Chapter 8, Problem 44PS

A growing niche in the restaurant business is gourmet-casual breakfast. lunch. and brunch. Chains in this group include EggSpectation and Panera Bread Suppose that the mean per—person check for breakfast at EggSpectation is approximately $\text{\$14}\text{.50,}$ and the mean per-person check for Panera Bread is $\text{\$8}\text{.50}$ .

a. Assuming a standard deviation of $\text{\$2}\text{.00,}$ what sample size is needed to estimate. with $95\%$ con�dence. the mean per-person check for EggSpectation to within $\pm \text{\$0}\text{.2}5$ ?

b. Assuming a standard deviation of $\text{\$2}\text{.00,}$ what sample size is needed to estimate. with $95\%$ con�dence. the mean per-person check for EggSpectation to within $\pm \text{\$}0.25$ ?

c. Assuming a standard deviation of $\text{\$3}\text{.00}$ , what sample site is needed to estimate, with $95\%$ con�dence. the mean per-person check for EggSpectation to within $\pm \text{\$}0.25$ ?

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