": ".31.", "probability": 0.907958984375}, {"start": 821.79, "end": 822.47, "word": " So,", "probability": 0.89208984375}, {"start": 822.55, "end": 822.65, "word": " we", "probability": 0.94384765625}, {"start": 822.65, "end": 822.97, "word": " have", "probability": 0.94775390625}, {"start": 822.97, "end": 823.13, "word": " to", "probability": 0.97119140625}, {"start": 823.13, "end": 823.49, "word": " compute", "probability": 0.91943359375}, {"start": 823.49, "end": 823.83, "word": " this", "probability": 0.94921875}, {"start": 823.83, "end": 824.11, "word": " one", "probability": 0.9296875}, {"start": 824.11, "end": 824.51, "word": " before", "probability": 0.595703125}, {"start": 824.51, "end": 824.95, "word": " either", "probability": 0.64013671875}, {"start": 824.95, "end": 825.53, "word": " before", "probability": 0.409423828125}, {"start": 825.53, "end": 826.07, "word": " using", "probability": 0.83203125}, {"start": 826.07, "end": 826.53, "word": " any", "probability": 0.87548828125}, {"start": 826.53, "end": 826.69, "word": " of", "probability": 0.95703125}, {"start": 826.69, "end": 826.83, "word": " the", "probability": 0.8671875}, {"start": 826.83, "end": 827.13, "word": " approaches", "probability": 0.5380859375}, {"start": 827.13, "end": 827.43, "word": " we", "probability": 0.8203125}, {"start": 827.43, "end": 827.65, "word": " have.", "probability": 0.73193359375}], "temperature": 1.0}, {"id": 32, "seek": 84372, "start": 830.94, "end": 843.72, "text": " If we are going to use their critical value approach, we have to find Z alpha over 2 which is 1 more than 6. 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So my decision is don't reject H0. My conclusion is there is not significant evidence of a difference in proportions who will vote yes between men and women. Even it seems to me that there is a difference between", "tokens": [309, 311, 1850, 300, 341, 2158, 11, 3671, 502, 13, 12967, 11, 9134, 294, 264, 2107, 12, 265, 1020, 313, 4458, 11, 370, 321, 500, 380, 8248, 257, 18184, 17291, 13, 407, 452, 3537, 307, 500, 380, 8248, 389, 15, 13, 1222, 10063, 307, 456, 307, 406, 4776, 4467, 295, 257, 2649, 294, 32482, 567, 486, 4740, 2086, 1296, 1706, 293, 2266, 13, 2754, 309, 2544, 281, 385, 300, 456, 307, 257, 2649, 1296], "avg_logprob": -0.17156249284744263, "compression_ratio": 1.569377990430622, "no_speech_prob": 0.0, "words": [{"start": 844.74, "end": 845.14, "word": " it's", "probability": 0.7017822265625}, {"start": 845.14, "end": 845.46, "word": " clear", "probability": 0.89013671875}, {"start": 845.46, "end": 845.76, "word": " that", "probability": 0.93408203125}, {"start": 845.76, "end": 846.1, "word": " this", "probability": 0.94091796875}, {"start": 846.1, "end": 846.5, "word": " value,", "probability": 0.98193359375}, {"start": 846.86, 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Still, this difference is not significant in order to say that there is significant difference between the proportions of men and women. So based on the critical value approach.", "tokens": [10905, 32482, 11, 2625, 4, 293, 24536, 6856, 8291, 11, 341, 2649, 307, 406, 4776, 294, 1668, 281, 584, 300, 456, 307, 4776, 2649, 1296, 264, 32482, 295, 1706, 293, 2266, 13, 407, 2361, 322, 264, 4924, 2158, 3109, 13], "avg_logprob": -0.2202743873363588, "compression_ratio": 1.4825174825174825, "no_speech_prob": 0.0, "words": [{"start": 873.43, "end": 873.95, "word": " Similar", "probability": 0.099365234375}, {"start": 873.95, "end": 874.55, "word": " proportions,", "probability": 0.86376953125}, {"start": 874.79, "end": 875.05, "word": " 50", "probability": 0.93701171875}, {"start": 875.05, "end": 875.09, "word": "%", "probability": 0.5048828125}, {"start": 875.09, "end": 875.23, "word": " and", "probability": 0.94873046875}, {"start": 875.23, "end": 876.11, "word": " 62%.", "probability": 0.738525390625}, {"start": 876.11, "end": 877.29, "word": " Still,", "probability": 0.6328125}, {"start": 877.49, "end": 877.63, "word": " this", "probability": 0.94287109375}, {"start": 877.63, "end": 877.99, "word": " difference", "probability": 0.892578125}, {"start": 877.99, "end": 878.17, "word": " is", "probability": 0.927734375}, {"start": 878.17, "end": 878.29, "word": " not", "probability": 0.947265625}, {"start": 878.29, "end": 878.91, "word": " significant", "probability": 0.85791015625}, {"start": 878.91, "end": 879.27, "word": " in", "probability": 0.67919921875}, {"start": 879.27, "end": 879.47, "word": " order", "probability": 0.923828125}, {"start": 879.47, "end": 879.75, "word": " to", "probability": 0.97119140625}, {"start": 879.75, "end": 879.99, "word": " say", "probability": 0.7255859375}, {"start": 879.99, "end": 881.17, "word": " that", "probability": 0.85888671875}, {"start": 881.17, "end": 881.49, "word": " there", "probability": 0.9140625}, {"start": 881.49, "end": 881.67, "word": " is", "probability": 0.92724609375}, {"start": 881.67, "end": 882.35, "word": " significant", "probability": 0.7734375}, {"start": 882.35, "end": 882.83, "word": " difference", "probability": 0.8642578125}, {"start": 882.83, "end": 883.27, "word": " between", "probability": 0.85546875}, {"start": 883.27, "end": 883.95, "word": " the", "probability": 0.78173828125}, {"start": 883.95, "end": 884.41, "word": " proportions", "probability": 0.85400390625}, {"start": 884.41, "end": 884.73, "word": " of", "probability": 0.966796875}, {"start": 884.73, "end": 885.21, "word": " men", "probability": 0.962890625}, {"start": 885.21, "end": 885.87, "word": " and", "probability": 0.943359375}, {"start": 885.87, "end": 886.55, "word": " women.", "probability": 0.90234375}, {"start": 887.25, "end": 887.47, "word": " So", "probability": 0.90966796875}, {"start": 887.47, "end": 887.83, "word": " based", "probability": 0.72607421875}, {"start": 887.83, "end": 888.33, "word": " on", "probability": 0.947265625}, {"start": 888.33, "end": 888.71, "word": " the", "probability": 0.8955078125}, {"start": 888.71, "end": 889.07, "word": " critical", "probability": 0.8818359375}, {"start": 889.07, "end": 889.39, "word": " value", "probability": 0.96484375}, {"start": 889.39, "end": 889.73, "word": " approach.", "probability": 0.90380859375}], "temperature": 1.0}, {"id": 35, "seek": 91820, "start": 890.58, "end": 918.2, "text": " We end with this result, which is we don't reject null hypotheses. That means the information you have is not sufficient in order to support alternative hypotheses. So your managerial conclusion should be there is not significant difference in proportion and proportions who will vote yes between men and women. That's for using critical value approach.", "tokens": [492, 917, 365, 341, 1874, 11, 597, 307, 321, 500, 380, 8248, 18184, 49969, 13, 663, 1355, 264, 1589, 291, 362, 307, 406, 11563, 294, 1668, 281, 1406, 8535, 49969, 13, 407, 428, 6598, 831, 10063, 820, 312, 456, 307, 406, 4776, 2649, 294, 16068, 293, 32482, 567, 486, 4740, 2086, 1296, 1706, 293, 2266, 13, 663, 311, 337, 1228, 4924, 2158, 3109, 13], "avg_logprob": -0.17704326923076924, "compression_ratio": 1.6090909090909091, "no_speech_prob": 0.0, "words": [{"start": 890.58, "end": 890.9, "word": " We", "probability": 0.440185546875}, {"start": 890.9, "end": 891.16, "word": " end", "probability": 0.90869140625}, {"start": 891.16, "end": 891.34, "word": " with", "probability": 0.8837890625}, {"start": 891.34, "end": 891.58, "word": " this", "probability": 0.94140625}, {"start": 891.58, "end": 892.02, "word": " result,", "probability": 0.94384765625}, {"start": 892.18, "end": 892.34, "word": " which", "probability": 0.9462890625}, 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The confidence interval, as we mentioned before, can be constructed by point estimate, plus or minus critical value times the standard error of the point estimate.", "tokens": [4546, 2354, 11, 321, 362, 281, 2248, 264, 6687, 15035, 337, 264, 2649, 3895, 502, 3175, 3895, 568, 13, 440, 6687, 15035, 11, 382, 321, 2835, 949, 11, 393, 312, 17083, 538, 935, 12539, 11, 1804, 420, 3175, 4924, 2158, 1413, 264, 3832, 6713, 295, 264, 935, 12539, 13], "avg_logprob": -0.151093747317791, "compression_ratio": 1.6352201257861636, "no_speech_prob": 0.0, "words": [{"start": 919.77, "end": 920.29, "word": " Before", "probability": 0.86767578125}, {"start": 920.29, "end": 920.83, "word": " continue,", "probability": 0.54248046875}, {"start": 921.01, "end": 921.13, "word": " we", "probability": 0.9580078125}, {"start": 921.13, "end": 921.35, "word": " have", "probability": 0.9453125}, {"start": 921.35, "end": 921.51, "word": " to", "probability": 0.970703125}, {"start": 921.51, "end": 922.09, "word": " discuss", "probability": 0.89892578125}, {"start": 922.09, "end": 922.39, "word": " the", "probability": 0.87548828125}, {"start": 922.39, "end": 922.89, "word": " confidence", "probability": 0.9677734375}, {"start": 922.89, "end": 923.45, "word": " interval", "probability": 0.958984375}, {"start": 923.45, "end": 924.73, "word": " for", "probability": 0.88232421875}, {"start": 924.73, "end": 924.93, "word": " the", "probability": 0.91650390625}, {"start": 924.93, "end": 925.49, "word": " difference", "probability": 0.82373046875}, {"start": 925.49, "end": 925.85, "word": " pi", "probability": 0.54345703125}, {"start": 925.85, "end": 926.05, "word": " 1", "probability": 0.484375}, {"start": 926.05, "end": 926.37, "word": " minus", "probability": 0.947265625}, {"start": 926.37, "end": 926.59, "word": " pi", "probability": 0.9443359375}, {"start": 926.59, "end": 926.85, "word": " 2.", "probability": 0.9794921875}, {"start": 928.05, "end": 928.43, "word": " The", "probability": 0.8876953125}, {"start": 928.43, "end": 928.89, "word": " confidence", "probability": 0.9775390625}, {"start": 928.89, "end": 929.37, "word": " interval,", "probability": 0.9599609375}, {"start": 929.71, "end": 929.91, "word": " as", "probability": 0.96728515625}, {"start": 929.91, "end": 930.05, "word": " we", "probability": 0.95849609375}, {"start": 930.05, "end": 930.43, "word": " mentioned", "probability": 0.8134765625}, {"start": 930.43, "end": 931.07, "word": " before,", "probability": 0.8701171875}, {"start": 931.69, "end": 931.85, "word": " can", "probability": 0.94189453125}, {"start": 931.85, "end": 932.01, "word": " be", "probability": 0.9560546875}, {"start": 932.01, "end": 932.63, "word": " constructed", "probability": 0.923828125}, {"start": 932.63, "end": 933.91, "word": " by", "probability": 0.97021484375}, {"start": 933.91, "end": 934.93, "word": " point", "probability": 0.88720703125}, {"start": 934.93, "end": 935.55, "word": " estimate,", "probability": 0.87060546875}, {"start": 936.29, "end": 937.53, "word": " plus", "probability": 0.76318359375}, {"start": 937.53, "end": 937.83, "word": " or", "probability": 0.95703125}, {"start": 937.83, "end": 938.11, "word": " minus", "probability": 0.9873046875}, {"start": 938.11, "end": 938.53, "word": " critical", "probability": 0.78564453125}, {"start": 938.53, "end": 939.15, "word": " value", "probability": 0.9658203125}, {"start": 939.15, "end": 939.91, "word": " times", "probability": 0.56884765625}, {"start": 939.91, "end": 940.17, "word": " the", "probability": 0.8857421875}, {"start": 940.17, "end": 940.61, "word": " standard", "probability": 0.93408203125}, {"start": 940.61, "end": 941.07, "word": " error", "probability": 0.875}, {"start": 941.07, "end": 941.41, "word": " of", "probability": 0.966796875}, {"start": 941.41, "end": 941.59, "word": " the", "probability": 0.908203125}, {"start": 941.59, "end": 941.89, "word": " point", "probability": 0.9755859375}, {"start": 941.89, "end": 942.35, "word": " estimate.", "probability": 0.90185546875}], "temperature": 1.0}, {"id": 37, "seek": 96795, "start": 944.83, "end": 967.95, "text": " In this case, the point estimate for pi 1 minus pi 2 is b1 minus b2. So that's your point estimate, plus or minus z alpha over 2. Now from the information from chapter 8, the standard error of the difference, b1 minus pi 2, is given by this equation.", "tokens": [682, 341, 1389, 11, 264, 935, 12539, 337, 3895, 502, 3175, 3895, 568, 307, 272, 16, 3175, 272, 17, 13, 407, 300, 311, 428, 935, 12539, 11, 1804, 420, 3175, 710, 8961, 670, 568, 13, 823, 490, 264, 1589, 490, 7187, 1649, 11, 264, 3832, 6713, 295, 264, 2649, 11, 272, 16, 3175, 3895, 568, 11, 307, 2212, 538, 341, 5367, 13], "avg_logprob": -0.17646329033942448, "compression_ratio": 1.5212121212121212, "no_speech_prob": 0.0, "words": [{"start": 944.83, "end": 945.11, "word": " In", "probability": 0.83056640625}, {"start": 945.11, "end": 945.43, "word": " this", "probability": 0.94921875}, {"start": 945.43, "end": 946.75, "word": " case,", "probability": 0.91796875}, {"start": 947.09, "end": 947.21, "word": " the", "probability": 0.916015625}, {"start": 947.21, "end": 947.47, "word": " point", "probability": 0.9755859375}, {"start": 947.47, "end": 947.93, "word": " estimate", "probability": 0.943359375}, {"start": 947.93, "end": 948.89, "word": " for", "probability": 0.92724609375}, {"start": 948.89, "end": 949.07, "word": " pi", "probability": 0.583984375}, {"start": 949.07, "end": 949.25, "word": " 1", "probability": 0.58203125}, {"start": 949.25, "end": 949.55, "word": " minus", "probability": 0.95361328125}, {"start": 949.55, "end": 949.73, "word": " pi", "probability": 0.9404296875}, {"start": 949.73, "end": 949.87, "word": " 2", "probability": 0.9765625}, {"start": 949.87, "end": 949.99, "word": " is", "probability": 0.93798828125}, {"start": 949.99, "end": 950.27, "word": " b1", "probability": 0.535400390625}, {"start": 950.27, "end": 950.55, "word": " minus", "probability": 0.984375}, {"start": 950.55, "end": 950.93, "word": " b2.", "probability": 0.976806640625}, {"start": 951.91, "end": 952.49, "word": " So", "probability": 0.9228515625}, {"start": 952.49, "end": 952.79, "word": " that's", "probability": 0.864013671875}, {"start": 952.79, "end": 952.95, "word": " your", "probability": 0.8935546875}, {"start": 952.95, "end": 953.23, "word": " point", "probability": 0.9775390625}, {"start": 953.23, "end": 953.73, "word": " estimate,", "probability": 0.9072265625}, {"start": 954.49, "end": 954.89, "word": " plus", "probability": 0.91455078125}, {"start": 954.89, "end": 955.17, "word": " or", "probability": 0.95556640625}, {"start": 955.17, "end": 955.43, "word": " minus", "probability": 0.990234375}, {"start": 955.43, "end": 955.63, "word": " z", "probability": 0.77880859375}, {"start": 955.63, "end": 955.83, "word": " alpha", "probability": 0.904296875}, {"start": 955.83, "end": 956.13, "word": " over", "probability": 0.9189453125}, {"start": 956.13, "end": 956.47, "word": " 2.", "probability": 0.75634765625}, {"start": 957.99, "end": 958.49, "word": " Now", "probability": 0.95166015625}, {"start": 958.49, "end": 959.43, "word": " from", "probability": 0.3203125}, {"start": 959.43, "end": 959.71, "word": " the", "probability": 0.90771484375}, {"start": 959.71, "end": 960.49, "word": " information", "probability": 0.83447265625}, {"start": 960.49, "end": 960.81, "word": " from", "probability": 0.828125}, {"start": 960.81, "end": 961.13, "word": " chapter", "probability": 0.61572265625}, {"start": 961.13, "end": 961.67, "word": " 8,", "probability": 0.6279296875}, {"start": 962.95, "end": 963.19, "word": " the", "probability": 0.91259765625}, {"start": 963.19, "end": 963.55, "word": " standard", "probability": 0.92578125}, {"start": 963.55, "end": 963.89, "word": " error", "probability": 0.90625}, {"start": 963.89, "end": 964.15, "word": " of", "probability": 0.96533203125}, {"start": 964.15, "end": 964.29, "word": " the", "probability": 0.92138671875}, {"start": 964.29, "end": 964.85, "word": " difference,", "probability": 0.86669921875}, {"start": 965.53, "end": 965.81, "word": " b1", "probability": 0.96533203125}, {"start": 965.81, "end": 966.11, "word": " minus", "probability": 0.98583984375}, {"start": 966.11, "end": 966.29, "word": " pi", "probability": 0.432861328125}, {"start": 966.29, "end": 966.53, "word": " 2,", "probability": 0.98583984375}, {"start": 966.61, "end": 966.85, "word": " is", "probability": 0.94677734375}, {"start": 966.85, "end": 967.07, "word": " given", "probability": 0.890625}, {"start": 967.07, "end": 967.27, "word": " by", "probability": 0.96728515625}, {"start": 967.27, "end": 967.53, "word": " this", "probability": 0.94873046875}, {"start": 967.53, "end": 967.95, "word": " equation.", "probability": 0.97412109375}], "temperature": 1.0}, {"id": 38, "seek": 99099, "start": 969.11, "end": 990.99, "text": " B1 times 1 minus B1, so B1 and its complement, divided by the first sample size, plus the second sample proportion times its complement divided by the sample size of the second sample. So that's your confidence interval. 