A 2010 Pew Research foundation poll indicates that among 1099 college graduates, 33% watch The Daily Show. Meanwhile, 22% of the 1110 people with a high school degree but no college degree in the poll watch The Daily Show. A 95% confidence interval for pCoegeGrad−pHighSchoo, where p is the proportion of those who watch The Daily Show, is (0.07, 0.15).
a. Verify that the 95% CI for pCoegeGrad−pHighSchoo is (0.07, 0.15). Show your computation.
b. Conduct a hypothesis test to determine if the data provide strong evidence that there is a higher percentage of college graduates watch The Daily Show than those with a high school degree but no college degree. State the hypotheses. Report the test statistic and the P-value.
c. Determine if the following statements are true or false, and explain your reasoning if you identify the statement as false.
i. 95% of random samples of 1,099 college graduates and 1,110 people with a high school degree but no college degree will yield differences in sample proportions between 7% and 15%.
ii. A 90% confidence interval for pCoegeGrad−pHighSchoo would be wider.
iii. A 95% confidence interval for pCoegeGrad−pHighSchoo grad is (−0.15, −0.07).