STAT 110: Homework 4 Solutions Fall 2014 On September 16-17, 2014, an NBC News/Marist Poll surveyed a random sample of 606 American adults. Respondents were asked the following question: “Do you think it is right or wrong for parents to discipline their children by striking them - either with a paddle, switch, or belt?” The results were tabulated according to whether or not the respondent currently had children in their household and are summarized in the following contingency table. Households with children No children in the household Totals Right 72 134 206 Not Right 152 248 400 Totals 224 382 606 1. Find the proportion of those surveyed with children in the household that feel this form of discipline is right. (2 pts) 72/224 = 32.14% 2. Find the proportion of those surveyed with no children in the household that feel this form of discipline is right. (2 pts) 134/382 = 35.08% 3. Sketch in the mosaic plot on the graph below. (1 pt) 1 4. Next, you will investigate this question: Do the data provide statistical evidence that the proportion of American adults that feel this form of discipline is right differs depending on whether or not they have kids in their household? Your solution should include the Pearson’s chi-square test statistic, its associated p-value, and a conclusion written in everyday language. (4 pts) Test Statistic: .542 p-value: .4615 Conclusion: The data do not provide enough evidence to support the hypothesis that the proportion of American adults that feel this form of discipline is right differs depending on whether or not they have kids in their household 5. Next, you will investigate this question: Do the data provide statistical evidence that American adults are more likely to say that this form of discipline is right if they don’t have kids in their household? Use Fisher’s exact test to investigate this question. Your solution should include the p-value and a conclusion written in everyday language. (3 pts) p-value: .2591 Conclusion: The data do not provide enough evidence to support the hypothesis that American adults are more likely to say that this form of discipline is right if they don’t have kids in their household. 2 Next, the results were tabulated according to the respondent’s gender and are summarized in the following contingency table. Men Women Totals Right Not Right Totals 119 178 297 87 222 309 206 400 606 6. Find the proportion of men surveyed that feel this form of discipline is right. (2 pts) 119/297 = 40.07% 7. Find the proportion of women surveyed that feel this form of discipline is right. (2 pts) 87/309 = 28.16% 8. Sketch in the mosaic plot on the graph below. (1 pt) 9. Next, you will investigate this question: Do the data provide statistical evidence that the proportion of American adults that feel this form of discipline is right differs across gender? Your solution should include the p-value for these data and a conclusion written in everyday language. (4 pts) p-value: .002 Conclusion: The data do provide statistical evidence that the proportion of American adults that feel this form of discipline is right differs across gender. 3 Finally, the results were tabulated according to the respondent’s race and are summarized in the following contingency table. White Non-white Totals Right Not Right Totals 130 276 406 76 124 200 206 400 606 The mosaic plot for these data is shown below. Note that the p-value for testing whether the proportion of American adults that feel this form of discipline is right differs across race is .1459. 10. On the following mosaic plot, sketch in hypothetical results that would produce a smaller p-value than what was actually obtained in the study. (2 pts) One possible answer is shown below. The big idea is that you should see a bigger difference between the proportions of each group that answer “right.” 11. On the following mosaic plot, sketch in hypothetical results that would indicate race is not at all related to whether or not one feels this form of discipline is right. (2 pts) If race is not related to whether or not one feels this form of discipline is right, then we should see no differences between groups. 4
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