Having carried out the study of Exercise 15.66, the investigator decided to take a second independent random sample of one student from each of the nine income–SAT score categories. The grade point averages found are given in the accompanying table.

Income Group Sat Score High Moderate Low Very high 3.9 3.7 3.8 High 3.2 3.6 3.4 Moderate 2.7 3.0 2.8

a. Prepare the analysis of variance table.

b. Test the null hypothesis that the population mean grade point averages are the same for all three income groups.

c. Test the null hypothesis that the population mean grade point averages are the same for all three SAT score groups.

d. Test the null hypothesis of no interaction between income group and SAT score.