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So my decision is we don't reject at zero. So the same conclusion as we reached by using critical penalty. So again, by using B value, we have to compute the probability that your Z statistic falls in the rejection regions.", "tokens": [12313, 5044, 813, 1025, 8923, 370, 321, 500, 380, 8248, 527, 5215, 13, 407, 452, 3537, 307, 321, 500, 380, 8248, 412, 4018, 13, 407, 264, 912, 10063, 382, 321, 6488, 538, 1228, 4924, 16263, 13, 407, 797, 11, 538, 1228, 363, 2158, 11, 321, 362, 281, 14722, 264, 8482, 300, 428, 1176, 29588, 8804, 294, 264, 26044, 10682, 13], "avg_logprob": -0.2635758138093792, "compression_ratio": 1.516304347826087, "no_speech_prob": 0.0, "words": [{"start": 1176.03, "end": 1176.35, "word": " Much", "probability": 0.1524658203125}, {"start": 1176.35, "end": 1176.67, "word": " greater", "probability": 0.89208984375}, {"start": 1176.67, "end": 1176.91, "word": " than", "probability": 0.93701171875}, {"start": 1176.91, "end": 1177.65, "word": " 5%,", "probability": 0.5904541015625}, {"start": 1177.65, "end": 1177.97, "word": " so", "probability": 0.91162109375}, {"start": 1177.97, "end": 1178.13, "word": " we", "probability": 0.888671875}, {"start": 1178.13, "end": 1178.37, "word": " don't", "probability": 0.96435546875}, {"start": 1178.37, "end": 1178.73, "word": " reject", "probability": 0.8466796875}, {"start": 1178.73, "end": 1178.91, "word": " our", "probability": 0.1566162109375}, {"start": 1178.91, "end": 1179.19, "word": " analysis.", "probability": 0.1812744140625}, {"start": 1180.43, "end": 1180.85, "word": " So", "probability": 0.94189453125}, {"start": 1180.85, "end": 1181.17, "word": " my", "probability": 0.82958984375}, {"start": 1181.17, "end": 1182.55, "word": " decision", "probability": 0.86767578125}, {"start": 1182.55, "end": 1182.91, "word": " is", "probability": 0.94482421875}, {"start": 1182.91, "end": 1183.13, "word": " we", "probability": 0.70263671875}, {"start": 1183.13, "end": 1184.51, "word": " don't", "probability": 0.9677734375}, {"start": 1184.51, "end": 1186.51, "word": " reject", "probability": 0.8818359375}, {"start": 1186.51, "end": 1187.33, "word": " at", "probability": 0.3310546875}, {"start": 1187.33, "end": 1187.65, "word": " zero.", "probability": 0.6142578125}, {"start": 1187.81, "end": 1187.99, "word": " So", "probability": 0.95263671875}, {"start": 1187.99, "end": 1188.15, "word": " the", "probability": 0.8154296875}, {"start": 1188.15, "end": 1188.39, "word": " same", "probability": 0.892578125}, {"start": 1188.39, "end": 1188.89, "word": " conclusion", "probability": 0.91015625}, {"start": 1188.89, "end": 1189.21, "word": " as", "probability": 0.94384765625}, {"start": 1189.21, "end": 1189.49, "word": " we", "probability": 0.94384765625}, {"start": 1189.49, "end": 1190.93, "word": " reached", "probability": 0.7763671875}, {"start": 1190.93, "end": 1191.49, "word": " by", "probability": 0.96240234375}, {"start": 1191.49, "end": 1191.93, "word": " using", "probability": 0.92919921875}, {"start": 1191.93, "end": 1192.69, "word": " critical", "probability": 0.88671875}, {"start": 1192.69, "end": 1193.09, "word": " penalty.", "probability": 0.33203125}, {"start": 1195.31, "end": 1195.95, "word": " So", "probability": 0.94873046875}, {"start": 1195.95, "end": 1196.21, "word": " again,", "probability": 0.90380859375}, {"start": 1196.29, "end": 1196.41, "word": " by", "probability": 0.96923828125}, {"start": 1196.41, "end": 1196.71, "word": " using", "probability": 0.9306640625}, {"start": 1196.71, "end": 1196.93, "word": " B", "probability": 0.384033203125}, {"start": 1196.93, "end": 1197.27, "word": " value,", "probability": 0.90576171875}, {"start": 1197.45, "end": 1197.57, "word": " we", "probability": 0.8583984375}, {"start": 1197.57, "end": 1197.73, "word": " have", "probability": 0.9384765625}, {"start": 1197.73, "end": 1197.85, "word": " to", "probability": 0.96484375}, {"start": 1197.85, "end": 1198.35, "word": " compute", "probability": 0.91552734375}, {"start": 1198.35, "end": 1198.87, "word": " the", "probability": 0.90478515625}, {"start": 1198.87, "end": 1199.31, "word": " probability", "probability": 0.9599609375}, {"start": 1199.31, "end": 1199.73, "word": " that", "probability": 0.9384765625}, {"start": 1199.73, "end": 1199.97, "word": " your", "probability": 0.7314453125}, {"start": 1199.97, "end": 1200.11, "word": " Z", "probability": 0.77099609375}, {"start": 1200.11, "end": 1200.77, "word": " statistic", "probability": 0.78515625}, {"start": 1200.77, "end": 1201.31, "word": " falls", "probability": 0.81298828125}, {"start": 1201.31, "end": 1201.83, "word": " in", "probability": 0.923828125}, {"start": 1201.83, "end": 1201.99, "word": " the", "probability": 0.9130859375}, {"start": 1201.99, "end": 1202.31, "word": " rejection", "probability": 0.9677734375}, {"start": 1202.31, "end": 1202.89, "word": " regions.", "probability": 0.96826171875}], "temperature": 1.0}, {"id": 47, "seek": 122685, "start": 1204.42, "end": 1226.86, "text": " I end with this result, my B value is around 19%. As we mentioned before, we reject null hypothesis if my B value is smaller than alpha. Now, my B value in this case is much, much bigger than 5%, so my decision is don't reject null hypothesis. Any questions?", "tokens": [286, 917, 365, 341, 1874, 11, 452, 363, 2158, 307, 926, 1294, 6856, 1018, 321, 2835, 949, 11, 321, 8248, 18184, 17291, 498, 452, 363, 2158, 307, 4356, 813, 8961, 13, 823, 11, 452, 363, 2158, 294, 341, 1389, 307, 709, 11, 709, 3801, 813, 1025, 8923, 370, 452, 3537, 307, 500, 380, 8248, 18184, 17291, 13, 2639, 1651, 30], "avg_logprob": -0.21951844946282809, "compression_ratio": 1.532544378698225, "no_speech_prob": 0.0, "words": [{"start": 1204.42, "end": 1204.72, "word": " I", "probability": 0.794921875}, {"start": 1204.72, "end": 1204.98, "word": " end", "probability": 0.87109375}, {"start": 1204.98, "end": 1205.12, "word": " with", "probability": 0.86328125}, {"start": 1205.12, "end": 1205.32, "word": " this", "probability": 0.92333984375}, {"start": 1205.32, "end": 1205.7, "word": " result,", "probability": 0.89111328125}, {"start": 1205.94, "end": 1205.98, "word": " my", "probability": 0.94140625}, {"start": 1205.98, "end": 1206.1, "word": " B", "probability": 0.5205078125}, {"start": 1206.1, "end": 1206.42, "word": " value", "probability": 0.66162109375}, {"start": 1206.42, "end": 1206.72, "word": " is", "probability": 0.4423828125}, {"start": 1206.72, "end": 1207.56, "word": " around", "probability": 0.9287109375}, {"start": 1207.56, "end": 1208.5, "word": " 19%.", "probability": 0.803955078125}, {"start": 1208.5, "end": 1210.18, "word": " As", "probability": 0.95654296875}, {"start": 1210.18, "end": 1210.32, "word": " we", "probability": 0.92431640625}, {"start": 1210.32, "end": 1210.6, "word": " mentioned", "probability": 0.8173828125}, {"start": 1210.6, "end": 1211.06, "word": " before,", "probability": 0.8701171875}, {"start": 1211.74, "end": 1211.98, "word": " we", "probability": 0.9140625}, {"start": 1211.98, "end": 1212.36, "word": " reject", "probability": 0.8681640625}, {"start": 1212.36, "end": 1212.52, "word": " null", "probability": 0.3232421875}, {"start": 1212.52, "end": 1213.04, "word": " hypothesis", "probability": 0.447265625}, {"start": 1213.04, "end": 1213.46, "word": " if", "probability": 0.84814453125}, {"start": 1213.46, "end": 1213.64, "word": " my", "probability": 0.94921875}, {"start": 1213.64, "end": 1213.8, "word": " B", "probability": 0.9453125}, {"start": 1213.8, "end": 1214.02, "word": " value", "probability": 0.9345703125}, {"start": 1214.02, "end": 1214.18, "word": " is", "probability": 0.94970703125}, {"start": 1214.18, "end": 1214.42, "word": " smaller", "probability": 0.83056640625}, {"start": 1214.42, "end": 1214.7, "word": " than", "probability": 0.947265625}, {"start": 1214.7, "end": 1214.98, "word": " alpha.", "probability": 0.66064453125}, {"start": 1216.1, "end": 1216.48, "word": " Now,", "probability": 0.931640625}, {"start": 1216.8, "end": 1216.96, "word": " my", "probability": 0.96337890625}, {"start": 1216.96, "end": 1217.16, "word": " B", "probability": 0.98681640625}, {"start": 1217.16, "end": 1217.4, "word": " value", "probability": 0.9599609375}, {"start": 1217.4, "end": 1217.52, "word": " in", "probability": 0.89013671875}, {"start": 1217.52, "end": 1217.68, "word": " this", "probability": 0.9482421875}, {"start": 1217.68, "end": 1217.92, "word": " case", "probability": 0.91357421875}, {"start": 1217.92, "end": 1218.14, "word": " is", "probability": 0.93212890625}, {"start": 1218.14, "end": 1218.48, "word": " much,", "probability": 0.91455078125}, {"start": 1218.74, "end": 1219.14, "word": " much", "probability": 0.91357421875}, {"start": 1219.14, "end": 1219.44, "word": " bigger", "probability": 0.94287109375}, {"start": 1219.44, "end": 1219.86, "word": " than", "probability": 0.94140625}, {"start": 1219.86, "end": 1221.08, "word": " 5%,", "probability": 0.6556396484375}, {"start": 1221.08, "end": 1221.88, "word": " so", "probability": 0.9423828125}, {"start": 1221.88, "end": 1222.12, "word": " my", "probability": 0.95703125}, {"start": 1222.12, "end": 1222.44, "word": " decision", "probability": 0.927734375}, {"start": 1222.44, "end": 1222.74, "word": " is", "probability": 0.94140625}, {"start": 1222.74, "end": 1223.0, "word": " don't", "probability": 0.8310546875}, {"start": 1223.0, "end": 1223.36, "word": " reject", "probability": 0.94384765625}, {"start": 1223.36, "end": 1223.58, "word": " null", "probability": 0.55908203125}, {"start": 1223.58, "end": 1224.14, "word": " hypothesis.", "probability": 0.8427734375}, {"start": 1226.32, "end": 1226.56, "word": " Any", "probability": 0.54931640625}, {"start": 1226.56, "end": 1226.86, "word": " questions?", "probability": 0.50537109375}], "temperature": 1.0}, {"id": 48, "seek": 126522, "start": 1236.14, "end": 1265.22, "text": " The other approach, the third one, confidence interval approach. Now, for the confidence interval approach, we have this equation, b1 minus b2. Again, the point estimate, plus or minus z square root b1 times 1 minus b1 divided by a1.", "tokens": [440, 661, 3109, 11, 264, 2636, 472, 11, 6687, 15035, 3109, 13, 823, 11, 337, 264, 6687, 15035, 3109, 11, 321, 362, 341, 5367, 11, 272, 16, 3175, 272, 17, 13, 3764, 11, 264, 935, 12539, 11, 1804, 420, 3175, 710, 3732, 5593, 272, 16, 1413, 502, 3175, 272, 16, 6666, 538, 257, 16, 13], "avg_logprob": -0.21163504038538253, "compression_ratio": 1.5496688741721854, "no_speech_prob": 0.0, "words": [{"start": 1236.14, "end": 1236.44, "word": " The", "probability": 0.7587890625}, {"start": 1236.44, "end": 1236.72, "word": " other", "probability": 0.6962890625}, {"start": 1236.72, "end": 1237.34, "word": " approach,", "probability": 0.90966796875}, {"start": 1239.0, "end": 1239.16, "word": " the", "probability": 0.529296875}, {"start": 1239.16, "end": 1239.42, "word": " third", "probability": 0.9345703125}, {"start": 1239.42, "end": 1239.76, "word": " one,", "probability": 0.927734375}, {"start": 1240.58, "end": 1241.16, "word": " confidence", "probability": 0.88232421875}, {"start": 1241.16, "end": 1241.9, "word": " interval", "probability": 0.97705078125}, {"start": 1241.9, "end": 1242.52, "word": " approach.", "probability": 0.921875}, {"start": 1246.26, "end": 1247.02, "word": " Now,", "probability": 0.87939453125}, {"start": 1247.08, "end": 1247.2, "word": " for", "probability": 0.95166015625}, {"start": 1247.2, "end": 1247.34, "word": " the", "probability": 0.92041015625}, {"start": 1247.34, "end": 1247.8, "word": " confidence", "probability": 0.98193359375}, {"start": 1247.8, "end": 1248.14, "word": " interval", "probability": 0.9638671875}, {"start": 1248.14, "end": 1248.58, "word": " approach,", "probability": 0.93603515625}, {"start": 1248.64, "end": 1248.76, "word": " we", "probability": 0.95703125}, {"start": 1248.76, "end": 1248.98, "word": " have", "probability": 0.94384765625}, {"start": 1248.98, "end": 1249.22, "word": " this", "probability": 0.9501953125}, {"start": 1249.22, "end": 1249.8, "word": " equation,", "probability": 0.98046875}, {"start": 1250.58, "end": 1250.96, "word": " b1", "probability": 0.659912109375}, {"start": 1250.96, "end": 1252.58, "word": " minus", "probability": 0.9248046875}, {"start": 1252.58, "end": 1253.0, "word": " b2.", "probability": 0.95263671875}, {"start": 1253.22, "end": 1253.46, "word": " Again,", "probability": 0.384765625}, {"start": 1253.64, "end": 1253.72, "word": " the", "probability": 0.8466796875}, {"start": 1253.72, "end": 1253.96, "word": " point", "probability": 0.9541015625}, {"start": 1253.96, "end": 1254.52, "word": " estimate,", "probability": 0.8701171875}, {"start": 1255.78, "end": 1256.26, "word": " plus", "probability": 0.90234375}, {"start": 1256.26, "end": 1256.72, "word": " or", "probability": 0.9462890625}, {"start": 1256.72, "end": 1257.22, "word": " minus", "probability": 0.98486328125}, {"start": 1257.22, "end": 1257.98, "word": " z", "probability": 0.849609375}, {"start": 1257.98, "end": 1259.72, "word": " square", "probability": 0.5732421875}, {"start": 1259.72, "end": 1260.1, "word": " root", "probability": 0.9443359375}, {"start": 1260.1, "end": 1261.74, "word": " b1", "probability": 0.837890625}, {"start": 1261.74, "end": 1263.52, "word": " times", "probability": 0.8828125}, {"start": 1263.52, "end": 1263.76, "word": " 1", "probability": 0.94140625}, {"start": 1263.76, "end": 1264.06, "word": " minus", "probability": 0.98681640625}, {"start": 1264.06, "end": 1264.4, "word": " b1", "probability": 0.968505859375}, {"start": 1264.4, "end": 1264.68, "word": " divided", "probability": 0.76953125}, {"start": 1264.68, "end": 1264.84, "word": " by", "probability": 0.9638671875}, {"start": 1264.84, "end": 1265.22, "word": " a1.", "probability": 0.7149658203125}], "temperature": 1.0}, {"id": 49, "seek": 129129, "start": 1267.81, "end": 1291.29, "text": " B2 times 1 minus B2 divided by N2. Now we have B1 and B2, so 0.5 minus 0.62. That's your calculations from previous information we have. Plus or minus Z alpha over 2, the critical value again is 1.96 times", "tokens": [363, 17, 1413, 502, 3175, 363, 17, 6666, 538, 426, 17, 13, 823, 321, 362, 363, 16, 293, 363, 17, 11, 370, 1958, 13, 20, 3175, 1958, 13, 28052, 13, 663, 311, 428, 20448, 490, 3894, 1589, 321, 362, 13, 7721, 420, 3175, 1176, 8961, 670, 568, 11, 264, 4924, 2158, 797, 307, 502, 13, 22962, 1413], "avg_logprob": -0.160425649634723, "compression_ratio": 1.3205128205128205, "no_speech_prob": 0.0, "words": [{"start": 1267.81, "end": 1268.47, "word": " B2", "probability": 0.506591796875}, {"start": 1268.47, "end": 1268.89, "word": " times", "probability": 0.8759765625}, {"start": 1268.89, "end": 1269.15, "word": " 1", "probability": 0.82666015625}, {"start": 1269.15, "end": 1269.45, "word": " minus", "probability": 0.97265625}, {"start": 1269.45, "end": 1269.81, "word": " B2", "probability": 0.85205078125}, {"start": 1269.81, "end": 1270.09, "word": " divided", "probability": 0.732421875}, {"start": 1270.09, "end": 1270.63, "word": " by", "probability": 0.966796875}, {"start": 1270.63, "end": 1271.65, "word": " N2.", "probability": 0.787109375}, {"start": 1273.85, "end": 1274.51, "word": " Now", "probability": 0.9306640625}, {"start": 1274.51, "end": 1274.65, "word": " we", "probability": 0.7958984375}, {"start": 1274.65, "end": 1274.95, "word": " have", "probability": 0.9462890625}, {"start": 1274.95, "end": 1275.61, "word": " B1", "probability": 0.9501953125}, {"start": 1275.61, "end": 1276.95, "word": " and", "probability": 0.92333984375}, {"start": 1276.95, "end": 1277.29, "word": " B2,", "probability": 0.996826171875}, {"start": 1277.37, "end": 1277.51, "word": " so", "probability": 0.916015625}, {"start": 1277.51, "end": 1277.77, "word": " 0", "probability": 0.88427734375}, {"start": 1277.77, "end": 1278.15, "word": ".5", "probability": 0.9921875}, {"start": 1278.15, "end": 1278.59, "word": " minus", "probability": 0.98388671875}, {"start": 1278.59, "end": 1279.53, "word": " 0", "probability": 0.98291015625}, {"start": 1279.53, "end": 1279.99, "word": ".62.", "probability": 0.9853515625}, {"start": 1280.31, "end": 1280.73, "word": " That's", "probability": 0.943359375}, {"start": 1280.73, "end": 1281.11, "word": " your", "probability": 0.892578125}, {"start": 1281.11, "end": 1282.55, "word": " calculations", "probability": 0.8720703125}, {"start": 1282.55, "end": 1283.05, "word": " from", "probability": 0.87841796875}, {"start": 1283.05, "end": 1283.99, "word": " previous", "probability": 0.82666015625}, {"start": 1283.99, "end": 1284.93, "word": " information", "probability": 0.849609375}, {"start": 1284.93, "end": 1285.17, "word": " we", "probability": 0.9375}, {"start": 1285.17, "end": 1285.47, "word": " have.", "probability": 0.861328125}, {"start": 1286.29, "end": 1286.69, "word": " Plus", "probability": 0.9189453125}, {"start": 1286.69, "end": 1286.89, "word": " or", "probability": 0.9560546875}, {"start": 1286.89, "end": 1287.21, "word": " minus", "probability": 0.98681640625}, {"start": 1287.21, "end": 1287.41, "word": " Z", "probability": 0.69970703125}, {"start": 1287.41, "end": 1287.61, "word": " alpha", "probability": 0.859375}, {"start": 1287.61, "end": 1287.83, "word": " over", "probability": 0.9169921875}, {"start": 1287.83, "end": 1288.01, "word": " 2,", "probability": 0.88525390625}, {"start": 1288.09, "end": 1288.19, "word": " the", "probability": 0.9091796875}, {"start": 1288.19, "end": 1288.47, "word": " critical", "probability": 0.92578125}, {"start": 1288.47, "end": 1288.75, "word": " value", "probability": 0.97705078125}, {"start": 1288.75, "end": 1288.99, "word": " again", "probability": 0.88330078125}, {"start": 1288.99, "end": 1289.15, "word": " is", "probability": 0.92626953125}, {"start": 1289.15, "end": 1289.35, "word": " 1", "probability": 0.994140625}, {"start": 1289.35, "end": 1289.97, "word": ".96", "probability": 0.9951171875}, {"start": 1289.97, "end": 1291.29, "word": " times", "probability": 0.50634765625}], "temperature": 1.0}, {"id": 50, "seek": 132051, "start": 1292.69, "end": 1320.51, "text": " Square root of P1.5 times 1 minus 0.5 divided by N1 plus P2 62 percent times 1 minus P2 divided by N2. 0.5 minus 62 percent is negative 12 percent plus or minus the margin of error. This amount is again as we mentioned before is the margin of error is 0.177. 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That means we are 95% confident that the difference between the proportions of men who will vote yes for a position A and men", "tokens": [440, 2649, 1296, 264, 732, 32482, 4544, 1296, 3671, 1958, 13, 11871, 21, 293, 1958, 13, 13328, 22, 13, 663, 1355, 321, 366, 13420, 4, 6679, 300, 264, 2649, 1296, 264, 32482, 295, 1706, 567, 486, 4740, 2086, 337, 257, 2535, 316, 293, 1706], "avg_logprob": -0.1819444457689921, "compression_ratio": 1.4892086330935252, "no_speech_prob": 0.0, "words": [{"start": 1321.26, "end": 1321.48, "word": " The", "probability": 0.481689453125}, {"start": 1321.48, "end": 1321.9, "word": " difference", "probability": 0.8232421875}, {"start": 1321.9, "end": 1322.22, "word": " between", "probability": 0.85986328125}, {"start": 1322.22, "end": 1322.4, "word": " the", "probability": 0.9140625}, {"start": 1322.4, "end": 1322.56, "word": " two", "probability": 0.93212890625}, {"start": 1322.56, "end": 1323.3, "word": " proportions", "probability": 0.853515625}, {"start": 1323.3, "end": 1324.86, "word": " lie", "probability": 0.5859375}, {"start": 1324.86, "end": 1325.24, "word": " between", "probability": 0.8740234375}, {"start": 1325.24, "end": 1325.64, "word": " negative", "probability": 0.408203125}, {"start": 1325.64, "end": 1326.04, "word": " 0", "probability": 0.465576171875}, {"start": 1326.04, "end": 1327.0, "word": ".296", "probability": 0.9752604166666666}, {"start": 1327.0, "end": 1328.08, "word": " and", "probability": 0.91650390625}, {"start": 1328.08, "end": 1328.36, "word": " 0", "probability": 0.96337890625}, {"start": 1328.36, "end": 1329.04, "word": ".057.", "probability": 0.8221028645833334}, {"start": 1329.16, "end": 1329.48, "word": " That", "probability": 0.89697265625}, {"start": 1329.48, "end": 1329.82, "word": " means", "probability": 0.92529296875}, {"start": 1329.82, "end": 1330.54, "word": " we", "probability": 0.8310546875}, {"start": 1330.54, "end": 1330.92, "word": " are", "probability": 0.9443359375}, {"start": 1330.92, "end": 1331.48, "word": " 95", "probability": 0.9296875}, {"start": 1331.48, "end": 1331.98, "word": "%", "probability": 0.828125}, {"start": 1331.98, "end": 1332.54, "word": " confident", "probability": 0.97216796875}, {"start": 1332.54, "end": 1332.98, "word": " that", "probability": 0.92724609375}, {"start": 1332.98, "end": 1333.7, "word": " the", "probability": 0.908203125}, {"start": 1333.7, "end": 1334.08, "word": " difference", "probability": 0.85009765625}, {"start": 1334.08, "end": 1334.58, "word": " between", "probability": 0.86474609375}, {"start": 1334.58, "end": 1335.36, "word": " the", "probability": 0.9189453125}, {"start": 1335.36, "end": 1335.98, "word": " proportions", "probability": 0.818359375}, {"start": 1335.98, "end": 1336.6, "word": " of", "probability": 0.96728515625}, {"start": 1336.6, "end": 1336.92, "word": " men", "probability": 0.92431640625}, {"start": 1336.92, "end": 1337.2, "word": " who", "probability": 0.89501953125}, {"start": 1337.2, "end": 1337.48, "word": " will", "probability": 0.88134765625}, {"start": 1337.48, "end": 1337.8, "word": " vote", "probability": 0.91259765625}, {"start": 1337.8, "end": 1338.2, "word": " yes", "probability": 0.69189453125}, {"start": 1338.2, "end": 1339.0, "word": " for", "probability": 0.90087890625}, {"start": 1339.0, "end": 1339.1, "word": " a", "probability": 0.51708984375}, {"start": 1339.1, "end": 1339.46, "word": " position", "probability": 0.779296875}, {"start": 1339.46, "end": 1339.92, "word": " A", "probability": 0.6884765625}, {"start": 1339.92, "end": 1341.22, "word": " and", "probability": 0.70263671875}, {"start": 1341.22, "end": 1342.12, "word": " men", "probability": 0.9345703125}], "temperature": 1.0}, {"id": 52, "seek": 136802, "start": 1343.96, "end": 1368.02, "text": " equals negative 0.297 up to 0.057. Now the question is since we are testing it's zero by one minus by two equals zero the question is does this interval contain zero or capture zero? 