Out of a random sample of 400 adult males it was found that 180 of them regularly take a multivitamin. In comparison, out of a random sample of 400 adult females it was found that 220 of them regularly take a multivitamin.

Letp1p1denote the true proportion of adult males that regularly take a multivitamin and letp2p2denote the true proportion adult females that regularly take a multivitamin. Suppose we want to test, at the 1% level of significance, whether the proportion of adult females who regularly take a multivitamin is greater than the proportion of adult males who regularly take a multivitamin.Suppose the assumptions of this hypothesis test are satisfied.

a.What is the test statistic and its distribution for the hypothesis test stated in the preamble of Section G

b.What is the decision rule for the hypothesis test stated in the preamble of Section G

c.Assume the assumptions for the confidence interval forp1p2p1p2are satisfied. What is the 99% confidence interval forp1p2

d.Does the confidence interval calculated in question 26 strongly support the claim that the proportion of adult females who regularly take a multivitamin is greater than the proportion of adult males who regularly take a multivitamin