Decreasing population standard deviation. Improved measurement systems, better technology, and changes to standard operating procedures are among various strategies to reduce population variability in manufacturing and service applications.

Suppose variation reduction strategies are implemented and reduce the population standard deviation by 50%; that is, it is half of its original value.

(a) If n is the sample size used for hypothesis testing under the original standard deviation, what sample size in terms of n is now required to maintain some specified power or Type II error probability?

(b) If the new sample size were used, what might you be concerned about? (Hint: Think about the sampling distribution.)