The per-store daily customer count (i.e., the mean number of customers in a store in one day) for a nationwide convenience store chain that operates nearly 10,000 stores has been steady, at 900, for some time. To increase the customer count, the chain is considering cutting prices for coffee beverages. The small size will now be $0.59 instead of $0.99, and medium size will be $0.69 instead of $1.19. Even with this reduction in price, the chain will have a 40% gross margin on coffee. The question to be determined is how much to cut prices to increase the daily customer count without reducing the gross margin on coffee sales too much. The chain decides to carry out an experiment in a sample of 30 stores where customer counts have been running almost exactly at the national average of 900. In 15 of the stores, the price of a small coffee will now be $0.59 instead of $0.99, and in 15 other stores, the price of a small coffee will now be $0.79. After four weeks, the 15 stores that priced the small coffee at $0.59 had a mean daily customer count of 964 and a standard deviation of 88, and the 15 stores that priced the small coffee at $0.79 had a mean daily customer count of 941 and a standard deviation of 76. Analyze these data (use the 0.05 level of significance) and answer the following questions.
a. Does reducing the price of a small coffee to either $0.59 or $0.79 increase the mean per-store daily customer count?
b. If reducing the price of a small coffee to either $0.59 or $0.79 increases the mean per-store daily customer count, is there any difference in the mean per-store daily customer count between stores in which a small coffee was priced at $0.59 and stores in which a small coffee was priced at $0.79?
c. What price do you recommend that a small coffee should be sold for?