A sample of 25 concession stand purchases at the October 22 matinee of Bride of

Question

A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed a mean purchase of $5.92 with a standard deviation of $3.20. 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 $2.41. The means appear to be very close, but not the variances. At a = .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.)

Explanation / Answer

Given n1=25, xbar1=5.92, s1=3.2 n2=25, xbar2=5.12, s2=2.41 The test hypothesis is Ho:s1^2=s2^2 Ha:s1^2 is not equal s2^2 The test statistic is F=s1^2/s2^2 = 3.2^2/2.41^2 =1.763 Given a=0.05, the critical value is numerator df's = 24 ; denominator df's = 24 F = 2.27 Since F=1.763

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