1 STAT 110: Homework 4 Solutions Fall 2014 On September 16

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)
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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.
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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.
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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.
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