Thirty-Eight Members of a Bowling League Sign Up for a Program

Thirty-eight members of a bowling league sign up for a program that claims to improve bowling scores. The participants bowl a set of five games before the program begins and : five games again at the end to measure their improvement.

The mean number of points improved (over the set of five games) was $\bar { x } = 16$ . Assume thi standard deviation is $\sigma = 67$ and let $\mu$ be the population mean number of points improved for the set of five games. To determine whether the program is effective, a test is made of the hypotheses $H _ { 0 } : \mu = 0$ versus $H _ { 1 } : \mu > 0$ .
Do you reject $H _ { 0 }$ at the $\alpha = 0.05$ level?

A) No
B) Yes
C) There is not enough information to draw a conclusion.