Chapter 6, Problem 9P

The Economic Policy Institute periodically issues reports on wages of entry-level workers. The institute reported that entry-level wages for male college graduates were $21.68 per hour and for female college graduates were $18.80 per hour in 2011. Assume that the standard deviation for male graduates is $2.30, and for female graduates it is $2.05.

1. a. What is the sampling distribution of $\bar{x}$ for a random sample of 50 male college graduates?
2. b. What is the sampling distribution of $\bar{x}$ for a random sample of 50 female college graduates?
3. c. In which of the preceding two cases, part (a) or part (b), is the standard error of $\bar{x}$ smaller? Why?