Conclusion Fail to reject since the p-value is more than 0.01. Interpretation There is not enough evidence to show that breastfeeding and autism are dependent. This means that you cannot say that the whether a child is breastfed or not will indicate if that the child will be diagnosed with autism. Example #11.1.3: Hypothesis Test with Chi-Square Test Using Formula The World Health Organization (WHO) keeps track of how many incidents of leprosy there are in the world. Using the WHO regions and the World Banks income groups, one can ask if an income level and a WHO region are dependent on each other in terms of predicting where the disease is. Data on leprosy cases in different countries was collected for the year 2011 and a summary is presented in table #11.1.3 ("Leprosy: Number of," 2013). Is there evidence to show that income level and WHO region are independent when dealing with the disease of leprosy? Test at the 5% level. Table #11.1.3: Number of Leprosy Cases WHO Region World Bank Income Group Row Total High Income Upper Middle Income Lower Middle Income Low Income Americas 174 36028 615 0 Eastern Mediterranean 54 6 1883 604 2547 Europe 10 0 0 0 10 Western Pacific 26 216 3689 1155 5086 Africa 0 39 1986 15928 South-East Asia 0 0 149896 10236 160132 Column 264 36289 158069 27923 222545 Solution: the null and alternative hypotheses and the level of significance WHO region and Income Level when dealing with the disease of leprosy are independent WHO region and Income Level when dealing with the disease of leprosy are dependent State and check the assumptions for the hypothesis test
Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made the time period of January 1 to March 31. Table #11.2.4 gives the defect and the number of defects. Table #11.2.4: Number of Defective Lenses Defect type Number of defects Scratch 5865 shaped – small 4613 Flaked 1992 axis 1838 Chamfer wrong 1596 Crazing, cracks 1546 Wrong shape 1485 Wrong PD 1398 Spots and bubbles 1371 Wrong height 1130 Right shape – big 1105 Lost in lab 976 Spots/bubble – intern 976 Do the data support the notion that each defect type occurs in the same proportion? Test at the 10% level. On occasion, medical studies need to model the proportion of the population that has a disease and compare that to observed frequencies of the disease actually occurring. Suppose the end-stage renal failure in south-west Wales was collected for different age groups. Do the data in table 11.2.5 show that the observed frequencies are in agreement with proportion of people in each age group (Boyle, Flowerdew & Williams, 1997)? Test at the 1% level. Table #11.2.5: Renal Failure Frequencies Age 16-29 30-44 45-59 60-75 75+ Total Observed Frequency 32 66 132 218 91 539 Expected Proportion 0.23 0.25 0.22 0.21 0.09 In Africa in 2011, the number of deaths of a female from cardiovascular disease for different age groups are in table #11.2.6 ("Global health observatory," 2013). In addition, the proportion of deaths of females from all causes for the same age groups are also in table #11.2.6. Do the data show that the death from cardiovascular disease are in the same proportion as all deaths for the different age groups? Test at the 5% level. Table #11.2.6: Deaths of Females for Different Age Groups Age 5-14 15-29 30-49 50-69 Total Cardiovascular Frequency 8 16 56 433 513 All Cause Proportion 0.10 0.12 0.26 0.52