Question 176335: A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed a mean purchase of $5.29 with a standard deviation of $3.02. For the October 26 evening showing of the same movie, for a sample of 25 purchases the mean was $5.12 with a standard deviation of $2.14. The means appear to be very close, but not the variances. At α = .05, is there a difference in variances? Show all steps clearly, including an illustration of the decision rule.
(Data are from a project by statistics students Kim Dyer, Amy Pease, and Lyndsey Smith.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed a mean purchase of $5.29 with a standard deviation of $3.02. For the October 26 evening showing of the same movie, for a sample of 25 purchases the mean was $5.12 with a standard deviation of $2.14. The means appear to be very close, but not the variances. At α = .05, is there a difference in variances? Show all steps clearly, including an illustration of the decision rule.
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Using a 2-Sample FTest
Ho: s1^2 = s2^2
Ha: They are not equal
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test statistic = 3.02^2/2.14^2 = 1.9915..
critical value 2.02677
Note: My F-chart provides this as a close approximation.
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p-value: 0.09811
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Conclusion: Since p-value > 5%, fail to reject Ho.
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The test does not support saying there is a difference between the variances.
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Note: An illustration of the decision rule is not possible on this site.
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Use Google to find "testing two variances" to see a good example.
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Cheers,
Stan H.
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