By incorporating certain process improvement methods, a company believes that it has reduced the proportion of nonconforming product and wishes to test this belief.

(a) If the operations manager selects an error bound for the difference in the proportion nonconforming before and after implementation of process changes as 4%, with a probability of 0.90, what sample size should be selected? Assume that samples of equal size will be chosen for before and after implementation of process changes.

(b) What measures could you take to reduce the sample size?

(c) Suppose that the hypothesized proportion nonconforming is 8% prior to process changes. We wish to detect reductions of 5% or more with a probability of 0.80. For a chosen level of significance of 10%, what should the sample sizes be? Assume samples of equal size before and after process changes.