1. (25 points) You work in the corporate office for a nationwide convenience store franchise that operates nearly 10,000 stores. The per-store daily customer count (i.e., the mean number of customers in a store in one day), 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 either $0.59 or $0.79 instead of $0.99. 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 100 stores where customer counts have been running almost exactly at the national average of 900. These stores have similar storewide sales volumes and shopper demographics. In 50 of the stores, the price of a small coffee will now be $0.59 instead of $0.99, and in 50 other stores, the price of a small coffee will now be $0.79 instead of $0.99. After four weeks of the price drop, you recorded the daily customer counts of these stores and stored the data in Coffee.xlsx. Analyze the data using the 0.05 level of significance and answer the following questions.

a. (10 points) Does reducing the price of a small coffee to $0.59 increase the mean per-store daily customer count? How about reducing the price to $0.79? Explain what test you use and why. Show how you reach the conclusion and interpret the results.

b. (10 points) 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? Explain what test you use and why. Show how you reach the conclusion and interpret the results.

c. (5 points) Based on your analysis in (a) and (b), what price do you recommend for a small coffee and why?

$0.59	$0.79
962	946
1117	895
1072	977
994	1067
850	890
955	982
989	940
869	1000
941	862
923	1106
1044	994
920	989
1171	953
951	1043
969	812
877	1031
1168	1004
962	974
846	1051
844	958
1060	955
963	909
1071	994
1027	1029
1066	869
854	820
975	846
1014	916
890	862
953	998
1068	1006
960	1035
984	984
990	971
934	964
944	968
1018	984
1028	839
922	953
856	806
887	887
1071	912
998	1007
957	879
779	1027
870	1019
910	890
932	789
1088	950
1059	808