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# Clarification of Analysis of Variance

There are four auto body shops in a community and they 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.

#### Solution Preview

Hypotheses: H0: u1 = u2 = u3 = u4 vs. HA: At least one of the means in H0 is different from the others.

Level of Significance: alpha = ...

#### Solution Summary

Solution briefly does the calculations and explains the findings for this hypothesis test.

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