Sample surveys on sensitive issues can give different results depending on how t
ID: 3157001 • Letter: S
Question
Sample surveys on sensitive issues can give different results depending on how the question is asked. A University of Wisconsin study divided 2700respondents into 3 groups at random. All were asked if they had ever used cocaine. One group of 900 was interviewed by phone; 20% said they had used cocaine. Another 900 people were asked the question in a one-on-one personal interview; 28% said "Yes." The remaining 900 were allowed to make an anonymous written response; 29% said "Yes." Are there statistically significant differences among these proportions? State the hypotheses, convert the information given into a two-way table of counts, give the test statistic and its P-value, and state your conclusions. (Round your test statistic and P-value to three decimal places.)
a) Fill out the table below:
b) Calculate chi^2 and the P-value.
c) Conclusion (PICK ONE):
-Reject H0. There is no evidence of differing proportions.
-Fail to reject H0. There is no evidence of differing proportions.
-Reject H0. There are statistically significant differences among these proportions.
-Fail to reject H0. There are statistically significant differences among these proportions.
No Yes Phone One-on- one AnonymousExplanation / Answer
a)
For the table, using the proportions given, consider:
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b)
Doing an Expected Value Chart,
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 22.95731175 [ANSWER]
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,
a = 2
b = 3
df = 2
Also, the p value is
P = 1.03486*10^-5 [ANSWER]
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c)
As P is very small, we
OPTION c: -Reject H0. There are statistically significant differences among these proportions. [ANSWER, C]
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