1)
An experiment analyzes imperfection rates for two processes used to fabricate silicon wafers for computer chips. For treatment A applied to 10 wafers, the number of imperfections is 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 µA and µB.
i) Fit a model of the form log(µ) = α + βx, where x = 0 for treatment A and x = 1 for treatment B.
ii) Show that β = log(µB/µA) and interpret your estimate of β obtained in part (i) above.
iii) Test H0: µA = µB against two sided alternative H1: µA ≠ µB using Wald test.
iv) Construct a Wald type 95% confidence interval for µB/µA.