15. Test 2 hypotheses : The publisher of a sports magazine plans to offer new su
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Question
15. Test 2 hypotheses : The publisher of a sports magazine plans to offer new subscribers one of three gifts: a sweatshirt, a coffee cup or a pair of earrings (each with the logo of their favorite team). In a sample of 500 new subscribers, the number selecting each gift is re- ported below. At a = 0.01, is there a preference for the gifts or should we conclude that the gifts are equally well liked? Gift sweatshirt coffee cup earrings Frequency 183 175 142 : A sample of employees at a large chemical plant was asked to indicate a preference for one of three pension plans. The results are given in the following table. Does it seem that there is a relationship between the pension plan selected and the jolb classification of the employees? Use a = 0.01 Pension Plan Job ClaSPlan A Plan B Plan C Supervisor 10 Clerical19 81 13 80 57 29 19 LaborExplanation / Answer
12(a)
The Hypothesis:
H0: There is no preference for the gift (they are equally liked)
Ha. There is a preference for the gifts.
The Test Statistic. Each expected value = 500/3 = 166.67. The calculations are as below.
2test = 5.668
The Critical Value: The critical value at = 0.01, degrees of freedom = (r – 1) = 2
2critical = 9.21
The Decision Rule: If 2 test is > 2 critical, then Reject H0.
The Decision: Since If 2 test (5.668) is < 2 critical (9.21), We Fail to reject H0.
The Conclusion: There is insufficient evidence at the 99% significance level to conclude that there here is a preference for the gifts.
(b)
The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 330
The Hypothesis:
H0: There is no relation between pension plan selected and the job classification of the employees.
Ha: There is a relation between pension plan selected and the job classification of the employees.
The Test Statistic: The table below gives the calculation of 2.
2test = 84.04
The Critical Value: The critical value at = 0.01, degrees of freedom = (r – 1) * (c -1) = ( 3 - 1) * (3 - 1) = 4
2critical = 13.276
The Decision Rule: If 2 test is > 2 critical, then Reject H0.
The Decision: Since If 2 test (84.04) is > 2 critical (13.276), We Reject H0.
The Conclusion: There is sufficient evidence at the 99% significance level to conclude that there here is a relation between pension plan selected and the job classification of the employees.
Observed Expected O-E (O-E)2 (O-E)2/E 183 166.67 16.33 266.6689 1.5999814 175 166.67 8.33 69.3889 0.41632507 142 166.67 -24.67 608.6089 3.65158037 500 500 Total 5.66788684Related Questions
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