Refer to Problem 4.6. The sample mean and variance are 5.0 and 4.2 for treatment A and 9.0 and 8.4 for treatment B.

a. Is there evidence of overdispersion for the Poisson model having a dummy variable for treatment? Explain.

b. Fit the negative binomial loglinear model. Note that the estimated dispersion parameter is O and that estimates of treatment means and standard errors are the same as with the Poisson loglinear GLM.

c. For the overall sample of 20 observations, the sample mean and variance are 7.0 and 10.2. Fit the loglinear model having only an intercept term under Poisson and negative binomial assumptions. Compare results, and compare confidence intervals for the overall mean response. Why do they differ?

Data from Prob. 4.6:

An experiment analyzes imperfection rates for two processes used to fabricate silicon wafers for computer chips. For treatment A applied to 10 wafers, the numbers of imperfections are 8, 7, 6, 6, 3, 4, 7, 2, 3, 4.

Treatment B applied to 10 other wafers has 9,9,8, 14,8, 13, 11,5, 7,6 imperfections. Treat the counts as independent poisson variates having means µ_A and µ_B.