Question
In: Math
A ski company in Vail owns two ski shops, one on the west side and one...
|
A ski company in Vail owns two ski shops, one on the west side and one on the east side of Vail. Ski hat sales data (in dollars) for a random sample of 5 Saturdays during the 2004 season showed the following results. Is there a significant difference in sales dollars of hats between the west side and east side stores at the 10 percent level of significance? |
| Saturday Sales Data ($) for Ski Hats | ||
| Saturday | East Side Shop | West Side Shop |
| 1 | 524 | 524 |
| 2 | 432 | 702 |
| 3 | 617 | 610 |
| 4 | 584 | 571 |
| 5 | 499 | 549 |
| (a) |
Choose the appropriate hypotheses. Assume μd is the difference in average sales between the east side and west side stores. |
| a. H0: μd = 0 versus H1: μd ≠ 0. | |
| b. H0: μd ≠ 0 versus H1: μd = 0. | |
|
| (b) |
State the decision rule for a 5 percent level of significance. (Round your answers to 3 decimal places.) |
| Reject the null hypothesis if tcalc < _____ or tcalc > _____. |
| (c-1) |
Find the test statistic tcalc. (Round your answer to 2 decimal places. A negative value should be indicated by a minus sign.) |
| tcalc |
| (c-2) |
What is your conclusion? |
| We (Click to select) cannot / can conclude that there is a significant difference in sales dollars of hats between the west side and east side stores.? |
Solutions
Expert Solution
| Number |
|
West Side Shop | Difference |
 |
|
| 524 | 524 | 0 | 3600 | ||
| 432 | 702 | -270 | 44100 | ||
| 617 | 610 | 7 | 4489 | ||
| 584 | 571 | 13 | 5329 | ||
| 499 | 549 | -50 | 100 | ||
| Total | 2656 | 2956 | -300 | 57618 |
Part a)
a. H0: μd = 0 versus H1: μd ≠ 0.
Part b)
t(0.05/2) = t( 0.05 /2 ) = 2.776
Reject the null hypothesis if tcalc < -2.776 or tcalc > 2.776
Part c)
t = -60 / ( 120.0187 / (5) )
t = -1.12
Part c2)
Test Criteria :-
Reject null hypothesis if | t | > t(0.05/2)
t(0.05/2) = t( 0.05 /2 ) = 2.776
Result :- Fail to reject null hypothesis
We cannot conclude that there is a significant difference in sales dollars of hats between the west side and east side stores.
milcah answered 4 months agoRelated Solutions
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