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    Statistics: Difference in Waiting Times

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    There are four auto body shops in a community and all claim to promptly serve customers. To check if there is any difference in service, customers are randomly selected from each repair shop and their waiting times in days are recorded. The output from a statistical software package is:
    Groups Count Sum Average Variance
    Body Shop A 3 15.4 5.133333 0.323333
    Body Shop B 4 32 8 1.433333
    Body Shop C 5 25.2 5.04 0.748
    Body Shop D 4 25.9 6.475 0.595833
    Source of Variation SS df MS F p-value
    Between Groups 23.37321 3 7.791069 9.612506 0.001632
    Within Groups 9.726167 12 0.810514
    Total 33.09938 15

    Is there evidence to suggest a difference in the mean waiting times at the four body shops? Use the .05 significance level.

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    Solution Preview

    The statistic we must look at in order to find whether there is evidence to suggest a difference in the mean waiting times at the four body shops is the F-statistics and its associated p-value. Basically, this test has the following hypotheses:

    H0: The means of all the groups are equal
    H1: The mean of at least one of the groups is not equal

    Since we already have the p-value for the test (which is 0.001632), we simply need to compare it to the significance level for the test. If ...

    Solution Summary

    This solution gives explanations for finding differences in waiting times.