Forty-six 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 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 $\bar { x } = 14$. Assume the standard deviation is $\sigma = 59$ 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 value of the test statistic.
A) 1.61
B) 12.36
C) 0.24
D) 0.0537

Question

Forty-six 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 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 $\bar { x } = 14$. Assume the standard deviation is $\sigma = 59$ 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 value of the test statistic.
A) 1.61
B) 12.36
C) 0.24
D) 0.0537

Quizplus · Accepted Answer

The test statistic for this hypothesis test is calculated using the formula $z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$, where $\bar{x} = 14$, $\mu = 0$, $\sigma = 59$, and $n = 46$. Plugging these values into the formula gives $z = \frac{14 - 0}{59 / \sqrt{46}} \approx 1.61$.

Forty-Six Members of a Bowling League Sign Up for a Program