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 very close, but not the variances.
At a=.05, is there a difference in variances?
Perform 5 steps hypothesis testing for: 9.22, 9.62, 9.66, &9.68
SOLUTION This solution is FREE courtesy of BrainMass!
(a) Hypotheses: H0: 1^2 = 2^2 vs Ha: 1^2 ≠ 2^2
(b) Level of Significance: = 5%
(c) Decision Rule: Reject the null hypothesis if p-value < 0.05.
(d) Test characteristic: F = s1^2 /s2^2 = 3.02^2 / 2.14^2 = 1.9915
For dof (numerator) = dof(denominator) = 24 and corresponding to F- value = 1.9915,
the p- value = 0.049057
(e) Conclusion: 0.049057 is just less than 0.05, we reject H0. There is just about enough statistical evidence to conclude at 5% level of significance that there is a difference in the variances.