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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.

  • a

  • b
(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
East Side Shop
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 3 months ago
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