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.
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 ...
This solution gives explanations for finding differences in waiting times.