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 $\bar { x } = 11$ 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) 0.28
B) 0.0307
C) 1.87
D) 11.80

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 $\bar { x } = 11$ 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) 0.28
B) 0.0307
C) 1.87
D) 11.80

Quizplus · Accepted Answer

To compute the test statistic, we use the formula:

$t = \frac{\bar{x} - \mu_{0}}{\frac{s}{\sqrt{n}}}$

where $\bar{x}$ is the sample mean (11), $\mu_{0}$ is the hypothesized population mean (0), $s$ is the sample standard deviation (40), and $n$ is the sample size (46).

Plugging in the values, we get:

$t = \frac{11 - 0}{\frac{40}{\sqrt{46}}} \approx 1.87$

Therefore, the test statistic is approximately 1.87.

The correct answer is C.

A Sample of 46 Students Enroll in a Program That xˉ=11\bar { x } = 11xˉ=11

A Sample of 46 Students Enroll in a Program That $\bar { x } = 11$