Thirty-seven 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 $\bar { x } = 19$. Assume thi standard deviation is $\sigma = 58$ 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 $H _ { 1 } : \mu 0$.
Compute the $P$-value.
A) 0.0116
B) 0.0058
C) 1.9926
D) 0.0232

Question

Thirty-seven 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 $\bar { x } = 19$. Assume thi standard deviation is $\sigma = 58$ 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 $H _ { 1 } : \mu > 0$.
Compute the $P$-value.
A) 0.0116
B) 0.0058
C) 1.9926
D) 0.0232

Quizplus · Accepted Answer

The test statistic is calculated using the formula $ z = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}} $, where $\bar{x} = 19$, $\mu_0 = 0$, $\sigma = 58$, and $n = 37$. This gives $ z = \frac{19}{58/\sqrt{37}} \approx 2.012 $. The $P$-value for a one-tailed test with $z = 2.012$ is approximately 0.0232.

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