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.

a. Fit the model log µ = α + βx, where x = 1 for treatment B and x = 0 for treatment A. Show that exp(β) = µ_B/µ_A, and interpret its estimate.

b. Test H₀: µ_A = µ_B with the Wald or likelihood ratio test of H₀:β = 0. Interpret.

c. Construct a 95% confidence interval for µ_A / µ_A.

d. Test H₀: µ_A = µ_B based on this result: If Y₁ and Y₂ are independent Poisson with means µ₁ and µ₂, then (Y₁|Y₁ + Y₂) is binomial with n = Y₁ + Y₂ and π = µ₁/(µ₁ + µ₂).