The Daily Show: A 2010 Pew Research foundation poll indicates that among 1,099 c

Question

The Daily Show: A 2010 Pew Research foundation poll indicates that among 1,099 college graduates, 33% watch The Daily Show. Meanwhile, 22% of the 1,110 people with a high school degree but no college degree in the poll watch The Daily Show. A 95% confidence interval for (pcollege grad - HS or less), where p is the proportion of those who watch The Daily Show, is (0.07, 0.15). Based on this information, determine if the following statements are true or false, and explain your reasoning if you identify the statement as false.

(a) At the 5% significance level, the data provide convincing evidence of a difference between the proportions of college graduates and those with a high school degree or less who watch The Daily Show.

(b) We are 95% confident that 7% less to 15% more college graduates watch The Daily Show than those with a high school degree or less.

(c) 95% of random samples of 1,099 college graduates and 1,110 people with a high school degree or less will yield differences in sample proportions between 7% and 15%.

(d) A 90% confidence interval for (pcollege grad - pHS or less) would be wider.

(e) A 95% confidence interval for (pHS or less - pcollege grad) is (-0.15,-0.07).

Explanation / Answer

solution=

A
Yes, there is a convincing evidence of a difference, as the 95% C.I. does not have 0 in it , which indicates no difference.

B
False. It indicates that we are 95% confident that the difference between college graduates and high school students watching The Daily Show is between 7% and 15%.

C
Yes, as this is what the purpose of a C.I. is.

D
False. Since, we just have to be 90% sure, there will be a lesser range.

E
True. As we are just reversing the mean.

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