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 and μB. Consider the model log μ = a + Bx, where x = 1 for treatment B and x = 0 for treatment A.

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An experiment analyzes imperfection rates for two processes used to fabricate silicon wafers for computer chips......

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 μA and µg. Consider the model
log μ = a + Bx, where x = 1 for treatment B and x = 0 for treatment A.
a. Show that B =
log Blog μA = log(B/A) and eß = Mb/MA.
b. Fit the model. Report the prediction equation and interpret ß.
c. Test Ho: A = μB by conducting the Wald or likelihood-ratio test of
Ho: B 0. Interpret.
=
d. Construct a 95% confidence interval for μB/A. [Hint: Construct one for
B = log(μB/μA) and then exponentiate.]
Transcribed Image Text: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 μA and µg. Consider the model log μ = a + Bx, where x = 1 for treatment B and x = 0 for treatment A. a. Show that B = log Blog μA = log(B/A) and eß = Mb/MA. b. Fit the model. Report the prediction equation and interpret ß. c. Test Ho: A = μB by conducting the Wald or likelihood-ratio test of Ho: B 0. Interpret. = d. Construct a 95% confidence interval for μB/A. [Hint: Construct one for B = log(μB/μA) and then exponentiate.]
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