In a study9 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. Output follows of modeling the 2 × 2 × 2 cross-classification of race, whether AZT was given immediately, and whether AIDS symptoms developed during the three-year study.

---------------------–----------------------------------------------------

> AIDS # Data file at text website race azt yes no # yes and no are categories of AIDS symptoms response 1 white yes 14 93 2 white no 32 81 3 black yes 11 52 4 black no 12 43

> fit <- glm(yes/(yes+no) ~ azt + race, weights=yes+no, family=binomial,

+ data=AIDS)

> summary(fit)

Estimate Std. Error z value Pr(>|z|)

(Intercept) -1.07357 0.26294 -4.083 4.45e-05 aztyes -0.71946 0.27898 -2.579 0.00991 racewhite 0.05548 0.28861 0.192 0.84755

---

Null deviance: 8.3499 on 3 degrees of freedom Residual deviance: 1.3835 on 1 degrees of freedom

---------------------–----------------------------------------------------

a. What null hypothesis is tested by the difference between the null deviance and the residual deviance? Interpret.

b. Explain how to set up indicator variables for azt and race to obtain the estimates shown.