Refer to Table 2.7.

a. Fit the logistic regression model using scores {0, .5, 1.5, 4, 7} for alcohol consumption. Check goodness of fit.

b. Test independence, using the likelihood-ratio test and the Wald test for the model in (a). (Note: The trend test of Section 2.5 is the "efficient score" test for this model.)

c. Conduct the tests of independence using scores {1, 2, 3, 4, 5}. Compare re- sults to (b), noting that results for highly unbalanced data can be sensitive to the choice of scores.

d. Check the sensitivity of the choice of model by repeating the analyses of (a)-

(c) using a different link function. Compare results to those obtained using the logit link.

e. The table has some small counts, and exact methods have greater validity than large-sample ones. Show that the exact test of independence using the scores in

(a) has one-sided P-value of .016.