10.38 Aimed at finding monthly tips earned by the waiter and waitress in a restaurant, a random sample of 11 waiters at a restaurant showed that the mean monthly tips earned by them was $67.058, and the sample standard deviation was $12.50. An independent random sample of 9 waitresses in the same restaurant showed mean monthly tips earned of $78 and a standard deviation of $8.14. Assume that the two population distributions are normal with equal standard deviations.

Test, at the 5% level, the null hypothesis that the population mean monthly tips earned are the same against the alternative that the true mean is higher for waitresses.