One question in a recent General Social Survey asked subjects howmany times they had had sexual intercourse in the previous month.

a. The sample means were 5.9 for males and 4.3 for females; the sample variances were 54.8 and 34.4. Does an ordinary Poisson GLM seem appropriate? Explain.

b. The GLM with log link and a dummy variable for gender (1 = males, 0 = females) has gender estimate 0.308. The SE is 0.038 assuming a Poisson distribution and 0.127 assuming a negative binomial model. Why are the SE values so different?

c. TheWald 95% confidence interval for the ratio of means is (1.26, 1.47) for the Poisson model and (1.06, 1.75) for the negative binomial model. Which interval do you think is more appropriate? Why?