The market research director for Dotty's Department Store wants to study women's spending on cosmetics. A survey of the store's customers is designed in order to estimate the proportion of women who purchase their cosmetics primarily from Dotty's Department Store and the mean yearly amount that women spend on cosmetics. A previous survey found that the standard deviation of the amount women spend on cosmetics in a year is approximately $18.
a. What sample size is needed to have 99% confidence of estimating the population mean amount spent to within ± $5?
b. How many of the store's credit card holders need to be selected to have 90% confidence of estimating the population proportion to within ± 0.045?