# Statistics: Difference in Waiting Times

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:

Summary

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

ANOVA

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.

© BrainMass Inc. brainmass.com June 3, 2020, 7:21 pm ad1c9bdddfhttps://brainmass.com/business/accounting/statistics-difference-waiting-times-94525

#### Solution Preview

Hello!

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.