Chapter 8, Problem 44PS

A growing niche in the restaurant business is gourmet-casual breakfast, lunch, and brunch. Chains in this group include Panera Bread. Suppose that the mean per-person check for breakfast at Panera Bread is approximately $\$\mathrm{9.50.}$

a. Assuming a standard deviation of $\$2.00,$ what sample size is needed to estimate, with $95\%$ confidence, the mean per-person check for Panera Bread to within $\pm \text{\$}0.25?$

b. Assuming a standard deviation of $\$2.50,$ what sample size is needed to estimate, with $95\%$ confidence, the mean per-person check for Panera Bread to within $\pm \text{\$}0.25?$

c. Assuming a standard deviation of $\$3.00,$ what sample size is needed to estimate, with $95\%$ confidence, the mean per-person check for Panera Bread to within $\pm \text{\$}0.25?$

d. Discuss the effect of variation on the sample size needed.