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# Maximum Likelihood Estimation - Hypothesis Testing of Mean

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You work in the corporate office for a nationwide convenience store franchise that operates nearly 10,000 stores. The per-store daily customer count has been steady, at 900, for some time (i.e., the mean number of customers in a store in one day is 900). To increase the customer count, the franchise is considering cutting coffee prices by approximately half. The 12-ounce size will now be \$0.59 instead of \$0.99, and the 16-ounce size will be \$0.69 instead of \$1.19. Even with this reduction in price, the franchise will have a 40% gross margin on coffee. To test the new initiative, the franchise 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. Is there some way to get a feel for what the mean per-store count in all the stores will be if you cut coffee prices nationwide? Do you think reducing coffee prices is a good strategy for increasing the mean customer count?