12.36. The 25 women faculty in the humanities division of a college have a mean salary of $76,000, and the five women in the science division have a mean salary of

$90,000. The 20 men in the humanities division have a mean salary of $75,000, and the 30 men in the science division have a mean salary of $89,000.

(a) Construct a table of sample mean incomes for the 2×2 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.

See Exercise 10.14 in Chapter 10.)