A sample of 39 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 $\bar { x } = 12$. Assume the standard deviation is $\sigma = 40$ and let $\mu 1$ 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 P-value.
A) 0.0305
B) 0.0076
C) 1.8735
D) 0.0153

Question

A sample of 39 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 $\bar { x } = 12$. Assume the standard deviation is $\sigma = 40$ and let $\mu 1$ 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 P-value.
A) 0.0305
B) 0.0076
C) 1.8735
D) 0.0153

Quizplus · Accepted Answer

The P-value is calculated using the formula for the z-test since the population standard deviation is known. The z-score is calculated as $z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}}$, where $\bar{x} = 12$, $\mu_0 = 0$, $\sigma = 40$, and $n = 39$. Plugging these values into the formula gives $z = \frac{12 - 0}{40 / \sqrt{39}}$, which results in a z-score that corresponds to a P-value of 0.0305, indicating the probability of observing a sample mean of 12 or more by chance if the true population mean improvement is 0. This supports the alternative hypothesis that the program is effective at improving scores.

A Sample of 39 Students Enroll in a Program That xˉ=12\bar { x } = 12xˉ=12

A Sample of 39 Students Enroll in a Program That $\bar { x } = 12$