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So zero inside the interval, I mean the confidence interval contains zero in this case, so we don't reject the null hypothesis because maybe the difference equals zero.", "tokens": [293, 917, 365, 3353, 11, 286, 914, 264, 3126, 5472, 307, 3671, 1958, 13, 11871, 22, 293, 264, 6597, 5472, 307, 1958, 13, 13328, 22, 13, 407, 4018, 1854, 264, 15035, 11, 286, 914, 264, 6687, 15035, 8306, 4018, 294, 341, 1389, 11, 370, 321, 500, 380, 8248, 264, 18184, 17291, 570, 1310, 264, 2649, 6915, 4018, 13], "avg_logprob": -0.21040783443693387, "compression_ratio": 1.5290697674418605, "no_speech_prob": 0.0, "words": [{"start": 1369.13, "end": 1369.51, "word": " and", "probability": 0.34375}, {"start": 1369.51, "end": 1369.75, "word": " end", "probability": 0.7158203125}, {"start": 1369.75, "end": 1369.93, "word": " with", "probability": 0.89111328125}, {"start": 1369.93, "end": 1370.35, "word": " positive,", "probability": 0.91455078125}, {"start": 1370.53, "end": 1370.61, "word": " I", "probability": 0.9580078125}, {"start": 1370.61, "end": 1370.79, "word": " mean", "probability": 0.9677734375}, {"start": 1370.79, "end": 1370.99, "word": " the", "probability": 0.67724609375}, {"start": 1370.99, "end": 1371.23, "word": " lower", "probability": 0.8642578125}, {"start": 1371.23, "end": 1371.61, "word": " bound", "probability": 0.896484375}, {"start": 1371.61, "end": 1371.81, "word": " is", "probability": 0.94384765625}, {"start": 1371.81, "end": 1372.23, "word": " negative", "probability": 0.69873046875}, {"start": 1372.23, "end": 1372.63, "word": " 0", "probability": 0.5126953125}, {"start": 1372.63, "end": 1373.51, "word": ".297", "probability": 0.92529296875}, {"start": 1373.51, "end": 1374.37, "word": " and", "probability": 0.69873046875}, {"start": 1374.37, "end": 1374.53, "word": " the", "probability": 0.50244140625}, {"start": 1374.53, "end": 1374.75, "word": " upper", "probability": 0.82666015625}, {"start": 1374.75, "end": 1375.03, "word": " bound", "probability": 0.84521484375}, {"start": 1375.03, "end": 1375.17, "word": " is", "probability": 0.87646484375}, {"start": 1375.17, "end": 1375.33, "word": " 0", "probability": 0.93994140625}, {"start": 1375.33, "end": 1376.27, "word": ".057.", "probability": 0.9612630208333334}, {"start": 1376.81, "end": 1377.33, "word": " So", "probability": 0.92529296875}, {"start": 1377.33, "end": 1377.83, "word": " zero", "probability": 0.5986328125}, {"start": 1377.83, "end": 1379.49, "word": " inside", "probability": 0.849609375}, {"start": 1379.49, "end": 1379.75, "word": " the", "probability": 0.91064453125}, {"start": 1379.75, "end": 1380.13, "word": " interval,", "probability": 0.98095703125}, {"start": 1380.25, "end": 1380.33, "word": " I", "probability": 0.98974609375}, {"start": 1380.33, "end": 1380.45, "word": " mean", "probability": 0.96142578125}, {"start": 1380.45, "end": 1380.61, "word": " the", "probability": 0.8310546875}, {"start": 1380.61, "end": 1381.07, "word": " confidence", "probability": 0.97900390625}, {"start": 1381.07, "end": 1381.59, "word": " interval", "probability": 0.978515625}, {"start": 1381.59, "end": 1382.73, "word": " contains", "probability": 0.82421875}, {"start": 1382.73, "end": 1383.07, "word": " zero", "probability": 0.86669921875}, {"start": 1383.07, "end": 1383.19, "word": " in", "probability": 0.927734375}, {"start": 1383.19, "end": 1383.41, "word": " this", "probability": 0.94677734375}, {"start": 1383.41, "end": 1383.67, "word": " case,", "probability": 0.9130859375}, {"start": 1383.79, "end": 1383.87, "word": " so", "probability": 0.93212890625}, {"start": 1383.87, "end": 1384.03, "word": " we", "probability": 0.94775390625}, {"start": 1384.03, "end": 1384.27, "word": " don't", "probability": 0.966064453125}, {"start": 1384.27, "end": 1384.61, "word": " reject", "probability": 0.91845703125}, {"start": 1384.61, "end": 1384.77, "word": " the", "probability": 0.308349609375}, {"start": 1384.77, "end": 1384.89, "word": " null", "probability": 0.98486328125}, {"start": 1384.89, "end": 1385.29, "word": " hypothesis", "probability": 0.93115234375}, {"start": 1385.29, "end": 1386.09, "word": " because", "probability": 0.366455078125}, {"start": 1386.09, "end": 1386.65, "word": " maybe", "probability": 0.9306640625}, {"start": 1386.65, "end": 1387.39, "word": " the", "probability": 0.900390625}, {"start": 1387.39, "end": 1387.83, "word": " difference", "probability": 0.880859375}, {"start": 1387.83, "end": 1388.17, "word": " equals", "probability": 0.89404296875}, {"start": 1388.17, "end": 1388.47, "word": " zero.", "probability": 0.8623046875}], "temperature": 1.0}, {"id": 54, "seek": 141702, "start": 1389.94, "end": 1417.02, "text": " So since this interval does contain the hypothesis difference zero, so we don't reject null hypothesis at 5% level. So the same conclusion as we got before by using critical value approach and de-value approach. So either one will end with the same decision. 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Do you have any question? Any question? So again, there are three different approaches in order to solve this problem. One is critical value approach, the standard one. The other two are the value approach and confidence interval. 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Because the confidence interval we have is just for two-tailed test, so it could be used only for testing about two-tailed test. As we mentioned before, I'm going to skip hypothesis for variances as well as ANOVA test. So that's all for chapter ten.", "tokens": [732, 12, 14430, 292, 1500, 13, 1436, 264, 6687, 15035, 321, 362, 307, 445, 337, 732, 12, 14430, 292, 1500, 11, 370, 309, 727, 312, 1143, 787, 337, 4997, 466, 732, 12, 14430, 292, 1500, 13, 1018, 321, 2835, 949, 11, 286, 478, 516, 281, 10023, 17291, 337, 1374, 21518, 382, 731, 382, 5252, 46, 20914, 1500, 13, 407, 300, 311, 439, 337, 7187, 2064, 13], "avg_logprob": -0.1898320846593202, "compression_ratio": 1.5257142857142858, "no_speech_prob": 0.0, "words": [{"start": 1448.77, "end": 1448.85, "word": " two", "probability": 0.15283203125}, {"start": 1448.85, "end": 1449.11, "word": "-tailed", "probability": 0.6897786458333334}, {"start": 1449.11, "end": 1449.35, "word": " test.", "probability": 0.7431640625}, {"start": 1451.55, "end": 1452.23, "word": " Because", "probability": 0.8857421875}, {"start": 1452.23, "end": 1452.41, "word": " the", "probability": 0.88818359375}, {"start": 1452.41, "end": 1452.79, "word": " confidence", "probability": 0.90185546875}, {"start": 1452.79, "end": 1453.11, "word": " interval", "probability": 0.943359375}, {"start": 1453.11, "end": 1453.33, "word": " we", "probability": 0.81787109375}, {"start": 1453.33, "end": 1453.57, "word": " have", "probability": 0.94189453125}, {"start": 1453.57, "end": 1453.81, "word": " is", "probability": 0.9072265625}, {"start": 1453.81, "end": 1454.09, "word": " just", "probability": 0.91796875}, {"start": 1454.09, "end": 1454.37, "word": " for", "probability": 0.93603515625}, {"start": 1454.37, "end": 1454.53, "word": " two", "probability": 0.92333984375}, {"start": 1454.53, "end": 1454.87, "word": "-tailed", "probability": 0.8883463541666666}, {"start": 1454.87, "end": 1455.17, "word": " test,", "probability": 0.6025390625}, {"start": 1455.37, "end": 1455.61, "word": " so", "probability": 0.93310546875}, {"start": 1455.61, "end": 1456.27, "word": " it", "probability": 0.6787109375}, {"start": 1456.27, "end": 1456.43, "word": " could", "probability": 0.884765625}, {"start": 1456.43, "end": 1456.61, "word": " be", "probability": 0.9443359375}, {"start": 1456.61, "end": 1457.01, "word": " used", "probability": 0.9111328125}, {"start": 1457.01, "end": 1458.15, "word": " only", "probability": 0.9248046875}, {"start": 1458.15, "end": 1458.49, "word": " for", "probability": 0.95458984375}, {"start": 1458.49, "end": 1458.95, "word": " testing", "probability": 0.87255859375}, {"start": 1458.95, "end": 1459.41, "word": " about", "probability": 0.9052734375}, {"start": 1459.41, "end": 1459.73, "word": " two", "probability": 0.91845703125}, {"start": 1459.73, "end": 1459.95, "word": "-tailed", "probability": 0.921875}, {"start": 1459.95, "end": 1460.21, "word": " test.", "probability": 0.8662109375}, {"start": 1463.35, "end": 1464.03, "word": " As", "probability": 0.9677734375}, {"start": 1464.03, "end": 1464.15, "word": " we", "probability": 0.93701171875}, {"start": 1464.15, "end": 1464.39, "word": " mentioned", "probability": 0.826171875}, {"start": 1464.39, "end": 1464.77, "word": " before,", "probability": 0.859375}, {"start": 1464.91, "end": 1465.17, "word": " I'm", "probability": 0.90771484375}, {"start": 1465.17, "end": 1465.39, "word": " going", "probability": 0.9482421875}, {"start": 1465.39, "end": 1465.59, "word": " to", "probability": 0.96630859375}, {"start": 1465.59, "end": 1465.99, "word": " skip", "probability": 0.98095703125}, {"start": 1465.99, "end": 1466.83, "word": " hypothesis", "probability": 0.80419921875}, {"start": 1466.83, "end": 1467.29, "word": " for", "probability": 0.931640625}, {"start": 1467.29, "end": 1467.77, "word": " variances", "probability": 0.890625}, {"start": 1467.77, "end": 1468.73, "word": " as", "probability": 0.59765625}, {"start": 1468.73, "end": 1468.95, "word": " well", "probability": 0.9345703125}, {"start": 1468.95, "end": 1469.47, "word": " as", "probability": 0.97216796875}, {"start": 1469.47, "end": 1469.93, "word": " ANOVA", "probability": 0.9200846354166666}, {"start": 1469.93, "end": 1471.23, "word": " test.", "probability": 0.6787109375}, {"start": 1471.97, "end": 1472.39, "word": " So", "probability": 0.955078125}, {"start": 1472.39, "end": 1472.75, "word": " that's", "probability": 0.923583984375}, {"start": 1472.75, "end": 1473.11, "word": " all", "probability": 0.9404296875}, {"start": 1473.11, "end": 1473.63, "word": " for", "probability": 0.94970703125}, {"start": 1473.63, "end": 1474.05, "word": " chapter", "probability": 0.5830078125}, {"start": 1474.05, "end": 1476.41, "word": " ten.", "probability": 0.489013671875}], "temperature": 1.0}, {"id": 57, "seek": 149527, "start": 1477.67, "end": 1495.27, "text": " But now I'm going to do some of the practice problems. Chapter 10. To practice, let's start with some practice problems for Chapter 10.", "tokens": [583, 586, 286, 478, 516, 281, 360, 512, 295, 264, 3124, 2740, 13, 18874, 1266, 13, 1407, 3124, 11, 718, 311, 722, 365, 512, 3124, 2740, 337, 18874, 1266, 13], "avg_logprob": -0.24067540803263265, "compression_ratio": 1.36, "no_speech_prob": 0.0, "words": [{"start": 1477.67, "end": 1478.01, "word": " But", "probability": 0.51953125}, {"start": 1478.01, "end": 1478.47, "word": " now", "probability": 0.8857421875}, {"start": 1478.47, "end": 1478.73, "word": " I'm", "probability": 0.645751953125}, {"start": 1478.73, "end": 1478.99, "word": " going", "probability": 0.94287109375}, {"start": 1478.99, "end": 1479.15, "word": " to", "probability": 0.9697265625}, {"start": 1479.15, "end": 1479.33, "word": " do", "probability": 0.9052734375}, {"start": 1479.33, "end": 1479.73, "word": " some", "probability": 0.912109375}, {"start": 1479.73, "end": 1481.63, "word": " of", "probability": 0.86865234375}, {"start": 1481.63, "end": 1481.89, "word": " the", "probability": 0.90771484375}, {"start": 1481.89, "end": 1482.39, "word": " practice", "probability": 0.92578125}, {"start": 1482.39, "end": 1483.73, "word": " problems.", "probability": 0.86572265625}, {"start": 1486.75, "end": 1487.23, "word": " Chapter", "probability": 0.88525390625}, {"start": 1487.23, "end": 1487.49, "word": " 10.", "probability": 0.783203125}, {"start": 1487.91, "end": 1488.17, "word": " To", "probability": 0.7705078125}, {"start": 1488.17, "end": 1488.77, "word": " practice,", "probability": 0.9091796875}, {"start": 1490.57, "end": 1491.09, "word": " let's", "probability": 0.954833984375}, {"start": 1491.09, "end": 1491.49, "word": " start", "probability": 0.923828125}, {"start": 1491.49, "end": 1491.87, "word": " with", "probability": 0.892578125}, {"start": 1491.87, "end": 1492.63, "word": " some", "probability": 0.89794921875}, {"start": 1492.63, "end": 1493.69, "word": " practice", "probability": 0.927734375}, {"start": 1493.69, "end": 1494.21, "word": " problems", "probability": 0.84228515625}, {"start": 1494.21, "end": 1494.51, "word": " for", "probability": 0.728515625}, {"start": 1494.51, "end": 1494.81, "word": " Chapter", "probability": 0.5498046875}, {"start": 1494.81, "end": 1495.27, "word": " 10.", "probability": 0.96630859375}], "temperature": 1.0}, {"id": 58, "seek": 152863, "start": 1499.27, "end": 1528.63, "text": " A few years ago, Pepsi invited consumers to take the Pepsi challenge. Consumers were asked to decide which of two sodas, Coke or Pepsi. They preferred an applied taste test. Pepsi was interested in determining what factors played a role in people's taste preferences. One of the factors studied was the gender of the consumer.", "tokens": [316, 1326, 924, 2057, 11, 42311, 9185, 11883, 281, 747, 264, 42311, 3430, 13, 6923, 449, 433, 645, 2351, 281, 4536, 597, 295, 732, 15047, 296, 11, 32996, 420, 42311, 13, 814, 16494, 364, 6456, 3939, 1500, 13, 42311, 390, 3102, 294, 23751, 437, 6771, 3737, 257, 3090, 294, 561, 311, 3939, 21910, 13, 1485, 295, 264, 6771, 9454, 390, 264, 7898, 295, 264, 9711, 13], "avg_logprob": -0.14552238138753976, "compression_ratio": 1.6029411764705883, "no_speech_prob": 0.0, "words": [{"start": 1499.27, "end": 1499.53, "word": " A", "probability": 0.953125}, {"start": 1499.53, "end": 1499.73, "word": " few", "probability": 0.9140625}, {"start": 1499.73, "end": 1499.93, "word": " years", "probability": 0.92529296875}, {"start": 1499.93, "end": 1500.45, "word": " ago,", "probability": 0.9033203125}, {"start": 1501.09, "end": 1501.21, "word": " Pepsi", "probability": 0.358154296875}, {"start": 1501.21, "end": 1501.73, "word": " 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"probability": 0.89404296875}, {"start": 1517.49, "end": 1517.69, "word": " Pepsi", "probability": 0.85888671875}, {"start": 1517.69, "end": 1517.93, "word": " was", "probability": 0.908203125}, {"start": 1517.93, "end": 1518.41, "word": " interested", "probability": 0.84619140625}, {"start": 1518.41, "end": 1518.73, "word": " in", "probability": 0.921875}, {"start": 1518.73, "end": 1519.31, "word": " determining", "probability": 0.9267578125}, {"start": 1519.31, "end": 1520.63, "word": " what", "probability": 0.92431640625}, {"start": 1520.63, "end": 1521.25, "word": " factors", "probability": 0.95458984375}, {"start": 1521.25, "end": 1521.67, "word": " played", "probability": 0.83447265625}, {"start": 1521.67, "end": 1521.93, "word": " a", "probability": 0.98193359375}, {"start": 1521.93, "end": 1522.19, "word": " role", "probability": 0.958984375}, {"start": 1522.19, "end": 1522.53, "word": " in", "probability": 0.94580078125}, {"start": 1522.53, "end": 1523.13, "word": " people's", 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For meals, size of 109. So that's your N1. And proportion.", "tokens": [36261, 366, 264, 3542, 295, 264, 5215, 15763, 264, 3939, 21910, 295, 1706, 293, 2266, 365, 264, 32482, 1367, 21490, 17502, 294, 420, 337, 42311, 13, 1171, 12832, 11, 2744, 295, 1266, 24, 13, 407, 300, 311, 428, 426, 16, 13, 400, 16068, 13], "avg_logprob": -0.2279513955116272, "compression_ratio": 1.385135135135135, "no_speech_prob": 0.0, "words": [{"start": 1529.65, "end": 1529.99, "word": " Below", "probability": 0.75439453125}, {"start": 1529.99, "end": 1530.19, "word": " are", "probability": 0.9052734375}, {"start": 1530.19, "end": 1530.35, "word": " the", "probability": 0.9033203125}, {"start": 1530.35, "end": 1530.79, "word": " results", "probability": 0.900390625}, {"start": 1530.79, "end": 1531.13, "word": " of", "probability": 0.94873046875}, {"start": 1531.13, "end": 1531.25, "word": " the", "probability": 0.8388671875}, {"start": 1531.25, "end": 1531.65, "word": " analysis", "probability": 0.86083984375}, {"start": 1531.65, "end": 1532.35, "word": " comparing", "probability": 0.87451171875}, {"start": 1532.35, "end": 1533.09, "word": " the", "probability": 0.9169921875}, {"start": 1533.09, "end": 1533.93, "word": " taste", "probability": 0.8046875}, {"start": 1533.93, "end": 1534.51, "word": " preferences", "probability": 0.91259765625}, {"start": 1534.51, "end": 1535.07, "word": " of", "probability": 0.96142578125}, {"start": 1535.07, "end": 1535.31, "word": " men", "probability": 0.935546875}, {"start": 1535.31, "end": 1535.49, "word": " and", "probability": 0.9404296875}, {"start": 1535.49, "end": 1535.81, "word": " women", "probability": 0.8994140625}, {"start": 1535.81, "end": 1536.63, "word": " with", "probability": 0.6865234375}, {"start": 1536.63, "end": 1536.87, "word": " the", "probability": 0.8935546875}, {"start": 1536.87, "end": 1537.71, "word": " proportions", "probability": 0.763671875}, {"start": 1537.71, "end": 1538.49, "word": " depicting", "probability": 0.84716796875}, {"start": 1538.49, "end": 1539.91, "word": " preference", "probability": 0.88671875}, {"start": 1539.91, "end": 1540.45, "word": " in", "probability": 0.68505859375}, {"start": 1540.45, "end": 1541.05, "word": " or", "probability": 0.59716796875}, {"start": 1541.05, "end": 1541.31, "word": " for", "probability": 0.9560546875}, {"start": 1541.31, "end": 1541.63, "word": " Pepsi.", "probability": 0.9384765625}, {"start": 1542.81, "end": 1543.53, "word": " For", "probability": 0.92138671875}, {"start": 1543.53, "end": 1543.99, "word": " meals,", "probability": 0.64453125}, {"start": 1545.99, "end": 1549.19, "word": " size", "probability": 0.634765625}, {"start": 1549.19, "end": 1551.87, "word": " of", "probability": 0.92578125}, {"start": 1551.87, "end": 1552.61, "word": " 109.", "probability": 0.86572265625}, {"start": 1553.41, "end": 1553.93, "word": " So", "probability": 0.9267578125}, {"start": 1553.93, "end": 1554.23, "word": " that's", "probability": 0.901611328125}, {"start": 1554.23, "end": 1554.43, "word": " your", "probability": 0.88427734375}, {"start": 1554.43, "end": 1554.79, "word": " N1.", "probability": 0.885986328125}, {"start": 1556.95, "end": 1557.45, "word": " And", "probability": 0.9384765625}, {"start": 1557.45, "end": 1557.99, "word": " proportion.", "probability": 0.5546875}], "temperature": 1.0}, {"id": 60, "seek": 158652, "start": 1560.48, "end": 1586.52, "text": " for males is around 4.2. For females, N2 equals 52, and proportion of females, 25%. 