Random samples of two freshmen, two sophomores, two juniors, and two seniors each from four dormitories were asked to rate, on a scale of 1 (poor) to 10 (excellent), the quality of the dormitory environment for studying. The results are shown in the following table:

a. Set up the analysis of variance table.
b. Test the null hypothesis that the population mean ratings are the same for the four dormitories.
c. Test the null hypothesis that the population mean ratings are the same for the four student years.
d. Test the null hypothesis of no interaction between student year and dormitory rating.

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Dormitory Year Freshman 5 8 6 9 8 99 Sophomore 6 8 5 5 7 8 89 Junior Senior