The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Sales can vary considerably depending on the day of the week and the season of the year, so she decides to eliminate such effects by making sure to record each store's sales on the same sample of days. After choosing a random sample of 12 days, she records the sales (in dollars) for each store on these days, as shown in the table below.
The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Sales can vary considerably depending on the day of the week and the season of the year, so she decides to eliminate such effects by making sure to record each store's sales on the same sample of days. After choosing a random sample of 12 days, she records the sales (in dollars) for each store on these days, as shown in the table below.
| Day |
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Store 1 |
941
|
734
|
877
|
300
|
517
|
805
|
441
|
557
|
496
|
727
|
556
|
785
|
| Store 2 |
676
|
787
|
750
|
253
|
514
|
646
|
276
|
672
|
495
|
757
|
700
|
730
|
| Difference (Store 1 - Store 2) |
265
|
−53
|
127
|
47
|
3
|
159
|
165
|
−115
|
1
|
−30
|
−144
|
55
|
Based on these data, can the owner conclude, at the 0.10 level of significance, that the mean daily sales of the two stores differ? Answer this question by performing a hypothesis test regarding μd (which is μ with a letter "d" subscript), the population mean daily sales difference between the two stores. Assume that this population of differences (Store 1 minus Store 2) is
a. State the null hypothesis H0 and the alternative hypothesis H1.
b. Find the value of the test statistic. Round to three or more decimal places.
c. Find the two critical values at the 0.10 level of significance. Round to three or more decimal places.
d. At the 0.10 level, can the owner conclude that the mean daily sales of the two stores differ?
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