Question: A growing niche in the restaurant business is gourmet-casual breakfast, lunch, and brunch. Chains in this group include Le Peep, Good Egg, Eggs & I, First Watch, and Eggs Up Grill. The mean per-person check for First Watch is approximately ±1$7, and the mean per-person check for Eggs Up Grill is $6.50. (Extracted from J. Hayes, Competition Heats Up as Breakfast Concepts Eye Growth, Nation s Restaurant News, April 24, 2006, pp. 8, 66.)

a. Assuming a standard deviation of $2.00, what sample size is needed to estimate the mean per-person check for Good Egg to within $0.25 with 95% confidence?

b. Assuming a standard deviation of $2.50, what sample size is needed to estimate the mean per-person check for Good Egg to within $0.25 with 95% confidence?

c. Assuming a standard deviation of $3.00, what sample size is needed to estimate the mean per-person check for Good Egg to within $0.25 with 95% confidence?

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