The Small Business Administration (SBA) wishes to estimate the mean annual sales of companies that employ fewer than 20 persons. Historical data suggest that the standard deviation of annual sales of such companies is about $5500.
(a) If the SBA wants to estimate mean annual sales to within $1000 with a probability of 0.90, how large a sample should be chosen?
(b) Suppose that the SBA has a tolerable type I error rate of 10%. It wishes to detect a difference in mean annual sales of $500 with a probability of 0.95. How large a sample should be chosen?