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And this statistic is given by 2.118, so approximately 2.12. 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A. B. Why B? Because the test defines between the new form A and the new form B. 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B. So that's incorrect. C. Why? Why C is the correct answer? 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So since we have difference here, it should be not equal to. And since we are talking about proportions, so you have to ignore A and B. So A and B should be ignored first. Then you either choose C or D. C is the correct answer. So C is the correct answer. That's for number one. 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Using the test statistic given, compute the appropriate p-value for the test. 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Now he asks about suppose the company wanted to test to determine if males prefer Pepsi more than females. Using again the statistic given which is 2.12 for example, compute appropriately value. 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So A is the correct answer. Now if the problem is two-tailed test, it should be multiplied by 2. So the answer, the correct should be B. So you have A and B.", "tokens": [6915, 1958, 293, 1614, 13, 407, 316, 307, 264, 3006, 1867, 13, 823, 498, 264, 1154, 307, 732, 12, 14430, 292, 1500, 11, 309, 820, 312, 17207, 538, 568, 13, 407, 264, 1867, 11, 264, 3006, 820, 312, 363, 13, 407, 291, 362, 316, 293, 363, 13], "avg_logprob": -0.24348957619319359, "compression_ratio": 1.359375, "no_speech_prob": 0.0, "words": [{"start": 1843.43, "end": 1843.99, "word": " equals", "probability": 0.338134765625}, {"start": 1843.99, "end": 1844.55, "word": " 0", "probability": 0.55517578125}, {"start": 1844.55, "end": 1844.73, "word": " and", "probability": 0.7109375}, {"start": 1844.73, "end": 1844.91, "word": " 7.", "probability": 0.90283203125}, {"start": 1846.03, "end": 1846.59, "word": " So", "probability": 0.89599609375}, {"start": 1846.59, "end": 1846.87, "word": " A", "probability": 0.4150390625}, {"start": 1846.87, "end": 1847.05, "word": " is", "probability": 0.95458984375}, {"start": 1847.05, "end": 1847.19, "word": " the", "probability": 0.916015625}, {"start": 1847.19, "end": 1847.45, "word": " correct", "probability": 0.8994140625}, {"start": 1847.45, "end": 1847.87, "word": " answer.", "probability": 0.9541015625}, {"start": 1849.27, "end": 1849.69, "word": " Now", "probability": 0.92041015625}, {"start": 1849.69, "end": 1849.89, "word": " if", "probability": 0.662109375}, {"start": 1849.89, "end": 1850.05, "word": " the", "probability": 0.90478515625}, {"start": 1850.05, "end": 1850.41, "word": " problem", "probability": 0.861328125}, {"start": 1850.41, "end": 1850.89, "word": " is", "probability": 0.9482421875}, {"start": 1850.89, "end": 1852.03, "word": " two", "probability": 0.52001953125}, {"start": 1852.03, "end": 1852.39, "word": "-tailed", "probability": 0.7342122395833334}, {"start": 1852.39, "end": 1852.63, "word": " test,", "probability": 0.8671875}, {"start": 1853.07, "end": 1853.67, "word": " it", "probability": 0.908203125}, {"start": 1853.67, "end": 1853.83, "word": " should", "probability": 0.96923828125}, {"start": 1853.83, "end": 1853.97, "word": " be", "probability": 0.9462890625}, {"start": 1853.97, "end": 1854.35, "word": " multiplied", "probability": 0.6650390625}, {"start": 1854.35, "end": 1854.69, "word": " by", "probability": 0.9697265625}, {"start": 1854.69, "end": 1854.99, "word": " 2.", "probability": 0.59326171875}, {"start": 1855.97, "end": 1856.21, "word": " So", "probability": 0.94580078125}, {"start": 1856.21, "end": 1856.37, "word": " the", "probability": 0.90576171875}, {"start": 1856.37, "end": 1856.67, "word": " answer,", "probability": 0.79931640625}, {"start": 1856.89, "end": 1856.99, "word": " the", "probability": 0.90771484375}, {"start": 1856.99, "end": 1857.23, "word": " correct", "probability": 0.9140625}, {"start": 1857.23, "end": 1857.45, "word": " should", "probability": 0.70556640625}, {"start": 1857.45, "end": 1857.77, "word": " be", "probability": 0.93798828125}, {"start": 1857.77, "end": 1858.39, "word": " B.", "probability": 0.92529296875}, {"start": 1859.43, "end": 1859.75, "word": " So", "probability": 0.947265625}, {"start": 1859.75, "end": 1859.85, "word": " you", "probability": 0.5966796875}, {"start": 1859.85, "end": 1860.03, "word": " have", "probability": 0.947265625}, {"start": 1860.03, "end": 1860.21, "word": " A", "probability": 0.4970703125}, {"start": 1860.21, "end": 1860.43, "word": " and", "probability": 0.9501953125}, {"start": 1860.43, "end": 1860.69, "word": " B.", "probability": 0.9990234375}], "temperature": 1.0}, {"id": 71, "seek": 188859, "start": 1861.33, "end": 1888.59, "text": " If it is one-third, your correct answer is A. If it is two-thirds, I mean if we are testing to determine if a difference exists, then you have to multiply this one by two. So that's your B value. Any question? Number three. 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"temperature": 1.0}, {"id": 72, "seek": 191805, "start": 1889.51, "end": 1918.05, "text": " If males prefer Pepsi less than females, using the statistic given, compute the product B value. Now, H1 in this case, B1 is smaller than Z by 2, by 1 smaller than 1. Now your B value, Z is smaller than, because here it is smaller than my statistic 2.12.", "tokens": [759, 20776, 4382, 42311, 1570, 813, 21529, 11, 1228, 264, 29588, 2212, 11, 14722, 264, 1674, 363, 2158, 13, 823, 11, 389, 16, 294, 341, 1389, 11, 363, 16, 307, 4356, 813, 1176, 538, 568, 11, 538, 502, 4356, 813, 502, 13, 823, 428, 363, 2158, 11, 1176, 307, 4356, 813, 11, 570, 510, 309, 307, 4356, 813, 452, 29588, 568, 13, 4762, 13], "avg_logprob": -0.40024038461538464, "compression_ratio": 1.6037735849056605, "no_speech_prob": 0.0, "words": [{"start": 1889.51, "end": 1890.13, "word": " If", "probability": 0.029510498046875}, {"start": 1890.13, "end": 1890.65, "word": " males", "probability": 0.880859375}, {"start": 1890.65, "end": 1891.53, "word": " prefer", "probability": 0.798828125}, {"start": 1891.53, "end": 1892.17, "word": " Pepsi", "probability": 0.751953125}, {"start": 1892.17, "end": 1892.75, "word": " less", "probability": 0.86474609375}, {"start": 1892.75, "end": 1893.23, "word": " than", "probability": 0.931640625}, {"start": 1893.23, "end": 1894.31, "word": " females,", "probability": 0.888671875}, {"start": 1894.81, "end": 1895.15, "word": " using", "probability": 0.7333984375}, {"start": 1895.15, "end": 1895.35, "word": " the", "probability": 0.4794921875}, {"start": 1895.35, "end": 1895.73, "word": " statistic", "probability": 0.37548828125}, {"start": 1895.73, "end": 1896.27, "word": " given,", "probability": 0.81982421875}, {"start": 1896.39, "end": 1896.63, "word": " compute", "probability": 0.7685546875}, {"start": 1896.63, "end": 1896.81, "word": " the", "probability": 0.87158203125}, {"start": 1896.81, "end": 1897.01, "word": " product", "probability": 0.1793212890625}, {"start": 1897.01, "end": 1897.17, "word": " B", "probability": 0.425048828125}, {"start": 1897.17, "end": 1897.43, "word": " value.", "probability": 0.54296875}, {"start": 1899.29, "end": 1899.55, "word": " Now,", "probability": 0.86181640625}, {"start": 1899.65, "end": 1900.19, "word": " H1", "probability": 0.7451171875}, {"start": 1900.19, "end": 1900.37, "word": " in", "probability": 0.81640625}, {"start": 1900.37, "end": 1900.57, "word": " this", "probability": 0.95068359375}, {"start": 1900.57, "end": 1901.05, "word": " case,", "probability": 0.91943359375}, {"start": 1902.27, "end": 1902.71, "word": " B1", "probability": 0.811767578125}, {"start": 1902.71, "end": 1902.99, "word": " is", "probability": 0.55712890625}, {"start": 1902.99, "end": 1903.37, "word": " smaller", "probability": 0.87158203125}, {"start": 1903.37, "end": 1903.93, "word": " than", "probability": 0.890625}, {"start": 1903.93, "end": 1904.27, "word": " Z", "probability": 0.169189453125}, {"start": 1904.27, "end": 1905.25, "word": " by", "probability": 0.765625}, {"start": 1905.25, "end": 1906.11, "word": " 2,", "probability": 0.7109375}, {"start": 1906.31, "end": 1906.49, "word": " by", "probability": 0.828125}, {"start": 1906.49, "end": 1906.69, "word": " 1", "probability": 0.72607421875}, {"start": 1906.69, "end": 1907.05, "word": " smaller", "probability": 0.55419921875}, {"start": 1907.05, "end": 1907.31, "word": " than", "probability": 0.94677734375}, {"start": 1907.31, "end": 1907.53, "word": " 1.", "probability": 0.890625}, {"start": 1907.95, "end": 1908.23, "word": " Now", "probability": 0.89892578125}, {"start": 1908.23, "end": 1908.49, "word": " your", "probability": 0.52783203125}, {"start": 1908.49, "end": 1908.69, "word": " B", "probability": 0.9716796875}, {"start": 1908.69, "end": 1909.09, "word": " value,", "probability": 0.96044921875}, {"start": 1910.57, "end": 1910.81, "word": " Z", "probability": 0.95263671875}, {"start": 1910.81, "end": 1912.89, "word": " is", "probability": 0.58935546875}, {"start": 1912.89, "end": 1913.33, "word": " smaller", "probability": 0.8671875}, {"start": 1913.33, "end": 1913.75, "word": " than,", "probability": 0.9296875}, {"start": 1913.79, "end": 1914.07, "word": " because", "probability": 0.8330078125}, {"start": 1914.07, "end": 1914.29, "word": " here", "probability": 0.68017578125}, {"start": 1914.29, "end": 1914.49, "word": " it", "probability": 0.332763671875}, {"start": 1914.49, "end": 1914.49, "word": " is", "probability": 0.5400390625}, {"start": 1914.49, "end": 1914.87, "word": " smaller", "probability": 0.8681640625}, {"start": 1914.87, "end": 1915.31, "word": " than", "probability": 0.9306640625}, {"start": 1915.31, "end": 1916.45, "word": " my", "probability": 0.68798828125}, {"start": 1916.45, "end": 1917.15, "word": " statistic", "probability": 0.875}, {"start": 1917.15, "end": 1917.51, "word": " 2", "probability": 0.8388671875}, {"start": 1917.51, "end": 1918.05, "word": ".12.", "probability": 0.977783203125}], "temperature": 1.0}, {"id": 73, "seek": 194827, "start": 1921.57, "end": 1948.27, "text": " We don't write negative sign. Because the value of the statistic is 2.12. But here we are going to test lower tail test. So my B value is B of Z smaller than. So smaller comes from the alternator. This is the sign under the alternator. And you have to take the value of the Z statistic as it is. 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Suppose that the two-tailed B value was really 0734. Now suppose my B value for two-tailed is 0734. That's for two-tailed. This is my B value. This is my B value.", "tokens": [823, 337, 1365, 11, 2870, 264, 1589, 321, 362, 370, 1400, 337, 363, 2158, 13, 21360, 300, 264, 732, 12, 14430, 292, 363, 2158, 390, 534, 1958, 22, 12249, 13, 823, 7297, 452, 363, 2158, 337, 732, 12, 14430, 292, 307, 1958, 22, 12249, 13, 663, 311, 337, 732, 12, 14430, 292, 13, 639, 307, 452, 363, 2158, 13, 639, 307, 452, 363, 2158, 13], "avg_logprob": -0.2440814459414193, "compression_ratio": 1.6618705035971224, "no_speech_prob": 0.0, "words": [{"start": 1980.2299999999998, "end": 1980.87, "word": " Now", "probability": 0.08782958984375}, {"start": 1980.87, "end": 1981.21, "word": " for", "probability": 0.546875}, {"start": 1981.21, "end": 1981.67, "word": " example,", "probability": 0.95849609375}, {"start": 1982.43, "end": 1982.77, "word": " forget", "probability": 0.80517578125}, {"start": 1982.77, "end": 1982.99, "word": " the", "probability": 0.8046875}, {"start": 1982.99, "end": 1983.39, "word": " information", "probability": 0.79345703125}, {"start": 1983.39, "end": 1983.65, "word": " we", "probability": 0.83056640625}, {"start": 1983.65, "end": 1983.91, "word": " have", "probability": 0.8388671875}, {"start": 1983.91, "end": 1984.29, "word": " so", "probability": 0.77783203125}, {"start": 1984.29, "end": 1984.61, "word": " far", "probability": 0.94775390625}, {"start": 1984.61, "end": 1984.91, "word": " for", "probability": 0.69677734375}, {"start": 1984.91, "end": 1985.09, "word": " B", "probability": 0.492431640625}, {"start": 1985.09, "end": 1985.47, "word": " value.", "probability": 0.79443359375}, {"start": 1985.95, "end": 1986.39, "word": " Suppose", "probability": 0.7236328125}, {"start": 1986.39, "end": 1986.81, "word": " that", "probability": 0.91162109375}, {"start": 1986.81, "end": 1987.15, "word": " the", "probability": 0.74853515625}, {"start": 1987.15, "end": 1987.39, "word": " two", "probability": 0.303466796875}, {"start": 1987.39, "end": 1987.77, "word": "-tailed", "probability": 0.6593424479166666}, {"start": 1987.77, "end": 1987.91, "word": " B", "probability": 0.865234375}, {"start": 1987.91, "end": 1988.23, "word": " value", "probability": 0.91455078125}, {"start": 1988.23, "end": 1988.55, "word": " was", "probability": 0.86279296875}, {"start": 1988.55, "end": 1988.95, "word": " really", "probability": 0.84130859375}, {"start": 1988.95, "end": 1990.17, "word": " 0734.", "probability": 0.732177734375}, {"start": 1990.79, "end": 1991.07, "word": " Now", "probability": 0.9306640625}, {"start": 1991.07, "end": 1991.49, "word": " suppose", "probability": 0.76220703125}, {"start": 1991.49, "end": 1991.69, "word": " my", "probability": 0.93701171875}, {"start": 1991.69, "end": 1991.91, "word": " B", "probability": 0.96728515625}, {"start": 1991.91, "end": 1992.25, "word": " value", "probability": 0.95751953125}, {"start": 1992.25, "end": 1992.57, "word": " for", "probability": 0.9365234375}, {"start": 1992.57, "end": 1992.83, "word": " two", "probability": 0.896484375}, {"start": 1992.83, "end": 1994.35, "word": "-tailed", "probability": 0.92822265625}, {"start": 1994.35, "end": 1995.03, "word": " is", "probability": 0.73486328125}, {"start": 1995.03, "end": 1996.45, "word": " 0734.", "probability": 0.9519856770833334}, {"start": 1996.63, "end": 1996.95, "word": " That's", "probability": 0.904296875}, {"start": 1996.95, "end": 1997.29, "word": " for", "probability": 0.810546875}, {"start": 1997.29, "end": 1999.01, "word": " two", "probability": 0.8984375}, {"start": 1999.01, "end": 1999.31, "word": "-tailed.", "probability": 0.9130859375}, {"start": 1999.35, "end": 1999.49, "word": " This", "probability": 0.591796875}, {"start": 1999.49, "end": 1999.55, "word": " is", "probability": 0.9443359375}, {"start": 1999.55, "end": 1999.69, "word": " my", "probability": 0.96923828125}, {"start": 1999.69, "end": 1999.89, "word": " B", "probability": 0.98681640625}, {"start": 1999.89, "end": 2000.21, "word": " value.", "probability": 0.9599609375}, {"start": 2003.07, "end": 2003.71, "word": " This", "probability": 0.87255859375}, {"start": 2003.71, "end": 2003.85, "word": " is", "probability": 0.95166015625}, {"start": 2003.85, "end": 2004.01, "word": " my", "probability": 0.97021484375}, {"start": 2004.01, "end": 2004.23, "word": " B", "probability": 0.9951171875}, {"start": 2004.23, "end": 2004.51, "word": " value.", "probability": 0.9765625}], "temperature": 1.0}, {"id": 76, "seek": 202949, "start": 2005.39, "end": 2029.49, "text": " It's 0, 7, 3, 4. Now we have four answers. Part A, B, C, and D. Which one is the correct? A says at 5% level, there is sufficient evidence to conclude the proportion of males", "tokens": [467, 311, 1958, 11, 1614, 11, 805, 11, 1017, 13, 823, 321, 362, 1451, 6338, 13, 4100, 316, 11, 363, 11, 383, 11, 293, 413, 13, 3013, 472, 307, 264, 3006, 30, 316, 1619, 412, 1025, 4, 1496, 11, 456, 307, 11563, 4467, 281, 16886, 264, 16068, 295, 20776], "avg_logprob": -0.28687499463558197, "compression_ratio": 1.2237762237762237, "no_speech_prob": 0.0, "words": [{"start": 2005.39, "end": 2005.79, "word": " It's", "probability": 0.39892578125}, {"start": 2005.79, "end": 2006.03, "word": " 0,", "probability": 0.72607421875}, {"start": 2006.11, "end": 2006.27, "word": " 7,", "probability": 0.357177734375}, {"start": 2006.39, "end": 2006.59, "word": " 3,", "probability": 0.98095703125}, {"start": 2006.67, "end": 2006.97, "word": " 4.", "probability": 0.95458984375}, {"start": 2007.77, "end": 2008.05, "word": " Now", "probability": 0.90087890625}, {"start": 2008.05, "end": 2008.27, "word": " we", "probability": 0.751953125}, {"start": 2008.27, "end": 2008.49, "word": " have", "probability": 0.94482421875}, {"start": 2008.49, "end": 2008.87, "word": " four", "probability": 0.70654296875}, {"start": 2008.87, "end": 2009.51, "word": " answers.", "probability": 0.88427734375}, {"start": 2009.97, "end": 2010.17, "word": " Part", "probability": 0.90478515625}, {"start": 2010.17, "end": 2010.47, "word": " A,", "probability": 0.73095703125}, {"start": 2011.29, "end": 2011.93, "word": " B,", "probability": 0.9755859375}, {"start": 2012.23, "end": 2012.45, "word": " C,", "probability": 0.984375}, {"start": 2012.65, "end": 2012.77, "word": " and", "probability": 0.892578125}, {"start": 2012.77, "end": 2012.93, "word": " D.", "probability": 0.9970703125}, {"start": 2013.07, "end": 2013.27, "word": " Which", "probability": 0.88330078125}, {"start": 2013.27, "end": 2013.49, "word": " one", "probability": 0.92919921875}, {"start": 2013.49, "end": 2013.65, "word": " is", "probability": 0.94921875}, {"start": 2013.65, "end": 2013.77, "word": " the", "probability": 0.501953125}, {"start": 2013.77, "end": 2014.05, "word": " correct?", "probability": 0.900390625}, {"start": 2022.03, "end": 2022.61, "word": " A", "probability": 0.6923828125}, {"start": 2022.61, "end": 2022.91, "word": " says", "probability": 0.6689453125}, {"start": 2022.91, "end": 2023.27, "word": " at", "probability": 0.5859375}, {"start": 2023.27, "end": 2023.59, "word": " 5", "probability": 0.67529296875}, {"start": 2023.59, "end": 2023.89, "word": "%", "probability": 0.82470703125}, {"start": 2023.89, "end": 2024.39, "word": " level,", "probability": 0.939453125}, {"start": 2025.01, "end": 2025.29, "word": " there", "probability": 0.88330078125}, {"start": 2025.29, "end": 2025.51, "word": " is", "probability": 0.880859375}, {"start": 2025.51, "end": 2026.07, "word": " sufficient", "probability": 0.89404296875}, {"start": 2026.07, "end": 2026.61, "word": " evidence", "probability": 0.95947265625}, {"start": 2026.61, "end": 2026.85, "word": " to", "probability": 0.9521484375}, {"start": 2026.85, "end": 2027.35, "word": " conclude", "probability": 0.83349609375}, {"start": 2027.35, "end": 2028.39, "word": " the", "probability": 0.85888671875}, {"start": 2028.39, "end": 2028.83, "word": " proportion", "probability": 0.78955078125}, {"start": 2028.83, "end": 2029.09, "word": " of", "probability": 0.97216796875}, {"start": 2029.09, "end": 2029.49, "word": " males", "probability": 0.93505859375}], "temperature": 1.0}, {"id": 77, "seek": 205753, "start": 2030.77, "end": 2057.53, "text": " Preferring Pepsi differs from the proportion of females preferring Pepsi. Which one is the correct answer? B value is 0.734. B it says at alpha equals 10 percent. There is sufficient evidence.", "tokens": [48401, 2937, 42311, 37761, 490, 264, 16068, 295, 21529, 4382, 2937, 42311, 13, 3013, 472, 307, 264, 3006, 1867, 30, 363, 2158, 307, 1958, 13, 22, 12249, 13, 363, 309, 1619, 412, 8961, 6915, 1266, 3043, 13, 821, 307, 11563, 