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

Essay

Thirty-seven members of a bowling league sign up for a program that claims to in bowling scores. The participants bowl a set of five games before the program begi a set of five games again at the end to measure their improvement.

The mean number of points improved (over the set of five games) was $\bar { x } = 22$ . Ass the standard deviation is $\sigma = 44$ 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 $H _ { 1 } : \mu > 0$ .
i). Compute the value of the test statistic.
ii). Compute the $P$ -value.
iii). Do you reject $H _ { 0 }$ at the $\alpha = 0.01$ level? ove