A Sample of 43 Students Enroll in a Program That $\bar { x } = 7$

Essay

A sample of 43 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 measure their improvement.

The mean number of points improved wa $\bar { x } = 7$ . Assume the standard deviation is $\sigma = 56$ 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 $H _ { 1 } : \mu > 0$ .
i). Compute the value of the test statistic.
ii). Compute the $P$ -value.
iii). Do you reject $H _ { 0 }$ at the $\alpha = 0.01$ level?