4467, 13], "avg_logprob": -0.2906976716462956, "compression_ratio": 1.3591549295774648, "no_speech_prob": 0.0, "words": [{"start": 2030.77, "end": 2031.51, "word": " Preferring", "probability": 0.7025146484375}, {"start": 2031.51, "end": 2031.83, "word": " Pepsi", "probability": 0.775390625}, {"start": 2031.83, "end": 2032.21, "word": " differs", "probability": 0.9345703125}, {"start": 2032.21, "end": 2032.83, "word": " from", "probability": 0.8701171875}, {"start": 2032.83, "end": 2033.01, "word": " the", "probability": 0.8095703125}, {"start": 2033.01, "end": 2033.41, "word": " proportion", "probability": 0.740234375}, {"start": 2033.41, "end": 2033.65, "word": " of", "probability": 0.3681640625}, {"start": 2033.65, "end": 2033.93, "word": " females", "probability": 0.8779296875}, {"start": 2033.93, "end": 2034.59, "word": " preferring", "probability": 0.9150390625}, {"start": 2034.59, "end": 2034.95, "word": " Pepsi.", "probability": 0.85205078125}, {"start": 2037.07, "end": 2037.87, "word": " Which", "probability": 0.7548828125}, {"start": 2037.87, "end": 2038.05, "word": " one", "probability": 0.88427734375}, {"start": 2038.05, "end": 2038.15, "word": " is", "probability": 0.869140625}, {"start": 2038.15, "end": 2038.29, "word": " the", "probability": 0.9013671875}, {"start": 2038.29, "end": 2038.57, "word": " correct", "probability": 0.88623046875}, {"start": 2038.57, "end": 2038.97, "word": " answer?", "probability": 0.9580078125}, {"start": 2042.29, "end": 2043.09, "word": " B", "probability": 0.630859375}, {"start": 2043.09, "end": 2043.39, "word": " value", "probability": 0.8095703125}, {"start": 2043.39, "end": 2043.59, "word": " is", "probability": 0.91455078125}, {"start": 2043.59, "end": 2043.81, "word": " 0", "probability": 0.8623046875}, {"start": 2043.81, "end": 2044.55, "word": ".734.", "probability": 0.8001302083333334}, {"start": 2050.37, "end": 2050.85, "word": " B", "probability": 0.7744140625}, {"start": 2050.85, "end": 2051.07, "word": " it", "probability": 0.638671875}, {"start": 2051.07, "end": 2051.47, "word": " says", "probability": 0.88330078125}, {"start": 2051.47, "end": 2052.51, "word": " at", "probability": 0.481689453125}, {"start": 2052.51, "end": 2053.39, "word": " alpha", "probability": 0.53125}, {"start": 2053.39, "end": 2053.71, "word": " equals", "probability": 0.385498046875}, {"start": 2053.71, "end": 2053.99, "word": " 10", "probability": 0.76708984375}, {"start": 2053.99, "end": 2054.47, "word": " percent.", "probability": 0.36865234375}, {"start": 2055.87, "end": 2056.49, "word": " There", "probability": 0.74755859375}, {"start": 2056.49, "end": 2056.65, "word": " is", "probability": 0.92041015625}, {"start": 2056.65, "end": 2057.13, "word": " sufficient", "probability": 0.89501953125}, {"start": 2057.13, "end": 2057.53, "word": " evidence.", "probability": 0.95849609375}], "temperature": 1.0}, {"id": 78, "seek": 208296, "start": 2058.44, "end": 2082.96, "text": " to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. C. At 5%, there is sufficient evidence to indicate the proportion of males preferring Pepsi equals the proportion of females preferring Pepsi. D. 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Again, suppose that here it's two-tailed test. It says two-tailed test. Two-tailed means Y1 does not equal Y2. 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So which one is the correct answer? B? D. Let's look at D. Let's look at D. 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So that's incorrect. B. At five, at 10% now, there is sufficient evidence. Sufficient means we reject. 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So we reject. That means you have to read carefully. There is sufficient evidence to include, to indicate the proportion of males preferring Pepsi differs from the proportion of females. That's correct. So B is the correct state. 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Now for D, we reject null hypothesis at 8%. Since this value 0.7 is smaller than alpha, so we reject. So this is incorrect. Now for C, be careful. At 5%, if this, if we change this one little bit, there is insufficient evidence. What do you think? 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You cannot say equal because this one maybe yes maybe no you don't know the exact answer. 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Don't reject the zero does not imply if zero is true. It means the evidence, the data you have is not sufficient to support the alternative evidence. 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So V is the correct answer. Six, seven, and eight. Construct 90% confidence interval, construct 95, construct 99. 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The last one is the widest because here 99 is the largest continence limit. So that means the width of the interval is the largest in this case. 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Simple calculation will give the confidence interval for each one. My question was, which one is the widest confidence interval? 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Corporation randomly selects 150 salespeople and finds that 66% who have never taken self-improvement course would like such a course. 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So in the past, into 160, and proportion is 60%. 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So suppose Pi 1 and Pi 2. Pi 1 for recent study and Pi 2 for the past study. So that's the question. 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Which is the correct? A is the correct answer. Why A is the correct answer? 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So A is the correct answer. Now B is incorrect because why B is incorrect? Exactly because under H0 we have pi 1 minus pi 2 does not equal 0. Always equal sign appears only under the null hypothesis. So it's the opposite here. 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This sign null hypothesis states incorrectly, because under H0 should have equal sign, and for alternate it should be not equal to. 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C is the correct answer. Because it says a greater proportion of workers work currently. So by one, greater than by two. So C is the correct answer. 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So it means by one is greater than by two. It means by one minus by two is positive. So the alternative is by one minus two by two is positive. So this one is the correct answer. Exactly. If if here we have what in the past should be it should be the correct answer.", "tokens": [682, 264, 1791, 13, 407, 309, 1355, 538, 472, 307, 5044, 813, 538, 732, 13, 467, 1355, 538, 472, 3175, 538, 732, 307, 3353, 13, 407, 264, 8535, 307, 538, 472, 3175, 732, 538, 732, 307, 3353, 13, 407, 341, 472, 307, 264, 3006, 1867, 13, 7587, 13, 759, 498, 510, 321, 362, 437, 294, 264, 1791, 820, 312, 309, 820, 312, 264, 3006, 1867, 13], "avg_logprob": -0.21653451759423784, "compression_ratio": 1.9047619047619047, "no_speech_prob": 0.0, "words": [{"start": 2821.73, "end": 2822.09, "word": " In", "probability": 0.5361328125}, {"start": 2822.09, "end": 2822.25, "word": " the", "probability": 0.92236328125}, {"start": 2822.25, "end": 2822.55, "word": " past.", "probability": 0.919921875}, {"start": 2822.91, "end": 2823.09, "word": " So", "probability": 0.884765625}, {"start": 2823.09, "end": 2823.55, "word": " it", "probability": 0.63232421875}, {"start": 2823.55, "end": 2823.77, "word": " means", 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"word": " should", "probability": 0.8056640625}, {"start": 2849.41, "end": 2849.57, "word": " be", "probability": 0.9482421875}, {"start": 2849.57, "end": 2849.75, "word": " the", "probability": 0.89892578125}, {"start": 2849.75, "end": 2850.01, "word": " correct", "probability": 0.91650390625}, {"start": 2850.01, "end": 2850.43, "word": " answer.", "probability": 0.95361328125}], "temperature": 1.0}, {"id": 107, "seek": 287441, "start": 2854.69, "end": 2874.41, "text": " That's to three. Any question for going to number three? Any question for number two? Three. What is the unbiased point estimate for the difference between the two population proportions?", "tokens": [663, 311, 281, 1045, 13, 2639, 1168, 337, 516, 281, 1230, 1045, 30, 2639, 1168, 337, 1230, 732, 30, 6244, 13, 708, 307, 264, 517, 5614, 1937, 935, 12539, 337, 264, 2649, 1296, 264, 732, 4415, 32482, 30], "avg_logprob": -0.18199118131246322, "compression_ratio": 1.46875, "no_speech_prob": 0.0, "words": [{"start": 2854.69, "end": 2855.27, "word": " That's", "probability": 0.711181640625}, {"start": 2855.27, "end": 2855.63, "word": " to", "probability": 0.397216796875}, {"start": 2855.63, "end": 2856.35, "word": " three.", "probability": 0.6982421875}, {"start": 2857.43, "end": 2857.79, "word": " Any", "probability": 0.90966796875}, {"start": 2857.79, "end": 2858.17, "word": " question", "probability": 0.640625}, {"start": 2858.17, "end": 2858.59, "word": " for", "probability": 0.578125}, {"start": 2858.59, "end": 2859.75, "word": " going", "probability": 0.81787109375}, {"start": 2859.75, "end": 2860.01, "word": " to", "probability": 0.9599609375}, {"start": 2860.01, "end": 2860.45, "word": " number", "probability": 0.93115234375}, {"start": 2860.45, "end": 2860.79, "word": " three?", "probability": 0.865234375}, {"start": 2863.09, "end": 2863.89, "word": " Any", "probability": 0.7978515625}, {"start": 2863.89, "end": 2864.21, "word": " question", "probability": 0.8896484375}, {"start": 2864.21, "end": 2864.45, "word": " for", "probability": 0.94189453125}, {"start": 2864.45, "end": 2864.67, "word": " number", "probability": 0.93359375}, {"start": 2864.67, "end": 2864.97, "word": " two?", "probability": 0.89501953125}, {"start": 2866.21, "end": 2866.53, "word": " Three.", "probability": 0.9052734375}, {"start": 2868.61, "end": 2869.21, "word": " What", "probability": 0.8564453125}, {"start": 2869.21, "end": 2869.59, "word": " is", "probability": 0.9453125}, {"start": 2869.59, "end": 2869.95, "word": " the", "probability": 0.92138671875}, {"start": 2869.95, "end": 2870.73, "word": " unbiased", "probability": 0.9521484375}, {"start": 2870.73, "end": 2871.11, "word": " point", "probability": 0.97607421875}, {"start": 2871.11, "end": 2871.65, "word": " estimate", "probability": 0.90283203125}, {"start": 2871.65, "end": 2872.13, "word": " for", "probability": 0.93701171875}, {"start": 2872.13, "end": 2872.31, "word": " the", "probability": 0.921875}, {"start": 2872.31, "end": 2872.79, "word": " difference", "probability": 0.85986328125}, {"start": 2872.79, "end": 2873.19, "word": " between", "probability": 0.87744140625}, {"start": 2873.19, "end": 2873.43, "word": " the", "probability": 0.89208984375}, {"start": 2873.43, "end": 2873.59, "word": " two", "probability": 0.93359375}, {"start": 2873.59, "end": 2874.07, "word": " population", "probability": 0.5947265625}, {"start": 2874.07, "end": 2874.41, "word": " proportions?", "probability": 0.6728515625}], "temperature": 1.0}, {"id": 108, "seek": 290452, "start": 2878.96, "end": 2904.52, "text": " B1 minus B2 which is straight forward calculation gives A the correct answer. Because the point estimate in this case is B1 minus B2. B1 is 66 percent, B2 is 60 percent, so the answer is 6 percent. So B1 minus B2 which is 6 percent.", "tokens": [363, 16, 3175, 363, 17, 597, 307, 2997, 2128, 17108, 2709, 316, 264, 3006, 1867, 13, 1436, 264, 935, 12539, 294, 341, 1389, 307, 363, 16, 3175, 363, 17, 13, 363, 16, 307, 21126, 3043, 11, 363, 17, 307, 4060, 3043, 11, 370, 264, 1867, 307, 1386, 3043, 13, 407, 363, 16, 3175, 363, 17, 597, 307, 1386, 3043, 13], "avg_logprob": -0.20555840163934427, "compression_ratio": 1.6293706293706294, "no_speech_prob": 0.0, "words": [{"start": 2878.9599999999996, "end": 2879.74, "word": " B1", "probability": 0.609130859375}, {"start": 2879.74, "end": 2880.52, "word": " minus", "probability": 0.7958984375}, {"start": 2880.52, "end": 2881.04, "word": " B2", "probability": 0.95458984375}, {"start": 2881.04, "end": 2881.36, "word": " which", "probability": 0.55419921875}, {"start": 2881.36, "end": 2881.76, "word": " is", "probability": 0.94091796875}, {"start": 2881.76, "end": 2883.24, "word": " straight", "probability": 0.40087890625}, {"start": 2883.24, "end": 2883.72, "word": " forward", "probability": 0.83349609375}, {"start": 2883.72, "end": 2884.36, "word": " calculation", "probability": 0.82568359375}, {"start": 2884.36, "end": 2884.74, "word": " gives", "probability": 0.68701171875}, {"start": 2884.74, "end": 2885.0, "word": " A", "probability": 0.75341796875}, {"start": 2885.0, "end": 2885.16, "word": " the", "probability": 0.51220703125}, {"start": 2885.16, "end": 2885.46, "word": " correct", "probability": 0.876953125}, {"start": 2885.46, "end": 2885.9, "word": " answer.", "probability": 0.95458984375}, {"start": 2886.36, "end": 2886.56, "word": " Because", "probability": 0.53125}, {"start": 2886.56, "end": 2886.7, "word": " the", "probability": 0.89306640625}, {"start": 2886.7, "end": 2886.98, "word": " point", "probability": 0.97509765625}, {"start": 2886.98, "end": 2887.56, "word": " estimate", "probability": 0.92919921875}, {"start": 2887.56, "end": 2888.7, "word": " in", "probability": 0.84228515625}, {"start": 2888.7, "end": 2888.96, "word": " this", "probability": 0.9482421875}, {"start": 2888.96, "end": 2889.28, "word": " case", "probability": 0.91455078125}, {"start": 2889.28, "end": 2889.46, "word": " is", "probability": 0.931640625}, {"start": 2889.46, "end": 2889.84, "word": " B1", "probability": 0.97802734375}, {"start": 2889.84, "end": 2890.28, "word": " minus", "probability": 0.9775390625}, {"start": 2890.28, "end": 2890.7, "word": " B2.", "probability": 0.97802734375}, {"start": 2892.14, "end": 2892.58, "word": " B1", "probability": 0.97900390625}, {"start": 2892.58, "end": 2892.74, "word": " is", "probability": 0.86767578125}, {"start": 2892.74, "end": 2893.32, "word": " 66", "probability": 0.7890625}, {"start": 2893.32, "end": 2894.22, "word": " percent,", "probability": 0.49462890625}, {"start": 2894.36, "end": 2894.58, "word": " B2", "probability": 0.987548828125}, {"start": 2894.58, "end": 2894.76, "word": " is", "probability": 0.9384765625}, {"start": 2894.76, "end": 2895.12, "word": " 60", "probability": 0.9599609375}, {"start": 2895.12, "end": 2895.6, "word": " percent,", "probability": 0.951171875}, {"start": 2895.78, "end": 2895.94, "word": " so", "probability": 0.9306640625}, {"start": 2895.94, "end": 2896.08, "word": " the", "probability": 0.91357421875}, {"start": 2896.08, "end": 2896.38, "word": " answer", "probability": 0.9521484375}, {"start": 2896.38, "end": 2897.42, "word": " is", "probability": 0.94921875}, {"start": 2897.42, "end": 2898.56, "word": " 6", "probability": 0.83837890625}, {"start": 2898.56, "end": 2898.98, "word": " percent.", "probability": 0.90673828125}, {"start": 2899.24, "end": 2899.44, "word": " So", "probability": 0.93994140625}, {"start": 2899.44, "end": 2900.0, "word": " B1", "probability": 0.850830078125}, {"start": 2900.0, "end": 2900.46, "word": " minus", "probability": 0.98193359375}, {"start": 2900.46, "end": 2901.18, "word": " B2", "probability": 0.758056640625}, {"start": 2901.18, "end": 2903.82, "word": " which", "probability": 0.39208984375}, {"start": 2903.82, "end": 2903.92, "word": " is", "probability": 0.91357421875}, {"start": 2903.92, "end": 2904.14, "word": " 6", "probability": 0.9052734375}, {"start": 2904.14, "end": 2904.52, "word": " percent.", "probability": 0.9580078125}], "temperature": 1.0}, {"id": 109, "seek": 293583, "start": 2905.97, "end": 2935.83, "text": " I think three is straightforward. Number four, what is or are the critical values which, when performing a z-test on whether population proportions are different at 5%. Here, yes, we are talking about two-tailed test, and alpha is 5%. So my critical values, they are two critical values, actually.", "tokens": [286, 519, 1045, 307, 15325, 13, 5118, 1451, 11, 437, 307, 420, 366, 264, 4924, 4190, 597, 11, 562, 10205, 257, 710, 12, 31636, 322, 1968, 4415, 32482, 366, 819, 412, 1025, 6856, 1692, 11, 2086, 11, 321, 366, 1417, 466, 732, 12, 14430, 292, 1500, 11, 293, 8961, 307, 1025, 6856, 407, 452, 4924, 4190, 11, 436, 366, 732, 4924, 4190, 11, 767, 13], "avg_logprob": -0.21638257936997848, "compression_ratio": 1.5520833333333333, "no_speech_prob": 0.0, "words": [{"start": 2905.97, "end": 2906.19, "word": " I", "probability": 0.6416015625}, {"start": 2906.19, "end": 2906.39, "word": " think", "probability": 0.91064453125}, {"start": 2906.39, "end": 2906.61, "word": " three", "probability": 0.77001953125}, {"start": 2906.61, "end": 2906.77, "word": " is", "probability": 0.61962890625}, {"start": 2906.77, "end": 2907.33, "word": " straightforward.", "probability": 0.87939453125}, {"start": 2909.17, "end": 2909.85, "word": " Number", "probability": 0.7822265625}, {"start": 2909.85, "end": 2910.31, "word": " four,", "probability": 0.91455078125}, {"start": 2912.03, "end": 2912.45, "word": " what", "probability": 0.892578125}, {"start": 2912.45, "end": 2912.91, "word": " is", "probability": 0.95166015625}, {"start": 2912.91, "end": 2913.19, "word": " or", "probability": 0.91943359375}, {"start": 2913.19, "end": 2913.63, "word": " are", "probability": 0.94873046875}, {"start": 2913.63, "end": 2915.89, "word": " the", "probability": 0.8037109375}, {"start": 2915.89, "end": 2916.25, "word": " critical", "probability": 0.93505859375}, {"start": 2916.25, "end": 2916.93, "word": " values", "probability": 0.97216796875}, {"start": 2916.93, "end": 2918.05, "word": " which,", "probability": 0.728515625}, {"start": 2918.33, "end": 2918.45, "word": " when", "probability": 0.9443359375}, {"start": 2918.45, "end": 2919.17, "word": " performing", "probability": 0.81005859375}, {"start": 2919.17, "end": 2920.23, "word": " a", "probability": 0.9130859375}, {"start": 2920.23, "end": 2920.35, "word": " z", "probability": 0.62451171875}, {"start": 2920.35, "end": 2920.63, "word": "-test", "probability": 0.759033203125}, {"start": 2920.63, "end": 2920.91, "word": " on", "probability": 0.9052734375}, {"start": 2920.91, "end": 2921.17, "word": " whether", "probability": 0.81591796875}, {"start": 2921.17, "end": 2921.87, "word": " population", "probability": 0.87353515625}, {"start": 2921.87, "end": 2922.55, "word": " proportions", "probability": 0.8251953125}, {"start": 2922.55, "end": 2922.87, "word": " are", "probability": 0.93896484375}, {"start": 2922.87, "end": 2923.29, "word": " different", "probability": 0.8994140625}, {"start": 2923.29, "end": 2923.77, "word": " at", "probability": 0.63330078125}, {"start": 2923.77, "end": 2924.73, "word": " 5%.", "probability": 0.5936279296875}, {"start": 2924.73, "end": 2925.81, "word": " Here,", "probability": 0.787109375}, {"start": 2925.95, "end": 2926.21, "word": " yes,", "probability": 0.9423828125}, {"start": 2926.29, "end": 2926.43, "word": " we", "probability": 0.9609375}, {"start": 2926.43, "end": 2926.57, "word": " are", "probability": 0.9365234375}, {"start": 2926.57, "end": 2926.87, "word": " talking", "probability": 0.85302734375}, {"start": 