A sample of 46 students enroll in a program that claims to improve scores on the quantitative reasoning portion of the Graduate Record Examination (GRE). The participants take a mock GRE test before the program begins and again at the end to measure their improvement.
The mean number of points improved was $\bar { x } = 24$. Assume the standard deviation is $\sigma = 40$ and let $\mu$ be the population mean number of points improved. 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) $0.0000$
B) $4.07$
C) $0.60$
D) $25.74$

Question

A sample of 46 students enroll in a program that claims to improve scores on the quantitative reasoning portion of the Graduate Record Examination (GRE). The participants take a mock GRE test before the program begins and again at the end to measure their improvement.
 The mean number of points improved was $\bar { x } = 24$. Assume the standard deviation is $\sigma = 40$ and let $\mu$ be the population mean number of points improved. 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) $0.0000$
B) $4.07$
C) $0.60$
D) $25.74$

Quizplus · Accepted Answer

The test statistic for this hypothesis test is calculated using the formula $z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$, where $\bar{x} = 24$, $\mu = 0$, $\sigma = 40$, and $n = 46$. Plugging these values into the formula gives $z = \frac{24 - 0}{40 / \sqrt{46}}$, which calculates to approximately 4.07.

A Sample of 46 Students Enroll in a Program That xˉ=24\bar { x } = 24xˉ=24

A Sample of 46 Students Enroll in a Program That $\bar { x } = 24$