24. The 25 women faculty in the humanities division of a college have a mean salary of $46,000, whereas the five in the science division have a mean salary of $60,000. On the TABLE 12.34 Suni of Source Mean Squares DF Square F Prob F Gender 100 Marital status 200 Interaction 100 - 4000 205 Total other hand, the 20 men in the humanities division have a mean salary of $45.000, and the 30 men in the science division have a mean salary of $59.000

a) Construct a table of sample mean incomes for the 2x2 cross-classification of gender and division of college. Find the overall means for men and wornen. Interpret.

b) Discuss how the results of a one-way comparison of mean incomes by gender would differ from the results of a two-way comparison of mean incomes by gender. controlling for division of college. (Note: This reversal of which gender has the higher mean salary. according to whether one controls division of college, illustrates Simpson's paradox. See Problem 10.8d.)