7.129 Interracial friendships in college. A study utilized the random roommate assignment process of a small college to investigate the interracial mix of friends among students in college.46 As part of this study, the researchers looked at 238 white students who were randomly assigned a roommate in their first year and recorded the proportion of their friends (not including the first-year roommate) who were black. The following table summarizes the results, broken down by roommate race, for the middle of the first and third years of college.

Middle of First Year
Randomly assigned n s
Black roommate 41 0.085 0.134
White roommate 197 0.063 0.112
Middle of Third Year
Randomly assigned n s
Black roommate 41 0.146 0.243
White roommate 197 0.062 0.154

  1. (a) Proportions are not Normally distributed. Explain why it may still be appropriate to use the t procedures for these data.

  2. (b) For each year, state the null and alternative hypotheses for comparing these two groups.

  3. (c) For each year, perform the significance test at the α = 0.05 level, making sure to report the test statistic, degrees of freedom, and P-value.

  4. (d) Write a one-paragraph summary of your conclusions from these two tests.