The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Though the two stores have been comparable in the past, the owner has made several improvements to Store 1 and wishes to see if the improvements have made Store 1 more popular than 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 8 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 Store 1 519 631 999 602 543 643 767 742 Store 2 581 324 874 380 257 459 635 564 Difference (Store 1 - Store 2) −62 307 125 222 286 184 132 178 Based on these data, can the owner conclude, at the 0.10 level of significance, that the mean daily sales of Store 1 exceeds that of Store 2? 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 normally distributed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. 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 critical value 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 Store 1 exceeds that of Store 2?
The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Though the two stores have been comparable in the past, the owner has made several improvements to Store 1 and wishes to see if the improvements have made Store 1 more popular than 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 8 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
|
|---|---|---|---|---|---|---|---|---|
| Store 1 |
519
|
631
|
999
|
602
|
543
|
643
|
767
|
742
|
| Store 2 |
581
|
324
|
874
|
380
|
257
|
459
|
635
|
564
|
| Difference (Store 1 - Store 2) |
−62
|
307
|
125
|
222
|
286
|
184
|
132
|
178
|
Based on these data, can the owner conclude, at the 0.10 level of significance, that the
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 critical value 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 Store 1 exceeds that of Store 2?
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