Chapter 13, Problem 70CP

AIDS and AZT In a study (reported in the New York Times, February 15, 1991) on the effects of AZT in slowing the development of AIDS symptoms, 338 veterans whose immune systems were beginning to falter after infection with the AIDS virus were randomly assigned either to receive AZT immediately or to wait until their T cells showed severe immune weakness. The study classified the veterans’ race, whether they received AZT immediately, and whether they developed AIDS symptoms during the three-year study. Let x₁ denote whether they used AZT (1 = yes, 0 = no) and let x₂ denote race (1 = white, 0 = black). A logistic regression analysis for the probability of developing AIDS symptoms gave the prediction equation

$\hat{p}=\frac{e^{-1.074-0.720x_1+0.056x_2}}{1+e^{-1.074-0.720x_1+0.056x_2}}.$

1. a. Interpret the sign of the effect of AZT.
2. b. Show how to interpret the AZT effect for a particular race by comparing the estimated probability of AIDS symptoms for black veterans with and without immediate AZT use.
3. c. The se value was 0.279 for the AZT use effect. Does AZT use have a significant effect at the 0.05 significance level? Show all steps of a test to justify your answer.