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# A Sample of 37 Students Enroll in a Program That $\bar { x } = 19$

Question 54
Question 54

## A sample of 37 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 wa $\bar { x } = 19$ . Assume the standard deviation is $\sigma = 58$ 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 $\alpha = 0.05$ level?

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