Question

The drug AZT was the first drug that seemed effective in delaying the onset of AIDS in people infected with HIV. Evidence for AZT's effectiveness came from a large randomized comparative experiment. The subjects were 13001300 HIV‑positive volunteers who had not yet developed AIDS.

The study assigned 435435 of the subjects at random to take 500500 milligrams of AZT each day, and another 435435 to take a placebo. At the end of the study, 3838 of the placebo recipients and 1717 of the AZT recipients had developed AIDS.

We want to test the claim that taking AZT lowers the proportion of infected people who will develop AIDS in a given period of time.

Let ?1p1 represent the population of people who are taking AZT, and ?2p2 represent the population of people who are taking the placebo.

(a) What are the null and alternative hypotheses?

a) ?0:?1=?2H0:p1=p2 versus ??:?1<?2Ha:p1<p2

b) ?0:?1=?2H0:p1=p2 versus ??:?1≠?2Ha:p1≠p2

c) ?0:?1=?2H0:p1=p2 versus ??:?1>?1Ha:p1>p1

d) ?0:?1≥?2H0:p1≥p2 versus ??:?1<?2

(b) How significant is the evidence that AZT is effective? Find ?z . (Enter your answer rounded to four decimal places.)

Answer 1