Solved: Two different plasma etchers in a semiconductor factory have the same mean etch
Chapter 7, Problem 7-17(choose chapter or problem)
Two different plasma etchers in a semiconductor factory have the same mean etch rate . However, machine 1 is newer than machine 2 and consequently has smaller variability in etch rate. We know that the variance of etch rate for machine 1 is and for machine 2 it is . Suppose that we have independent observations on etch rate from machine 1 and independent observations on etch rate from machine 2. (a) Show that 1 (1 ) 2 is an unbiased estimator of for any value of between 0 and 1. (b) Find the standard error of the point estimate of in part (a). (c) What value of would minimize the standard error of the point estimate of ? (d) Suppose that and n1 2n2. What value of would you select to minimize the standard error of the point estimate of . How bad would it be to arbitrarily choose in this case?
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