Counselors at two colleges (College Blue and College Gold) want to estimate the average grade point average (GPA) of students attending their respective colleges. The College Blue counselor collects GPAs from 10 students (N = 10); however, the College Gold counselor collects GPAs from 30 students (N = 30).

In analyzing their data, by an amazing coincidence, they calculate the same mean and standard deviation

(X̅ = 2.81, s = .90).

a. Calculate the 95% confidence interval for the mean (σ not known) for the two colleges.

b. Which college has the narrower confidence interval? Why?