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...

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 to measure their improvement.
The mean number of points improved was  x=7.   Assume the standard deviation is  =56 and let
μ be the population mean number of points improved.

To determine whether the program is effective, a test is made of the hypotheses  ( photo attached below)


i). Compute the value of the test statistic.
ii). Compute theP-value.
iii). Do you rejectH
₀
at the a=0.01 level?

Extracted text: 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 to measure their improvement. The mean number of points improved was x=7. Assume the standard deviation is = 56 and let u be the population mean number of points improved. To determine whether the program is effective, a test is made of the hypotheses H H= 0 versus H, p>0, i). Compute the value of the test statistic, ii). Compute the P-value, 111). Do you reject H at the a = 001 level?