1. In a research paper by UT Economics professor Dan Hammermesh, data on course instructor surveys for 463 UT courses is analyzed. In each course, the overall instructor rating is noted. Here we'll consider differences in these ratings based on the gender of the instructor. Previous work has established strong evidence of gender bias in these sorts of ratings (here we'll only consider whether there are differences in average ratings by gender which, on its own, isn't evidence of bias, but could be consistent with it).

Out of 195 courses taught by women, the sample mean of the ratings was 3.90 and the sample standard deviation of the ratings was .54. For the 268 courses taught by men the sample mean was 4.07 and the sample standard deviation was .56. Conduct a formal hypothesis test to assess whether male and female faculty get the same ratings on average. Be sure to formally specify your hypotheses, show the steps of your calculation and explain briefly what your result tells you about gender differences in ratings.