A sample of 41 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 $\bar { x } = 17$. Assume the standard deviation is $\sigma = 69$ 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 $H _ { 1 } : \mu 0$.
Do you reject $H _ { 0 }$ at the $\alpha = 0.01$ level?
A) There is not enough information to draw a conclusion.
B) Yes
C) $\mathrm { No }$

Question

A sample of 41 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 $\bar { x } = 17$. Assume the standard deviation is $\sigma = 69$ 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 $H _ { 1 } : \mu > 0$.
Do you reject $H _ { 0 }$ at the $\alpha = 0.01$ level?
A) There is not enough information to draw a conclusion.
B) Yes
C) $\mathrm { No }$

Quizplus · Accepted Answer

Given the sample size (n = 41), sample mean ($\bar{x} = 17$), population standard deviation ($\sigma = 69$), and the null hypothesis ($H_0: \mu = 0$), we can calculate the z-score to test the hypothesis. The formula for the z-score in this context is $z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$. Substituting the given values, we find $z = \frac{17 - 0}{69 / \sqrt{41}}$, which yields a z-score that we can compare against the critical value for $\alpha = 0.01$ in a one-tailed test. The critical z-value for $\alpha = 0.01$ is approximately 2.33. If the calculated z-score is less than 2.33, we do not reject $H_0$, indicating the program's effectiveness is not statistically significant at the 0.01 level.

A Sample of 41 Students Enroll in a Program That xˉ=17\bar { x } = 17xˉ=17

A Sample of 41 Students Enroll in a Program That $\bar { x } = 17$