[ajbonkoski]

(sigh) They're comparing averages, so the whole theory is suspect.

Averages are a terrible way to do a comparison. Averages aren't terribly useful unless you know that your data is Gaussian (or a sum of IID Random Variable => see the CLT). Folks love to erroneously assume Gaussian.

In this particular problem, I would expect to see a multimodal distribution for the liberal arts majors.. (i.e. some folks have massive salaries (famous authors) and some have small salaries (high school English teachers)).

In such a case, the average can end up at a value that basically doesn't exist in the underlying distribution. So you end up comparing nonsense.