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 8 days, chosen at random. She records the sales (in dollars) for each store on these days, as shown in the table below. Day 1 2 7 8 Store 1 977 560 253 485 653 495 977 563 Store 2 976 613 44 341 487 389 916 366 Difference 1 (Store 1 - Store 2) - 53 209 144 166 106 61 197 Send data to calculator 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 u, (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. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H, : H :0 nl
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 8 days, chosen at random. She records the sales (in dollars) for each store on these days, as shown in the table below. Day 1 2 7 8 Store 1 977 560 253 485 653 495 977 563 Store 2 976 613 44 341 487 389 916 366 Difference 1 (Store 1 - Store 2) - 53 209 144 166 106 61 197 Send data to calculator 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 u, (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. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H, : H :0 nl
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text: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 8 days, chosen at random. She records the sales (in dollars) for each store on these days, as shown in the table below.
s 6 7
Day
1
4
8
Store 1
977
560
253
485
653
495
977
563
Store 2
976
613
44
341
487
389
916
366
Difference
1
(Store 1 - Store 2)
- 53
209
144
166
106
61
197
Send data to calculator
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 u, (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. (If necessary, consult a list of formulas.)
(a) State the null hypothesis H, and the alternative hypothesis H,.
H, :0
H, :0
Transcribed Image Text: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. (If necessary, consult a list of formulas.)
(a) State the null hypothesis H, and the alternative hypothesis H,.
H, :0
H, :0
(b) Determine the type of test statistic to use.
Type of test statistic: (Choose one)
O=0
OSO
(c) Find the value of the test statistic. (Round to three or more decimal places.)
O<O
(d) Find the critical value at the 0.10 level of significance. (Round to three or more decimal places.)
(e) At the 0.10 level, can the owner conclude that the mean daily sales of Store 1 exceeds that of
Store 2?
O Yes ONo
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