A sample of 46 students enroll in a program that claims to improve scores on the quantita reasoning portion of the Graduate Record Examination (GRE). The participants take a mc GRE test before the program begins and again at the end to measure their improvement.
The mean number of points improved was $\bar { x } = 16$. Assume the standard deviation is $\sigma = 53$ 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 $H _ { 1 } : \mu 0$. ive Compute the value of the test statistic.
A) 14.91
B) 0.0202
C) 0.30
D) 2.05

Question

A sample of 46 students enroll in a program that claims to improve scores on the quantita reasoning portion of the Graduate Record Examination (GRE). The participants take a mc GRE test before the program begins and again at the end to measure their improvement.
The mean number of points improved was $\bar { x } = 16$. Assume the standard deviation is $\sigma = 53$ 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 $H _ { 1 } : \mu > 0$. ive Compute the value of the test statistic.
A) 14.91
B) 0.0202
C) 0.30
D) 2.05

Quizplus · Accepted Answer

The test statistic for this hypothesis test is calculated using the formula $Z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$, where $\bar{x} = 16$, $\mu = 0$, $\sigma = 53$, and $n = 46$. Plugging these values into the formula gives $Z = \frac{16 - 0}{53 / \sqrt{46}}$, which calculates to approximately 2.05.

A Sample of 46 Students Enroll in a Program That xˉ=16\bar { x } = 16xˉ=16

A Sample of 46 Students Enroll in a Program That $\bar { x } = 16$