Question: Treating AIDS The drug AZT was the first drug that seemed effective in delaying the onset of AIDS. Evidence for AZT's effectiveness came from a large randomized comparative experiment. The subjects were 870 volunteers who were infected with HIV, the virus that causes AIDS, but did not yet have AIDS. The study assigned 435 of the subjects at random to take 500 milligrams of AZT each day and another 435 to take a placebo. At the end of the study, 38 of the placebo subjects and 17 of the AZT subjects had developed AIDS.

(a) Do the data provide convincing evidence at the a = 0.05 level that taking AZT lowers the proportion of infected people who will develop AIDS in a given period of time?

(b) Describe a Type I error and a Type II error in this setting and give a consequence of each error. Based on your conclusion in part (a), which error could have been made in this study?