Fifty 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 $\bar { x } = 10$. Assume th standard deviation is $\sigma = 56$ 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) $1.26$
B) $0.18$
C) $0.1038$
D) $9.45$

Question

Fifty 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 $\bar { x } = 10$. Assume th standard deviation is $\sigma = 56$ 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) $1.26$
B) $0.18$
C) $0.1038$
D) $9.45$

Quizplus · Accepted Answer

The test statistic is calculated using the formula $z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$, where $\bar{x} = 10$, $\mu = 0$, $\sigma = 56$, and $n = 50$. Plugging these values into the formula gives $z = \frac{10 - 0}{56 / \sqrt{50}} \approx 1.26$.

Fifty Members of a Bowling League Sign Up for a Program