2926.87, "end": 2927.27, "word": " about", "probability": 0.9033203125}, {"start": 2927.27, "end": 2927.57, "word": " two", "probability": 0.87890625}, {"start": 2927.57, "end": 2927.91, "word": "-tailed", "probability": 0.7060546875}, {"start": 2927.91, "end": 2928.19, "word": " test,", "probability": 0.6513671875}, {"start": 2928.93, "end": 2929.87, "word": " and", "probability": 0.93603515625}, {"start": 2929.87, "end": 2930.15, "word": " alpha", "probability": 0.830078125}, {"start": 2930.15, "end": 2930.33, "word": " is", "probability": 0.94873046875}, {"start": 2930.33, "end": 2930.91, "word": " 5%.", "probability": 0.947021484375}, {"start": 2930.91, "end": 2932.25, "word": " So", "probability": 0.9443359375}, {"start": 2932.25, "end": 2932.79, "word": " my", "probability": 0.4609375}, {"start": 2932.79, "end": 2933.25, "word": " critical", "probability": 0.9345703125}, {"start": 2933.25, "end": 2933.93, "word": " values,", "probability": 0.96044921875}, {"start": 2934.31, "end": 2934.53, "word": " they", "probability": 0.65087890625}, {"start": 2934.53, "end": 2934.69, "word": " are", "probability": 0.93359375}, {"start": 2934.69, "end": 2934.91, "word": " two", "probability": 0.90087890625}, {"start": 2934.91, "end": 2935.23, "word": " critical", "probability": 0.8681640625}, {"start": 2935.23, "end": 2935.55, "word": " values,", "probability": 0.9736328125}, {"start": 2935.63, "end": 2935.83, "word": " actually.", "probability": 0.880859375}], "temperature": 1.0}, {"id": 110, "seek": 297924, "start": 2967.08, "end": 2979.24, "text": " What is or are the critical values when testing whether population proportions are different at 10%? The same instead here we have 10 instead of 5%.", "tokens": [708, 307, 420, 366, 264, 4924, 4190, 562, 4997, 1968, 4415, 32482, 366, 819, 412, 1266, 4, 30, 440, 912, 2602, 510, 321, 362, 1266, 2602, 295, 1025, 6856], "avg_logprob": -0.275781257947286, "compression_ratio": 1.2735042735042734, "no_speech_prob": 0.0, "words": [{"start": 2967.0799999999995, "end": 2967.8799999999997, "word": " What", "probability": 0.05267333984375}, {"start": 2967.8799999999997, "end": 2968.68, "word": " is", "probability": 0.72998046875}, {"start": 2968.68, "end": 2968.86, "word": " or", "probability": 0.81396484375}, {"start": 2968.86, "end": 2969.16, "word": " are", "probability": 0.9326171875}, {"start": 2969.16, "end": 2969.3, "word": " the", "probability": 0.908203125}, {"start": 2969.3, "end": 2969.62, "word": " critical", "probability": 0.91259765625}, {"start": 2969.62, "end": 2970.1, "word": " values", "probability": 0.9658203125}, {"start": 2970.1, "end": 2970.38, "word": " when", "probability": 0.9140625}, {"start": 2970.38, "end": 2971.0, "word": " testing", "probability": 0.83935546875}, {"start": 2971.0, "end": 2971.32, "word": " whether", "probability": 0.91259765625}, {"start": 2971.32, "end": 2971.9, "word": " population", "probability": 0.75830078125}, {"start": 2971.9, "end": 2972.5, "word": " proportions", "probability": 0.646484375}, {"start": 2972.5, "end": 2972.98, "word": " are", "probability": 0.94091796875}, {"start": 2972.98, "end": 2973.48, "word": " different", "probability": 0.88232421875}, {"start": 2973.48, "end": 2973.82, "word": " at", "probability": 0.88720703125}, {"start": 2973.82, "end": 2974.26, "word": " 10", "probability": 0.87744140625}, {"start": 2974.26, "end": 2974.66, "word": "%?", "probability": 0.63916015625}, {"start": 2975.44, "end": 2975.84, "word": " The", "probability": 0.69970703125}, {"start": 2975.84, "end": 2976.14, "word": " same", "probability": 0.8837890625}, {"start": 2976.14, "end": 2976.64, "word": " instead", "probability": 0.6044921875}, {"start": 2976.64, "end": 2977.02, "word": " here", "probability": 0.52490234375}, {"start": 2977.02, "end": 2977.18, "word": " we", "probability": 0.80810546875}, {"start": 2977.18, "end": 2977.34, "word": " have", "probability": 0.94775390625}, {"start": 2977.34, "end": 2977.6, "word": " 10", "probability": 0.8740234375}, {"start": 2977.6, "end": 2978.06, "word": " instead", "probability": 0.791015625}, {"start": 2978.06, "end": 2978.28, "word": " of", "probability": 0.9658203125}, {"start": 2978.28, "end": 2979.24, "word": " 5%.", "probability": 0.89404296875}], "temperature": 1.0}, {"id": 111, "seek": 300358, "start": 2980.92, "end": 3003.58, "text": " So A is the correct answer. So just use the table. Now for the previous one, we have 0 to 5, 0 to 5. The other one, alpha is 10%. So 0, 5 to the right, the same as to the left. So plus or minus 164.", "tokens": [407, 316, 307, 264, 3006, 1867, 13, 407, 445, 764, 264, 3199, 13, 823, 337, 264, 3894, 472, 11, 321, 362, 1958, 281, 1025, 11, 1958, 281, 1025, 13, 440, 661, 472, 11, 8961, 307, 1266, 6856, 407, 1958, 11, 1025, 281, 264, 558, 11, 264, 912, 382, 281, 264, 1411, 13, 407, 1804, 420, 3175, 3165, 19, 13], "avg_logprob": -0.20039062226812046, "compression_ratio": 1.4014084507042253, "no_speech_prob": 0.0, "words": [{"start": 2980.92, "end": 2981.26, "word": " So", "probability": 0.67138671875}, {"start": 2981.26, "end": 2981.46, "word": " A", "probability": 0.33544921875}, {"start": 2981.46, "end": 2981.56, "word": " is", "probability": 0.92529296875}, {"start": 2981.56, "end": 2981.72, "word": " the", "probability": 0.90185546875}, {"start": 2981.72, "end": 2982.0, "word": " correct", "probability": 0.88232421875}, {"start": 2982.0, "end": 2982.44, "word": " answer.", "probability": 0.95068359375}, {"start": 2983.84, "end": 2984.14, "word": " So", "probability": 0.8095703125}, {"start": 2984.14, "end": 2984.36, "word": " just", "probability": 0.81103515625}, {"start": 2984.36, "end": 2984.62, "word": " use", "probability": 0.85693359375}, {"start": 2984.62, "end": 2984.78, "word": " the", "probability": 0.90966796875}, {"start": 2984.78, "end": 2985.1, "word": " table.", "probability": 0.8173828125}, {"start": 2987.34, "end": 2987.86, "word": " Now", "probability": 0.7783203125}, {"start": 2987.86, "end": 2988.04, "word": " for", "probability": 0.7470703125}, {"start": 2988.04, "end": 2988.18, "word": " the", "probability": 0.92041015625}, {"start": 2988.18, "end": 2988.46, "word": " previous", "probability": 0.80224609375}, {"start": 2988.46, "end": 2988.7, "word": " one,", "probability": 0.9287109375}, {"start": 2988.78, "end": 2988.88, "word": " we", "probability": 0.9296875}, {"start": 2988.88, "end": 2989.04, "word": " have", "probability": 0.9208984375}, {"start": 2989.04, "end": 2989.26, "word": " 0", "probability": 0.8076171875}, {"start": 2989.26, "end": 2989.4, "word": " to", "probability": 0.92138671875}, {"start": 2989.4, "end": 2989.78, "word": " 5,", "probability": 0.9853515625}, {"start": 2990.52, "end": 2991.02, "word": " 0", "probability": 0.9091796875}, {"start": 2991.02, "end": 2991.18, "word": " to", "probability": 0.97021484375}, {"start": 2991.18, "end": 2991.44, "word": " 5.", "probability": 0.99609375}, {"start": 2991.98, "end": 2992.24, "word": " The", "probability": 0.869140625}, {"start": 2992.24, "end": 2992.48, "word": " other", "probability": 0.89501953125}, {"start": 2992.48, "end": 2992.82, "word": " one,", "probability": 0.9296875}, {"start": 2993.46, "end": 2993.84, "word": " alpha", "probability": 0.68310546875}, {"start": 2993.84, "end": 2994.12, "word": " is", "probability": 0.951171875}, {"start": 2994.12, "end": 2994.94, "word": " 10%.", "probability": 0.620849609375}, {"start": 2994.94, "end": 2996.52, "word": " So", "probability": 0.92822265625}, {"start": 2996.52, "end": 2996.84, "word": " 0,", "probability": 0.853515625}, {"start": 2996.94, "end": 2997.16, "word": " 5", "probability": 0.708984375}, {"start": 2997.16, "end": 2997.34, "word": " to", "probability": 0.92724609375}, {"start": 2997.34, "end": 2997.48, "word": " the", "probability": 0.91455078125}, {"start": 2997.48, "end": 2997.74, "word": " right,", "probability": 0.91748046875}, {"start": 2997.88, "end": 2998.06, "word": " the", "probability": 0.8837890625}, {"start": 2998.06, "end": 2998.3, "word": " same", "probability": 0.90966796875}, {"start": 2998.3, "end": 2998.64, "word": " as", "probability": 0.96630859375}, {"start": 2998.64, "end": 2998.8, "word": " to", "probability": 0.94384765625}, {"start": 2998.8, "end": 2998.96, "word": " the", "probability": 0.912109375}, {"start": 2998.96, "end": 2999.22, "word": " left.", "probability": 0.9384765625}, {"start": 2999.94, "end": 3000.18, "word": " So", "probability": 0.94775390625}, {"start": 3000.18, "end": 3000.46, "word": " plus", "probability": 0.912109375}, {"start": 3000.46, "end": 3000.68, "word": " or", "probability": 0.9609375}, {"start": 3000.68, "end": 3001.2, "word": " minus", "probability": 0.98583984375}, {"start": 3001.2, "end": 3003.58, "word": " 164.", "probability": 0.5557861328125}], "temperature": 1.0}, {"id": 112, "seek": 303544, "start": 3006.7, "end": 3035.44, "text": " So 4 and 5 by using the z table. So exactly, since alpha here is 1, 0, 2, 5, so the area becomes smaller than, so it should be z greater than. So 1.106, the other one 1.645, number 6. 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Higher means above. Above 10. Above 10, 5%. So which? B. B is the correct. Z alpha.", "tokens": [440, 4924, 2158, 294, 4997, 1968, 264, 2190, 4415, 307, 2946, 813, 13, 31997, 1355, 3673, 13, 32691, 1266, 13, 32691, 1266, 11, 1025, 6856, 407, 597, 30, 363, 13, 363, 307, 264, 3006, 13, 1176, 8961, 13], "avg_logprob": -0.4258814117847345, "compression_ratio": 1.288, "no_speech_prob": 0.0, "words": [{"start": 3036.69, "end": 3037.05, "word": " The", "probability": 0.404052734375}, {"start": 3037.05, "end": 3037.45, "word": " critical", "probability": 0.8271484375}, {"start": 3037.45, "end": 3037.79, "word": " value", "probability": 0.93798828125}, {"start": 3037.79, "end": 3038.03, "word": " in", "probability": 0.6904296875}, {"start": 3038.03, "end": 3038.37, "word": " testing", "probability": 0.83544921875}, {"start": 3038.37, "end": 3038.81, "word": " whether", "probability": 0.822265625}, {"start": 3038.81, "end": 3039.05, "word": " the", "probability": 0.91064453125}, {"start": 3039.05, "end": 3039.37, "word": " current", "probability": 0.8984375}, {"start": 3039.37, "end": 3040.09, "word": " population", "probability": 0.9365234375}, {"start": 3040.09, "end": 3041.85, "word": " is", "probability": 0.87255859375}, {"start": 3041.85, "end": 3042.45, "word": " higher", "probability": 0.88232421875}, {"start": 3042.45, "end": 3042.83, "word": " than.", "probability": 0.92822265625}, {"start": 3044.21, "end": 3044.51, "word": " Higher", "probability": 0.8291015625}, {"start": 3044.51, "end": 3044.95, "word": " means", "probability": 0.90625}, {"start": 3044.95, "end": 3045.29, "word": " above.", "probability": 0.457763671875}, {"start": 3046.21, "end": 3046.73, "word": " Above", "probability": 0.76220703125}, {"start": 3046.73, "end": 3047.03, "word": " 10.", "probability": 0.1258544921875}, {"start": 3048.89, "end": 3049.69, "word": " Above", "probability": 0.861328125}, {"start": 3049.69, "end": 3050.03, "word": " 10,", "probability": 0.9306640625}, {"start": 3050.13, "end": 3050.99, "word": " 5%.", "probability": 0.7822265625}, {"start": 3050.99, "end": 3052.99, "word": " So", "probability": 0.84130859375}, {"start": 3052.99, "end": 3053.29, "word": " which?", "probability": 0.68115234375}, {"start": 3055.07, "end": 3055.87, "word": " B.", "probability": 0.4150390625}, {"start": 3058.47, "end": 3059.27, "word": " B", "probability": 0.947265625}, {"start": 3059.27, "end": 3059.47, "word": " is", "probability": 0.78271484375}, {"start": 3059.47, "end": 3059.61, "word": " the", "probability": 0.853515625}, {"start": 3059.61, "end": 3059.91, "word": " correct.", "probability": 0.89892578125}, {"start": 3060.23, "end": 3060.41, "word": " Z", "probability": 0.873046875}, {"start": 3060.41, "end": 3060.81, "word": " alpha.", "probability": 0.65380859375}], "temperature": 1.0}, {"id": 114, "seek": 309074, "start": 3066.7, "end": 3090.74, "text": " So, B is the correct answer. 7. 7 and 8 we should have to calculate number 1. 7 was the estimated standard error of the difference between the two sample proportions. We should have a standard error.", "tokens": [407, 11, 363, 307, 264, 3006, 1867, 13, 1614, 13, 1614, 293, 1649, 321, 820, 362, 281, 8873, 1230, 502, 13, 1614, 390, 264, 14109, 3832, 6713, 295, 264, 2649, 1296, 264, 732, 6889, 32482, 13, 492, 820, 362, 257, 3832, 6713, 13], "avg_logprob": -0.3297230120409619, "compression_ratio": 1.4705882352941178, "no_speech_prob": 0.0, "words": [{"start": 3066.7000000000003, "end": 3067.38, "word": " So,", "probability": 0.26611328125}, {"start": 3067.5, "end": 3067.52, "word": " B", "probability": 0.5625}, {"start": 3067.52, "end": 3067.68, "word": " is", "probability": 0.94189453125}, {"start": 3067.68, "end": 3067.8, "word": " the", "probability": 0.88818359375}, {"start": 3067.8, "end": 3068.06, "word": " correct", "probability": 0.884765625}, {"start": 3068.06, "end": 3068.44, "word": " answer.", "probability": 0.9638671875}, {"start": 3071.2, "end": 3071.84, "word": " 7.", "probability": 0.4912109375}, {"start": 3074.74, "end": 3075.42, "word": " 7", "probability": 0.76220703125}, {"start": 3075.42, "end": 3075.66, "word": " and", "probability": 0.91845703125}, {"start": 3075.66, "end": 3075.94, "word": " 8", "probability": 0.982421875}, {"start": 3075.94, "end": 3076.12, "word": " we", "probability": 0.646484375}, {"start": 3076.12, "end": 3076.42, "word": " should", "probability": 0.9619140625}, {"start": 3076.42, "end": 3076.78, "word": " have", "probability": 0.92041015625}, {"start": 3076.78, "end": 3077.78, "word": " to", "probability": 0.919921875}, {"start": 3077.78, "end": 3078.44, "word": " calculate", "probability": 0.90966796875}, {"start": 3078.44, "end": 3080.44, "word": " number", "probability": 0.59228515625}, {"start": 3080.44, "end": 3080.74, "word": " 1.", "probability": 0.58056640625}, {"start": 3080.92, "end": 3081.32, "word": " 7", "probability": 0.8662109375}, {"start": 3081.32, "end": 3081.9, "word": " was", "probability": 0.18798828125}, {"start": 3081.9, "end": 3082.12, "word": " the", "probability": 0.80517578125}, {"start": 3082.12, "end": 3082.7, "word": " estimated", "probability": 0.81591796875}, {"start": 3082.7, "end": 3083.32, "word": " standard", "probability": 0.9248046875}, {"start": 3083.32, "end": 3083.72, "word": " error", "probability": 0.92041015625}, {"start": 3083.72, "end": 3085.2, "word": " of", "probability": 0.82080078125}, {"start": 3085.2, "end": 3085.4, "word": " the", "probability": 0.9140625}, {"start": 3085.4, "end": 3085.88, "word": " difference", "probability": 0.853515625}, {"start": 3085.88, "end": 3086.28, "word": " between", "probability": 0.87646484375}, {"start": 3086.28, "end": 3086.52, "word": " the", "probability": 0.8681640625}, {"start": 3086.52, "end": 3086.7, "word": " two", "probability": 0.78857421875}, {"start": 3086.7, "end": 3087.04, "word": " sample", "probability": 0.55029296875}, {"start": 3087.04, "end": 3087.8, "word": " proportions.", "probability": 0.73974609375}, {"start": 3088.5, "end": 3089.18, "word": " We", "probability": 0.79638671875}, {"start": 3089.18, "end": 3089.4, "word": " should", "probability": 0.96044921875}, {"start": 3089.4, "end": 3089.66, "word": " have", "probability": 0.94189453125}, {"start": 3089.66, "end": 3089.94, "word": " a", "probability": 0.344482421875}, {"start": 3089.94, "end": 3090.46, "word": " standard", "probability": 0.939453125}, {"start": 3090.46, "end": 3090.74, "word": " error.", "probability": 0.919921875}], "temperature": 1.0}, {"id": 115, "seek": 312204, "start": 3094.62, "end": 3122.04, "text": " Square root, B dash 1 minus B dash multiplied by 1 over N1 plus 1 over N2. And we have to find B dash here. Let's see how can we find B dash. B dash equal x1 plus x2.", "tokens": [16463, 5593, 11, 363, 8240, 502, 3175, 363, 8240, 17207, 538, 502, 670, 426, 16, 1804, 502, 670, 426, 17, 13, 400, 321, 362, 281, 915, 363, 8240, 510, 13, 961, 311, 536, 577, 393, 321, 915, 363, 8240, 13, 363, 8240, 2681, 2031, 16, 1804, 2031, 17, 13], "avg_logprob": -0.23578124344348908, "compression_ratio": 1.3688524590163935, "no_speech_prob": 0.0, "words": [{"start": 3094.62, "end": 3095.1, "word": " Square", "probability": 0.458251953125}, {"start": 3095.1, "end": 3095.46, "word": " root,", "probability": 0.84814453125}, {"start": 3096.66, "end": 3096.86, "word": " B", "probability": 0.55078125}, {"start": 3096.86, "end": 3097.18, "word": " dash", "probability": 0.5634765625}, {"start": 3097.18, "end": 3097.42, "word": " 1", "probability": 0.464599609375}, {"start": 3097.42, "end": 3097.74, "word": " minus", "probability": 0.9619140625}, {"start": 3097.74, "end": 3097.96, "word": " B", "probability": 0.97021484375}, {"start": 3097.96, "end": 3098.26, "word": " dash", "probability": 0.85595703125}, {"start": 3098.26, "end": 3099.6, "word": " multiplied", "probability": 0.47509765625}, {"start": 3099.6, "end": 3100.04, "word": " by", "probability": 0.9599609375}, {"start": 3100.04, "end": 3100.32, "word": " 1", "probability": 0.90771484375}, {"start": 3100.32, "end": 3100.56, "word": " over", "probability": 0.8876953125}, {"start": 3100.56, "end": 3100.86, "word": " N1", "probability": 0.7763671875}, {"start": 3100.86, "end": 3101.1, "word": " plus", "probability": 0.93603515625}, {"start": 3101.1, "end": 3101.32, "word": " 1", "probability": 0.947265625}, {"start": 3101.32, "end": 3101.5, "word": " over", "probability": 0.90234375}, {"start": 3101.5, "end": 3101.86, "word": " N2.", "probability": 0.989013671875}, {"start": 3103.68, "end": 3103.98, "word": " And", "probability": 0.89404296875}, {"start": 3103.98, "end": 3104.12, "word": " we", "probability": 0.92724609375}, {"start": 3104.12, "end": 3104.28, "word": " have", "probability": 0.94287109375}, {"start": 3104.28, "end": 3104.4, "word": " to", "probability": 0.96533203125}, {"start": 3104.4, "end": 3104.72, "word": " find", "probability": 0.91650390625}, {"start": 3104.72, "end": 3105.06, "word": " B", "probability": 0.97998046875}, {"start": 3105.06, "end": 3105.3, "word": " dash", "probability": 0.81787109375}, {"start": 3105.3, "end": 3105.52, "word": " here.", "probability": 0.26318359375}, {"start": 3107.48, "end": 3108.04, "word": " Let's", "probability": 0.8505859375}, {"start": 3108.04, "end": 3108.14, "word": " see", "probability": 0.91455078125}, {"start": 3108.14, "end": 3108.22, "word": " how", "probability": 0.90771484375}, {"start": 3108.22, "end": 3108.4, "word": " can", "probability": 0.7880859375}, {"start": 3108.4, "end": 3108.5, "word": " we", "probability": 0.93408203125}, {"start": 3108.5, "end": 3108.72, "word": " find", "probability": 0.90478515625}, {"start": 3108.72, "end": 3108.94, "word": " B", "probability": 0.9892578125}, {"start": 3108.94, "end": 3109.22, "word": " dash.", "probability": 0.875}, {"start": 3112.72, "end": 3113.28, "word": " B", "probability": 0.6171875}, {"start": 3113.28, "end": 3119.7, "word": " dash", "probability": 0.85546875}, {"start": 3119.7, "end": 3119.94, "word": " equal", "probability": 0.4482421875}, {"start": 3119.94, "end": 3121.22, "word": " x1", "probability": 0.7110595703125}, {"start": 