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 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. You decide to carry out an experiment in a sample of 24 stores where customer counts have been running almost exactly at the national average of 900. In 6 of the stores, the price of a small coffee will now be $0.59, in 6 stores the price of a small coffee will now be $0.69, in 6 stores, the price of a small coffee will now be $0.79, and in 6 stores, the price of a small coffee will now be $0.89. After four weeks of selling the coffee at the new price, the daily customer count in the stores was recorded and stored in CoffeeSales.
a. At the 0.05 level of significance, is there evidence of a difference in the daily customer count based on the price of a small coffee?
b. If appropriate, determine which prices differ in daily customer counts.
c. At the 0.05 level of significance, is there evidence of a difference in the variation in daily customer count among the different prices?
d. What effect does your result in (c) have on the validity of the results in (a) and (b)?