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 by approximately half. The small size will now be $0.59 instead of $0.99, and the 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. To test the new initiative, the chain has reduced coffee prices in a sample of 34 stores, where customer counts have been running almost exactly at the national average of 900. After four weeks, the sample stores stabilize at a mean customer count of 974 and a standard deviation of 96. This increase seems like a substantial amount to you, but it also seems like a pretty small sample. Do you think reducing coffee prices is a good strategy for increasing the mean customer count?
a. State the null and alternative hypotheses.
b. Explain the meaning of the Type I and Type II errors in the context of this scenario.
c. At the 0.01 level of significance, is there evidence that reducing coffee prices is a good strategy for increasing the mean customer count?
d. Interpret the meaning of the p-value in (c).