3121.22, "end": 3121.5, "word": " plus", "probability": 0.95556640625}, {"start": 3121.5, "end": 3122.04, "word": " x2.", "probability": 0.99755859375}], "temperature": 1.0}, {"id": 116, "seek": 315106, "start": 3124.06, "end": 3151.06, "text": " Now what's the value of X1? Exactly. Since B1 is X1 over N1. So that means X1 is N1 times B1. So N1 is 150 times 60%. So that's 99. And similarly, X2", "tokens": [823, 437, 311, 264, 2158, 295, 1783, 16, 30, 7587, 13, 4162, 363, 16, 307, 1783, 16, 670, 426, 16, 13, 407, 300, 1355, 1783, 16, 307, 426, 16, 1413, 363, 16, 13, 407, 426, 16, 307, 8451, 1413, 4060, 6856, 407, 300, 311, 11803, 13, 400, 14138, 11, 1783, 17], "avg_logprob": -0.25390626318179643, "compression_ratio": 1.2096774193548387, "no_speech_prob": 0.0, "words": [{"start": 3124.06, "end": 3124.9, "word": " Now", "probability": 0.274658203125}, {"start": 3124.9, "end": 3125.08, "word": " what's", "probability": 0.684326171875}, {"start": 3125.08, "end": 3125.18, "word": " the", "probability": 0.916015625}, {"start": 3125.18, "end": 3125.32, "word": " value", "probability": 0.9765625}, {"start": 3125.32, "end": 3125.44, "word": " of", "probability": 0.943359375}, {"start": 3125.44, "end": 3125.8, "word": " X1?", "probability": 0.64794921875}, {"start": 3130.4, "end": 3130.84, "word": " Exactly.", "probability": 0.51318359375}, {"start": 3131.26, "end": 3132.1, "word": " Since", "probability": 0.7236328125}, {"start": 3132.1, "end": 3132.56, "word": " B1", "probability": 0.746337890625}, {"start": 3132.56, "end": 3132.76, "word": " is", "probability": 0.382568359375}, {"start": 3132.76, "end": 3133.22, "word": " X1", "probability": 0.95458984375}, {"start": 3133.22, "end": 3133.54, "word": " over", "probability": 0.884765625}, {"start": 3133.54, "end": 3133.96, "word": " N1.", "probability": 0.8076171875}, {"start": 3134.92, "end": 3135.18, "word": " So", "probability": 0.87109375}, {"start": 3135.18, "end": 3135.42, "word": " that", "probability": 0.87109375}, {"start": 3135.42, "end": 3135.64, "word": " means", "probability": 0.9130859375}, {"start": 3135.64, "end": 3136.22, "word": " X1", "probability": 0.916748046875}, {"start": 3136.22, "end": 3136.78, "word": " is", "probability": 0.861328125}, {"start": 3136.78, "end": 3137.2, "word": " N1", "probability": 0.982421875}, {"start": 3137.2, "end": 3137.54, "word": " times", "probability": 0.8974609375}, {"start": 3137.54, "end": 3137.96, "word": " B1.", "probability": 0.992919921875}, {"start": 3138.98, "end": 3139.26, "word": " So", "probability": 0.9130859375}, {"start": 3139.26, "end": 3139.64, "word": " N1", "probability": 0.97314453125}, {"start": 3139.64, "end": 3139.78, "word": " is", "probability": 0.93408203125}, {"start": 3139.78, "end": 3140.4, "word": " 150", "probability": 0.857421875}, {"start": 3140.4, "end": 3142.14, "word": " times", "probability": 0.466796875}, {"start": 3142.14, "end": 3143.22, "word": " 60%.", "probability": 0.84521484375}, {"start": 3143.22, "end": 3144.94, "word": " So", "probability": 0.9443359375}, {"start": 3144.94, "end": 3146.6, "word": " that's", "probability": 0.9521484375}, {"start": 3146.6, "end": 3147.42, "word": " 99.", "probability": 0.9248046875}, {"start": 3148.24, "end": 3148.58, "word": " And", "probability": 0.8564453125}, {"start": 3148.58, "end": 3150.24, "word": " similarly,", "probability": 0.869140625}, {"start": 3150.52, "end": 3151.06, "word": " X2", "probability": 0.991455078125}], "temperature": 1.0}, {"id": 117, "seek": 317936, "start": 3152.0, "end": 3179.36, "text": " N2, which is 160, times 60% gives 96. So your B dash is x1 plus x2 divided by N1 plus N2, which is 150 plus 310. So complete B dash versus the bold estimate of overall proportion", "tokens": [426, 17, 11, 597, 307, 21243, 11, 1413, 4060, 4, 2709, 24124, 13, 407, 428, 363, 8240, 307, 2031, 16, 1804, 2031, 17, 6666, 538, 426, 16, 1804, 426, 17, 11, 597, 307, 8451, 1804, 805, 3279, 13, 407, 3566, 363, 8240, 5717, 264, 11928, 12539, 295, 4787, 16068], "avg_logprob": -0.2951562589406967, "compression_ratio": 1.3161764705882353, "no_speech_prob": 0.0, "words": [{"start": 3152.0, "end": 3152.66, "word": " N2,", "probability": 0.726806640625}, {"start": 3152.84, "end": 3153.06, "word": " which", "probability": 0.85595703125}, {"start": 3153.06, "end": 3153.14, "word": " is", "probability": 0.939453125}, {"start": 3153.14, "end": 3153.62, "word": " 160,", "probability": 0.87109375}, {"start": 3154.1, "end": 3154.98, "word": " times", "probability": 0.91357421875}, {"start": 3154.98, "end": 3155.42, "word": " 60", "probability": 0.93701171875}, {"start": 3155.42, "end": 3155.98, "word": "%", "probability": 0.48583984375}, {"start": 3155.98, "end": 3158.68, "word": " gives", "probability": 0.7958984375}, {"start": 3158.68, "end": 3159.7, "word": " 96.", "probability": 0.97119140625}, {"start": 3160.92, "end": 3161.32, "word": " So", "probability": 0.94970703125}, {"start": 3161.32, "end": 3161.9, "word": " your", "probability": 0.73193359375}, {"start": 3161.9, "end": 3162.18, "word": " B", "probability": 0.607421875}, {"start": 3162.18, "end": 3162.52, "word": " dash", "probability": 0.6005859375}, {"start": 3162.52, "end": 3164.18, "word": " is", "probability": 0.89453125}, {"start": 3164.18, "end": 3166.04, "word": " x1", "probability": 0.69580078125}, {"start": 3166.04, "end": 3166.42, "word": " plus", "probability": 0.9208984375}, {"start": 3166.42, "end": 3167.04, "word": " x2", "probability": 0.998779296875}, {"start": 3167.04, "end": 3168.16, "word": " divided", "probability": 0.65283203125}, {"start": 3168.16, "end": 3168.42, "word": " by", "probability": 0.96435546875}, {"start": 3168.42, "end": 3168.72, "word": " N1", "probability": 0.886474609375}, {"start": 3168.72, "end": 3169.04, "word": " plus", "probability": 0.951171875}, {"start": 3169.04, "end": 3169.44, "word": " N2,", "probability": 0.997802734375}, {"start": 3169.52, "end": 3169.68, "word": " which", "probability": 0.94482421875}, {"start": 3169.68, "end": 3169.82, "word": " is", "probability": 0.9443359375}, {"start": 3169.82, "end": 3170.3, "word": " 150", "probability": 0.9189453125}, {"start": 3170.3, "end": 3171.56, "word": " plus", "probability": 0.935546875}, {"start": 3171.56, "end": 3173.24, "word": " 310.", "probability": 0.57861328125}, {"start": 3173.6, "end": 3174.06, "word": " So", "probability": 0.9521484375}, {"start": 3174.06, "end": 3174.98, "word": " complete", "probability": 0.5029296875}, {"start": 3174.98, "end": 3175.2, "word": " B", "probability": 0.98583984375}, {"start": 3175.2, "end": 3175.42, "word": " dash", "probability": 0.875}, {"start": 3175.42, "end": 3175.78, "word": " versus", "probability": 0.06304931640625}, {"start": 3175.78, "end": 3176.06, "word": " the", "probability": 0.8095703125}, {"start": 3176.06, "end": 3176.24, "word": " bold", "probability": 0.459228515625}, {"start": 3176.24, "end": 3177.78, "word": " estimate", "probability": 0.9111328125}, {"start": 3177.78, "end": 3178.24, "word": " of", "probability": 0.96533203125}, {"start": 3178.24, "end": 3178.76, "word": " overall", "probability": 0.83984375}, {"start": 3178.76, "end": 3179.36, "word": " proportion", "probability": 0.87548828125}], "temperature": 1.0}, {"id": 118, "seek": 320903, "start": 3180.89, "end": 3209.03, "text": " So 9 and 9 plus 9 is 6. That's just B-. 6 to 9. 6 to 9. So this is not your answer. It's just B-. Now take this value and the square root of 6 to 9.", "tokens": [407, 1722, 293, 1722, 1804, 1722, 307, 1386, 13, 663, 311, 445, 363, 12, 13, 1386, 281, 1722, 13, 1386, 281, 1722, 13, 407, 341, 307, 406, 428, 1867, 13, 467, 311, 445, 363, 12, 13, 823, 747, 341, 2158, 293, 264, 3732, 5593, 295, 1386, 281, 1722, 13], "avg_logprob": -0.31109374403953555, "compression_ratio": 1.3185840707964602, "no_speech_prob": 0.0, "words": [{"start": 3180.89, "end": 3181.35, "word": " So", "probability": 0.31396484375}, {"start": 3181.35, "end": 3181.93, "word": " 9", "probability": 0.444091796875}, {"start": 3181.93, "end": 3182.09, "word": " and", "probability": 0.370849609375}, {"start": 3182.09, "end": 3182.43, "word": " 9", "probability": 0.9716796875}, {"start": 3182.43, "end": 3182.79, "word": " plus", "probability": 0.73291015625}, {"start": 3182.79, "end": 3183.11, "word": " 9", "probability": 0.86181640625}, {"start": 3183.11, "end": 3183.23, "word": " is", "probability": 0.28515625}, {"start": 3183.23, "end": 3183.57, "word": " 6.", "probability": 0.9306640625}, {"start": 3186.39, "end": 3187.03, "word": " That's", "probability": 0.620849609375}, {"start": 3187.03, "end": 3187.27, "word": " just", "probability": 0.89990234375}, {"start": 3187.27, "end": 3187.45, "word": " B", "probability": 0.78857421875}, {"start": 3187.45, "end": 3187.73, "word": "-.", "probability": 0.2349853515625}, {"start": 3193.21, "end": 3193.85, "word": " 6", "probability": 0.8251953125}, {"start": 3193.85, "end": 3194.01, "word": " to", "probability": 0.912109375}, {"start": 3194.01, "end": 3194.29, "word": " 9.", "probability": 0.994140625}, {"start": 3197.15, "end": 3197.49, "word": " 6", "probability": 0.65185546875}, {"start": 3197.49, "end": 3197.69, "word": " to", "probability": 0.9677734375}, {"start": 3197.69, "end": 3197.97, "word": " 9.", "probability": 0.99755859375}, {"start": 3199.59, "end": 3199.77, "word": " So", "probability": 0.91943359375}, {"start": 3199.77, "end": 3200.01, "word": " this", "probability": 0.56787109375}, {"start": 3200.01, "end": 3200.11, "word": " is", "probability": 0.92724609375}, {"start": 3200.11, "end": 3200.27, "word": " not", "probability": 0.9208984375}, {"start": 3200.27, "end": 3200.45, "word": " your", "probability": 0.89404296875}, {"start": 3200.45, "end": 3200.81, "word": " answer.", "probability": 0.94873046875}, {"start": 3201.65, "end": 3202.29, "word": " It's", "probability": 0.641357421875}, {"start": 3202.29, "end": 3202.61, "word": " just", "probability": 0.8876953125}, {"start": 3202.61, "end": 3202.85, "word": " B", "probability": 0.9921875}, {"start": 3202.85, "end": 3203.19, "word": "-.", "probability": 0.931640625}, {"start": 3203.77, "end": 3203.97, "word": " Now", "probability": 0.84814453125}, {"start": 3203.97, "end": 3204.31, "word": " take", "probability": 0.74951171875}, {"start": 3204.31, "end": 3204.61, "word": " this", "probability": 0.9482421875}, {"start": 3204.61, "end": 3205.05, "word": " value", "probability": 0.974609375}, {"start": 3205.05, "end": 3207.15, "word": " and", "probability": 0.444091796875}, {"start": 3207.15, "end": 3207.33, "word": " the", "probability": 0.341064453125}, {"start": 3207.33, "end": 3207.61, "word": " square", "probability": 0.91845703125}, {"start": 3207.61, "end": 3207.83, "word": " root", "probability": 0.93603515625}, {"start": 3207.83, "end": 3208.13, "word": " of", "probability": 0.97412109375}, {"start": 3208.13, "end": 3208.55, "word": " 6", "probability": 0.951171875}, {"start": 3208.55, "end": 3208.75, "word": " to", "probability": 0.97314453125}, {"start": 3208.75, "end": 3209.03, "word": " 9.", "probability": 0.998046875}], "temperature": 1.0}, {"id": 119, "seek": 323974, "start": 3210.06, "end": 3239.74, "text": " times 1.629 multiplied by 1 over N1 which is 150 plus 160. That's your standard error. B dash is not standard error. B dash is the bold estimate of overall proportion. Now simple calculation will give C. So C is the correct answer.", "tokens": [1413, 502, 13, 21, 11871, 17207, 538, 502, 670, 426, 16, 597, 307, 8451, 1804, 21243, 13, 663, 311, 428, 3832, 6713, 13, 363, 8240, 307, 406, 3832, 6713, 13, 363, 8240, 307, 264, 11928, 12539, 295, 4787, 16068, 13, 823, 2199, 17108, 486, 976, 383, 13, 407, 383, 307, 264, 3006, 1867, 13], "avg_logprob": -0.1862215974114158, "compression_ratio": 1.4591194968553458, "no_speech_prob": 0.0, "words": [{"start": 3210.06, "end": 3210.42, "word": " times", "probability": 0.2958984375}, {"start": 3210.42, "end": 3210.68, "word": " 1", "probability": 0.88427734375}, {"start": 3210.68, "end": 3211.68, "word": ".629", "probability": 0.96044921875}, {"start": 3211.68, "end": 3213.1, "word": " multiplied", "probability": 0.54248046875}, {"start": 3213.1, "end": 3213.54, "word": " by", "probability": 0.96875}, {"start": 3213.54, "end": 3214.04, "word": " 1", "probability": 0.8818359375}, {"start": 3214.04, "end": 3214.24, "word": " over", "probability": 0.81201171875}, {"start": 3214.24, "end": 3214.7, "word": " N1", "probability": 0.743896484375}, {"start": 3214.7, "end": 3215.5, "word": " which", "probability": 0.671875}, {"start": 3215.5, "end": 3215.68, "word": " is", "probability": 0.9287109375}, {"start": 3215.68, "end": 3216.28, "word": " 150", "probability": 0.71240234375}, {"start": 3216.28, "end": 3218.96, "word": " plus", "probability": 0.89697265625}, {"start": 3218.96, "end": 3219.64, "word": " 160.", "probability": 0.82958984375}, {"start": 3221.32, "end": 3222.12, "word": " That's", "probability": 0.835205078125}, {"start": 3222.12, "end": 3222.4, "word": " your", "probability": 0.88330078125}, {"start": 3222.4, "end": 3222.82, "word": " standard", "probability": 0.9052734375}, {"start": 3222.82, "end": 3223.22, "word": " error.", "probability": 0.87744140625}, {"start": 3224.32, "end": 3224.48, "word": " B", "probability": 0.8720703125}, {"start": 3224.48, "end": 3224.76, "word": " dash", "probability": 0.61181640625}, {"start": 3224.76, "end": 3224.98, "word": " is", "probability": 0.93408203125}, {"start": 3224.98, "end": 3225.24, "word": " not", "probability": 0.92333984375}, {"start": 3225.24, "end": 3225.64, "word": " standard", "probability": 0.88818359375}, {"start": 3225.64, "end": 3225.88, "word": " error.", "probability": 0.87841796875}, {"start": 3225.96, "end": 3226.06, "word": " B", "probability": 0.98779296875}, {"start": 3226.06, "end": 3226.3, "word": " dash", "probability": 0.8466796875}, {"start": 3226.3, "end": 3226.5, "word": " is", "probability": 0.9501953125}, {"start": 3226.5, "end": 3226.68, "word": " the", "probability": 0.89013671875}, {"start": 3226.68, "end": 3227.04, "word": " bold", "probability": 0.69140625}, {"start": 3227.04, "end": 3228.38, "word": " estimate", "probability": 0.91552734375}, {"start": 3228.38, "end": 3229.08, "word": " of", "probability": 0.96435546875}, {"start": 3229.08, "end": 3229.54, "word": " overall", "probability": 0.77294921875}, {"start": 3229.54, "end": 3230.18, "word": " proportion.", "probability": 0.80078125}, {"start": 3232.24, "end": 3232.6, "word": " Now", "probability": 0.93212890625}, {"start": 3232.6, "end": 3232.92, "word": " simple", "probability": 0.63330078125}, {"start": 3232.92, "end": 3233.48, "word": " calculation", "probability": 0.92138671875}, {"start": 3233.48, "end": 3233.74, "word": " will", "probability": 0.8798828125}, {"start": 3233.74, "end": 3234.14, "word": " give", "probability": 0.8837890625}, {"start": 3234.14, "end": 3235.44, "word": " C.", "probability": 0.845703125}, {"start": 3236.98, "end": 3237.78, "word": " So", "probability": 0.9375}, {"start": 3237.78, "end": 3238.06, "word": " C", "probability": 0.6796875}, {"start": 3238.06, "end": 3238.34, "word": " is", "probability": 0.9521484375}, {"start": 3238.34, "end": 3238.52, "word": " the", "probability": 0.9150390625}, {"start": 3238.52, "end": 3238.94, "word": " correct", "probability": 0.908203125}, {"start": 3238.94, "end": 3239.74, "word": " answer.", "probability": 0.94921875}], "temperature": 1.0}, {"id": 120, "seek": 327184, "start": 3247.06, "end": 3271.84, "text": " What's the standard error of the difference between the two proportions given by this equation? Here first we have to compute P' by using x1 plus x2 over n1 plus n2. In this example, the x's are not given, but we have the proportions.", "tokens": [708, 311, 264, 3832, 6713, 295, 264, 2649, 1296, 264, 732, 32482, 2212, 538, 341, 5367, 30, 1692, 700, 321, 362, 281, 14722, 430, 6, 538, 1228, 2031, 16, 1804, 2031, 17, 670, 297, 16, 1804, 297, 17, 13, 682, 341, 1365, 11, 264, 2031, 311, 366, 406, 2212, 11, 457, 321, 362, 264, 32482, 13], "avg_logprob": -0.2539747890673186, "compression_ratio": 1.46875, "no_speech_prob": 0.0, "words": [{"start": 3247.0600000000004, "end": 3247.6600000000003, "word": " What's", "probability": 0.4329833984375}, {"start": 3247.6600000000003, "end": 3248.26, "word": " the", "probability": 0.68701171875}, {"start": 3248.26, "end": 3250.88, "word": " standard", "probability": 0.319091796875}, {"start": 3250.88, "end": 3253.74, "word": " error", "probability": 0.85791015625}, {"start": 3253.74, "end": 3255.06, "word": " of", "probability": 0.6328125}, {"start": 3255.06, "end": 3255.22, "word": " the", "probability": 0.68798828125}, {"start": 3255.22, "end": 3255.6, "word": " difference", "probability": 0.78662109375}, {"start": 3255.6, "end": 3256.1, "word": " between", "probability": 0.86181640625}, {"start": 3256.1, "end": 3256.22, "word": " the", "probability": 0.6923828125}, {"start": 3256.22, "end": 3256.36, "word": " two", "probability": 0.85986328125}, {"start": 3256.36, "end": 3256.92, "word": " proportions", "probability": 0.70654296875}, {"start": 3256.92, "end": 3257.24, "word": " given", "probability": 0.7666015625}, {"start": 3257.24, "end": 3257.44, "word": " by", "probability": 0.9638671875}, {"start": 3257.44, "end": 3257.6, "word": " this", "probability": 0.90576171875}, {"start": 3257.6, "end": 3258.04, "word": " equation?", "probability": 0.98583984375}, {"start": 3258.78, "end": 3259.38, "word": " Here", "probability": 0.57373046875}, {"start": 3259.38, "end": 3259.72, "word": " first", "probability": 0.61767578125}, {"start": 3259.72, "end": 3259.88, "word": " we", "probability": 0.77197265625}, {"start": 3259.88, "end": 3260.06, "word": " have", "probability": 0.9072265625}, {"start": 3260.06, "end": 3260.16, "word": " to", "probability": 0.9638671875}, {"start": 3260.16, "end": 3260.46, "word": " compute", "probability": 0.93408203125}, {"start": 3260.46, "end": 3260.66, "word": " P'", "probability": 0.83203125}, {"start": 3260.96, "end": 3263.32, "word": " by", "probability": 0.83740234375}, {"start": 3263.32, "end": 3263.88, "word": " using", "probability": 0.88037109375}, {"start": 3263.88, "end": 3264.28, "word": " x1", "probability": 0.73388671875}, {"start": 3264.28, "end": 3264.52, "word": " plus", "probability": 0.452880859375}, {"start": 3264.52, "end": 3264.86, "word": " x2", "probability": 0.991943359375}, {"start": 3264.86, "end": 3265.1, "word": " over", "probability": 0.9091796875}, {"start": 3265.1, "end": 3265.4, "word": " n1", "probability": 0.8642578125}, {"start": 3265.4, "end": 3265.7, "word": " plus", "probability": 0.9638671875}, {"start": 3265.7, "end": 3266.1, "word": " n2.", "probability": 0.99755859375}, {"start": 3266.96, "end": 3267.56, "word": " In", "probability": 0.92626953125}, {"start": 3267.56, "end": 3267.84, "word": " this", "probability": 0.94384765625}, {"start": 3267.84, "end": 3268.3, "word": " example,", "probability": 0.9755859375}, {"start": 3269.42, "end": 3269.6, "word": " the", "probability": 0.8701171875}, {"start": 3269.6, "end": 3269.9, "word": " x's", "probability": 0.856201171875}, {"start": 3269.9, "end": 3270.04, "word": " are", "probability": 0.94189453125}, {"start": 