12.34 Writing contrasts. You’ve been asked to help some administrators analyze survey data on textbook expenditures collected at a large public university. Let μ1, μ2, μ3, and μ4 represent the population mean expenditures on textbooks for the freshmen, sophomores, juniors, and seniors, respectively.

  1. (a) Because freshman and sophomores take lower-level courses, which might use more expensive introductory textbooks, the administrators want to compare the average of the freshmen and sophomores with the average of the juniors and seniors. Write a contrast that expresses this comparison.

  2. (b) Write a contrast for comparing the freshmen with the sophomores.

  3. (c) Write a contrast for comparing the juniors with the seniors.