Question 195486This question is from textbook
: 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.)
This question is from textbook
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.
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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.
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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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Ho: variance1 = variance 2
H1: variance 1 is not equal to variance 2
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test statistic: F = 3.02^2/2.14^2 = 1.9915...
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alpha = 5%
numerator df = 24 (not on the F chart so use df=25)
denominator df = 25
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Use Appendix F to find the critical values: (p. 288)
Critical F value 2.23
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Conclusion: Since the test statistic is not in the reject interval,
Fail to reject Ho.
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Cheers,
Stan H.
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