3270.04, "end": 3270.24, "word": " not", "probability": 0.94287109375}, {"start": 3270.24, "end": 3270.5, "word": " given,", "probability": 0.892578125}, {"start": 3270.72, "end": 3270.86, "word": " but", "probability": 0.92333984375}, {"start": 3270.86, "end": 3271.02, "word": " we", "probability": 0.94287109375}, {"start": 3271.02, "end": 3271.14, "word": " have", "probability": 0.943359375}, {"start": 3271.14, "end": 3271.28, "word": " the", "probability": 0.88818359375}, {"start": 3271.28, "end": 3271.84, "word": " proportions.", "probability": 0.83154296875}], "temperature": 1.0}, {"id": 121, "seek": 329161, "start": 3272.77, "end": 3291.61, "text": " And we know that B1 equals X1 over N1. So X1 equals N1 times B1. So I got 99. Similarly, X2 and 2 times B2 is 96. So B dash is 629. So plug this value here, you will get 055.", "tokens": [400, 321, 458, 300, 363, 16, 6915, 1783, 16, 670, 426, 16, 13, 407, 1783, 16, 6915, 426, 16, 1413, 363, 16, 13, 407, 286, 658, 11803, 13, 13157, 11, 1783, 17, 293, 568, 1413, 363, 17, 307, 24124, 13, 407, 363, 8240, 307, 1386, 11871, 13, 407, 5452, 341, 2158, 510, 11, 291, 486, 483, 1958, 13622, 13], "avg_logprob": -0.20117188071211178, "compression_ratio": 1.286764705882353, "no_speech_prob": 0.0, "words": [{"start": 3272.77, "end": 3273.03, "word": " And", "probability": 0.339599609375}, {"start": 3273.03, "end": 3273.21, "word": " we", "probability": 0.822265625}, {"start": 3273.21, "end": 3273.37, "word": " know", "probability": 0.87841796875}, {"start": 3273.37, "end": 3273.69, "word": " that", "probability": 0.91455078125}, {"start": 3273.69, "end": 3274.13, "word": " B1", "probability": 0.755126953125}, {"start": 3274.13, "end": 3274.43, "word": " equals", "probability": 0.6005859375}, {"start": 3274.43, "end": 3274.81, "word": " X1", "probability": 0.756591796875}, {"start": 3274.81, "end": 3275.01, "word": " over", "probability": 0.88720703125}, {"start": 3275.01, "end": 3275.35, "word": " N1.", "probability": 0.962646484375}, {"start": 3275.43, "end": 3275.53, "word": " So", "probability": 0.923828125}, {"start": 3275.53, "end": 3275.93, "word": " X1", "probability": 0.833251953125}, {"start": 3275.93, "end": 3276.29, "word": " equals", "probability": 0.865234375}, {"start": 3276.29, "end": 3277.19, "word": " N1", "probability": 0.979736328125}, {"start": 3277.19, "end": 3277.51, "word": " times", "probability": 0.9189453125}, {"start": 3277.51, "end": 3277.95, "word": " B1.", "probability": 0.992919921875}, {"start": 3278.65, "end": 3278.83, "word": " So", "probability": 0.93408203125}, {"start": 3278.83, "end": 3278.97, "word": " I", "probability": 0.94677734375}, {"start": 3278.97, "end": 3279.19, "word": " got", "probability": 0.67236328125}, {"start": 3279.19, "end": 3279.59, "word": " 99.", "probability": 0.888671875}, {"start": 3280.29, "end": 3280.93, "word": " Similarly,", "probability": 0.82666015625}, {"start": 3281.05, "end": 3281.37, "word": " X2", "probability": 0.986572265625}, {"start": 3281.37, "end": 3281.55, "word": " and", "probability": 0.229736328125}, {"start": 3281.55, "end": 3281.71, "word": " 2", "probability": 0.6845703125}, {"start": 3281.71, "end": 3282.03, "word": " times", "probability": 0.91015625}, {"start": 3282.03, "end": 3282.43, "word": " B2", "probability": 0.989501953125}, {"start": 3282.43, "end": 3282.93, "word": " is", "probability": 0.44482421875}, {"start": 3282.93, "end": 3283.59, "word": " 96.", "probability": 0.9853515625}, {"start": 3284.03, "end": 3284.41, "word": " So", "probability": 0.9599609375}, {"start": 3284.41, "end": 3284.61, "word": " B", "probability": 0.97607421875}, {"start": 3284.61, "end": 3284.89, "word": " dash", "probability": 0.80859375}, {"start": 3284.89, "end": 3285.07, "word": " is", "probability": 0.8740234375}, {"start": 3285.07, "end": 3285.79, "word": " 629.", "probability": 0.691162109375}, {"start": 3287.17, "end": 3287.39, "word": " So", "probability": 0.958984375}, {"start": 3287.39, "end": 3287.63, "word": " plug", "probability": 0.833984375}, {"start": 3287.63, "end": 3287.97, "word": " this", "probability": 0.93701171875}, {"start": 3287.97, "end": 3288.75, "word": " value", "probability": 0.947265625}, {"start": 3288.75, "end": 3289.11, "word": " here,", "probability": 0.77783203125}, {"start": 3289.23, "end": 3289.37, "word": " you", "probability": 0.94580078125}, {"start": 3289.37, "end": 3289.53, "word": " will", "probability": 0.88037109375}, {"start": 3289.53, "end": 3289.97, "word": " get", "probability": 0.93505859375}, {"start": 3289.97, "end": 3291.61, "word": " 055.", "probability": 0.804443359375}], "temperature": 1.0}, {"id": 122, "seek": 332325, "start": 3296.17, "end": 3323.25, "text": " What's the value that is satisfactory to use in evaluating the alternative hypothesis? That there is a difference in the two population proportions. So we have to compute Z score, Z stat, which is V1 minus V2, which is 6%, minus 0, divided by this amount, 0.55. Now, 0.6 over 0.5 around 1.", "tokens": [708, 311, 264, 2158, 300, 307, 48614, 281, 764, 294, 27479, 264, 8535, 17291, 30, 663, 456, 307, 257, 2649, 294, 264, 732, 4415, 32482, 13, 407, 321, 362, 281, 14722, 1176, 6175, 11, 1176, 2219, 11, 597, 307, 691, 16, 3175, 691, 17, 11, 597, 307, 1386, 8923, 3175, 1958, 11, 6666, 538, 341, 2372, 11, 1958, 13, 13622, 13, 823, 11, 1958, 13, 21, 670, 1958, 13, 20, 926, 502, 13], "avg_logprob": -0.3515625112765544, "compression_ratio": 1.4427860696517414, "no_speech_prob": 0.0, "words": [{"start": 3296.17, "end": 3296.83, "word": " What's", "probability": 0.4130859375}, {"start": 3296.83, "end": 3297.15, "word": " the", "probability": 0.90380859375}, {"start": 3297.15, "end": 3297.65, "word": " value", "probability": 0.89453125}, {"start": 3297.65, "end": 3297.89, "word": " that", "probability": 0.7685546875}, {"start": 3297.89, "end": 3298.11, "word": " is", "probability": 0.229248046875}, {"start": 3298.11, "end": 3298.65, "word": " satisfactory", 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Now 9. 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So the critical regions are 1.96 and above or smaller than minus 1.96. Now, my z statistic is 1.903. Now this value falls in the non-rejection region. So we don't reject the non-hypothesis.", "tokens": [43230, 7998, 11, 4924, 4190, 286, 914, 13, 407, 264, 4924, 10682, 366, 502, 13, 22962, 293, 3673, 420, 4356, 813, 3175, 502, 13, 22962, 13, 823, 11, 452, 710, 29588, 307, 502, 13, 7771, 18, 13, 823, 341, 2158, 8804, 294, 264, 2107, 12, 265, 1020, 313, 4458, 13, 407, 321, 500, 380, 8248, 264, 2107, 12, 3495, 79, 4624, 271, 13], "avg_logprob": -0.24841307708993554, "compression_ratio": 1.4430379746835442, "no_speech_prob": 0.0, "words": [{"start": 3408.17, "end": 3408.65, "word": " Negative", "probability": 0.07171630859375}, {"start": 3408.65, "end": 3409.45, "word": " 196,", "probability": 0.77978515625}, {"start": 3410.39, "end": 3411.01, "word": " critical", "probability": 0.7744140625}, {"start": 3411.01, "end": 3411.37, "word": " values", "probability": 0.66015625}, {"start": 3411.37, "end": 3411.51, "word": " I", "probability": 0.84814453125}, {"start": 3411.51, "end": 3411.77, "word": " mean.", "probability": 0.95849609375}, {"start": 3412.81, "end": 3412.95, "word": " So", "probability": 0.84619140625}, {"start": 3412.95, "end": 3413.15, "word": " the", "probability": 0.70361328125}, {"start": 3413.15, "end": 3414.37, "word": " critical", "probability": 0.93310546875}, {"start": 3414.37, "end": 3414.91, "word": " regions", "probability": 0.927734375}, {"start": 3414.91, "end": 3415.25, "word": " are", "probability": 0.93310546875}, {"start": 3415.25, "end": 3415.69, "word": " 1", "probability": 0.7626953125}, {"start": 3415.69, "end": 3416.31, "word": ".96", "probability": 0.939208984375}, {"start": 3416.31, "end": 3416.55, "word": " and", "probability": 0.90380859375}, {"start": 3416.55, "end": 3416.93, "word": " above", "probability": 0.95458984375}, {"start": 3416.93, "end": 3417.87, "word": " or", "probability": 0.54931640625}, {"start": 3417.87, "end": 3418.23, "word": " smaller", "probability": 0.79248046875}, {"start": 3418.23, "end": 3418.49, "word": " than", "probability": 0.919921875}, {"start": 3418.49, "end": 3419.19, "word": " minus", "probability": 0.55224609375}, {"start": 3419.19, "end": 3419.45, "word": " 1", "probability": 0.9814453125}, {"start": 3419.45, "end": 3420.15, "word": ".96.", "probability": 0.906494140625}, {"start": 3421.43, "end": 3421.73, "word": " Now,", "probability": 0.87939453125}, {"start": 3422.63, "end": 3423.65, "word": " my", "probability": 0.9541015625}, {"start": 3423.65, "end": 3423.81, "word": " z", "probability": 0.60009765625}, {"start": 3423.81, "end": 3424.09, "word": " statistic", "probability": 0.58251953125}, {"start": 3424.09, "end": 3424.51, "word": " is", "probability": 0.9462890625}, {"start": 3424.51, "end": 3424.75, "word": " 1", "probability": 0.986328125}, {"start": 3424.75, "end": 3425.99, "word": ".903.", "probability": 0.76025390625}, {"start": 3427.29, "end": 3427.55, "word": " Now", "probability": 0.91650390625}, {"start": 3427.55, "end": 3427.91, "word": " this", "probability": 0.64697265625}, {"start": 3427.91, "end": 3428.37, "word": " value", "probability": 0.955078125}, {"start": 3428.37, "end": 3429.67, "word": " falls", "probability": 0.79541015625}, {"start": 3429.67, "end": 3430.17, "word": " in", "probability": 0.93359375}, {"start": 3430.17, "end": 3430.39, "word": " the", "probability": 0.908203125}, {"start": 3430.39, "end": 3430.57, "word": " non", "probability": 0.9345703125}, {"start": 3430.57, "end": 3431.05, "word": "-rejection", "probability": 0.8441162109375}, {"start": 3431.05, "end": 3431.45, "word": " region.", "probability": 0.90234375}, {"start": 3431.93, "end": 3432.61, "word": " So", "probability": 0.953125}, {"start": 3432.61, "end": 3432.77, "word": " we", "probability": 0.86669921875}, {"start": 3432.77, "end": 3433.03, "word": " don't", "probability": 0.95947265625}, {"start": 3433.03, "end": 3433.43, "word": " reject", "probability": 0.92333984375}, {"start": 3433.43, "end": 3433.59, "word": " the", "probability": 0.5947265625}, {"start": 3433.59, "end": 3433.67, "word": " non", "probability": 0.473876953125}, {"start": 3433.67, "end": 3434.31, "word": "-hypothesis.", "probability": 0.9009765625}], "temperature": 1.0}, {"id": 127, "seek": 345210, "start": 3436.9, "end": 3452.1, "text": " Ignore A and C, so the answer is either B or D. Now let's read B. Don't reject the null and conclude that the proportion of employees who are interested in self-improvement course has not changed.", "tokens": [24754, 418, 316, 293, 383, 11, 370, 264, 1867, 307, 2139, 363, 420, 413, 13, 823, 718, 311, 1401, 363, 13, 1468, 380, 8248, 264, 18184, 293, 16886, 300, 264, 16068, 295, 6619, 567, 366, 3102, 294, 2698, 12, 332, 46955, 518, 1164, 575, 406, 3105, 13], "avg_logprob": -0.263671883692344, "compression_ratio": 1.3493150684931507, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3436.9, "end": 3437.5, "word": " Ignore", "probability": 0.5670166015625}, {"start": 3437.5, "end": 3437.74, "word": " A", "probability": 0.60009765625}, {"start": 3437.74, "end": 3438.84, "word": " and", "probability": 0.7783203125}, {"start": 3438.84, "end": 3439.18, "word": " C,", "probability": 0.89404296875}, {"start": 3439.64, "end": 3439.74, "word": " so", "probability": 0.40380859375}, {"start": 3439.74, "end": 3439.86, "word": " the", "probability": 0.84375}, {"start": 3439.86, "end": 3440.16, "word": " answer", "probability": 0.95947265625}, {"start": 3440.16, "end": 3440.42, "word": " is", "probability": 0.9375}, {"start": 3440.42, "end": 3440.74, "word": " either", "probability": 0.9453125}, {"start": 3440.74, "end": 3440.92, "word": " B", "probability": 0.9267578125}, {"start": 3440.92, "end": 3441.18, "word": " or", "probability": 0.96044921875}, {"start": 3441.18, "end": 3441.4, "word": " D.", "probability": 0.9697265625}, {"start": 3442.26, "end": 3442.46, "word": " Now", "probability": 0.59912109375}, {"start": 3442.46, "end": 3443.62, "word": " let's", "probability": 0.70654296875}, {"start": 3443.62, "end": 3443.98, "word": " read", "probability": 0.95458984375}, {"start": 3443.98, "end": 3444.6, "word": " B.", "probability": 0.54931640625}, {"start": 3445.14, "end": 3445.44, "word": " Don't", "probability": 0.914306640625}, {"start": 3445.44, "end": 3445.74, "word": " reject", "probability": 0.96435546875}, {"start": 3445.74, "end": 3445.94, "word": " the", "probability": 0.7158203125}, {"start": 3445.94, "end": 3446.1, "word": " null", "probability": 0.93505859375}, {"start": 3446.1, "end": 3446.36, "word": " and", "probability": 0.90478515625}, {"start": 3446.36, "end": 3446.8, "word": " conclude", "probability": 0.8466796875}, {"start": 3446.8, "end": 3447.1, "word": " that", "probability": 0.94091796875}, {"start": 3447.1, "end": 3447.22, "word": " the", "probability": 0.8681640625}, {"start": 3447.22, "end": 3447.62, "word": " proportion", "probability": 0.783203125}, {"start": 3447.62, "end": 3447.84, "word": " of", "probability": 0.974609375}, {"start": 3447.84, "end": 3448.24, "word": " employees", "probability": 0.0802001953125}, {"start": 3448.24, "end": 3448.62, "word": " who", "probability": 0.91748046875}, {"start": 3448.62, "end": 3448.82, "word": " are", "probability": 0.94775390625}, {"start": 3448.82, "end": 3449.3, "word": " interested", "probability": 0.84326171875}, {"start": 3449.3, "end": 3449.56, "word": " in", "probability": 0.94873046875}, {"start": 3449.56, "end": 3449.9, "word": " self", "probability": 0.62548828125}, {"start": 3449.9, "end": 3450.54, "word": "-improvement", "probability": 0.954345703125}, {"start": 3450.54, "end": 3450.86, "word": " course", "probability": 0.80810546875}, {"start": 3450.86, "end": 3451.4, "word": " has", "probability": 0.927734375}, {"start": 3451.4, "end": 3451.6, "word": " not", "probability": 0.93701171875}, {"start": 3451.6, "end": 3452.1, "word": " changed.", "probability": 0.912109375}], "temperature": 1.0}, {"id": 128, "seek": 348546, "start": 3457.04, "end": 3485.46, "text": " That's correct. Because we don't reject the null hypothesis. It means there is no significant difference. So it has not changed. Now, D, don't reject the null hypothesis and conclude the proportion of Obliques who are interested in a certain point has increased, which is incorrect. So B is the correct answer. So again, since my Z statistic falls in the non-rejection region, we don't reject the null hypothesis. So either B or D is the correct answer.", "tokens": [663, 311, 3006, 13, 1436, 321, 500, 380, 8248, 264, 18184, 17291, 13, 467, 1355, 456, 307, 572, 4776, 2649, 13, 407, 309, 575, 406, 3105, 13, 823, 11, 413, 11, 500, 380, 8248, 264, 18184, 17291, 293, 16886, 264, 16068, 295, 4075, 2081, 7519, 567, 366, 3102, 294, 257, 1629, 935, 575, 6505, 11, 597, 307, 18424, 13, 407, 363, 307, 264, 3006, 1867, 13, 407, 797, 11, 1670, 452, 1176, 29588, 8804, 294, 264, 2107, 12, 265, 1020, 313, 4458, 11, 321, 500, 380, 8248, 264, 18184, 17291, 13, 407, 2139, 363, 420, 413, 307, 264, 3006, 1867, 13], "avg_logprob": -0.24540441424823276, "compression_ratio": 1.853061224489796, "no_speech_prob": 0.0, "words": [{"start": 3457.04, "end": 3457.36, "word": " That's", "probability": 0.57470703125}, {"start": 3457.36, "end": 3457.74, "word": " correct.", "probability": 0.89208984375}, {"start": 3458.5, "end": 3459.02, "word": " Because", "probability": 0.8974609375}, {"start": 3459.02, "end": 3459.14, "word": 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That means we don't have sufficient evidence support that there is significant change between the two proportions. So there is no difference. So it has not changed. It's the correct one. So you have to choose B. So B is the most correct answer. Now, 10, 11, and 12.", "tokens": [583, 510, 321, 366, 1417, 466, 6022, 420, 500, 380, 8248, 264, 18184, 17291, 13, 663, 1355, 321, 500, 380, 362, 11563, 4467, 1406, 300, 456, 307, 4776, 1319, 1296, 264, 732, 32482, 13, 407, 456, 307, 572, 2649, 13, 407, 309, 575, 406, 3105, 13, 467, 311, 264, 3006, 472, 13, 407, 291, 362, 281, 2826, 363, 13, 407, 363, 307, 264, 881, 3006, 1867, 13, 823, 11, 1266, 11, 2975, 11, 293, 2272, 13], "avg_logprob": -0.15168425556901213, "compression_ratio": 1.5648148148148149, "no_speech_prob": 0.0, "words": [{"start": 3486.31, "end": 3486.59, "word": " But", "probability": 0.7353515625}, {"start": 3486.59, "end": 3486.77, "word": " here", "probability": 0.83740234375}, {"start": 3486.77, "end": 3486.89, "word": " we", "probability": 0.80615234375}, {"start": 3486.89, "end": 3487.01, "word": " are", "probability": 0.90576171875}, {"start": 3487.01, "end": 3487.35, "word": " talking", "probability": 0.85791015625}, {"start": 3487.35, "end": 3487.93, "word": " 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For 11, 0.5, negative 0.5 to 17. For 90%, negative 0.3 to 0.15. So this is the widest confidence interval, which was for 99%. So similar as the previous one we had discussed. 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Any question? That's all. Next time shall start chapter 12, Chi-square test of independence.", "tokens": [440, 5274, 377, 6687, 15035, 13, 2639, 1168, 30, 663, 311, 439, 13, 3087, 565, 4393, 722, 7187, 2272, 11, 17730, 12, 33292, 543, 1500, 295, 14640, 13], "avg_logprob": -0.3098060468147541, "compression_ratio": 1.1160714285714286, "no_speech_prob": 0.0, "words": [{"start": 3567.81, "end": 3568.09, "word": " The", "probability": 0.387939453125}, {"start": 3568.09, "end": 3568.59, "word": " widest", "probability": 0.912841796875}, {"start": 3568.59, "end": 3569.09, "word": " confidence", "probability": 0.350830078125}, {"start": 3569.09, "end": 3570.61, "word": " interval.", "probability": 0.96435546875}, {"start": 3572.05, "end": 3572.23, "word": " Any", "probability": 0.728515625}, {"start": 3572.23, "end": 3572.57, "word": " question?", "probability": 0.626953125}, {"start": 3574.25, "end": 3575.17, "word": " That's", "probability": 0.8994140625}, {"start": 3575.17, "end": 3575.53, "word": " all.", "probability": 0.86962890625}, {"start": 3576.35, "end": 3576.65, "word": " Next", "probability": 0.92626953125}, {"start": 3576.65, "end": 3576.85, "word": " time", "probability": 0.64599609375}, {"start": 3576.85, "end": 3577.05, "word": " shall", "probability": 0.354248046875}, {"start": 3577.05, "end": 3577.49, "word": " start", "probability": 0.6982421875}, {"start": 3577.49, "end": 3577.95, "word": " chapter", "probability": 0.59326171875}, {"start": 3577.95, "end": 3578.47, "word": " 12,", "probability": 0.734375}, {"start": 3579.35, "end": 3579.55, "word": " Chi", "probability": 0.44482421875}, {"start": 3579.55, "end": 3579.93, "word": "-square", "probability": 0.7141927083333334}, {"start": 3579.93, "end": 3580.39, "word": " test", "probability": 0.86962890625}, {"start": 3580.39, "end": 3580.85, "word": " of", "probability": 0.9599609375}, {"start": 3580.85, "end": 3581.35, "word": " independence.", "probability": 0.77685546875}], "temperature": 1.0}], "language": "en", "language_probability": 1.0, "duration": 3582.81575, "duration_after_vad": 3362.065343749984}