A growing niche in the restaurant business is gourmetcasual breakfast, lunch, and brunch. Chains in this group include EggSpectation and Panera Bread. Suppose that the mean per-person check for EggSpectation is approximately $12.50, and the mean per-person check for Panera Bread is $7.50.
a. Assuming a standard deviation of $2.00, what sample size is needed to estimate, with 95% confidence, the mean per-person check for EggSpectation to within ± $0.25?
b. Assuming a standard deviation of $2.50, what sample size is needed to estimate, with 95% confidence, the mean perperson check for EggSpectation to within ± $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 EggSpectation to within ± $0.25?
d. Discuss the effect of variation on the sample size needed.