12.48. The 25 women faculty in the humanities division of a college have a mean salary of $66,000, whereas the five in the science division have a mean salary of $80,000. On the other hand, the 20 men in the humanities division have a mean salary of $65,000, and the 30 men in the science division have a mean salary of $79,000.

(a) Construct a table ofsample mean incomes for the 2x2 cross-classification of gender and division of college. Find the overall means for men and women. 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. Sec Exercise 10.14 in Chapter 10.)