A Sample of 35 Students Enroll in a Program That $\bar { x } = 10$

A sample of 35 students enroll in a program that claims to improve scores on the quantita reasoning portion of the Graduate Record Examination (GRE) . The participants take a mc GRE test before the program begins and again at the end to measure their improvement.
The mean number of points improved was $\bar { x } = 10$ . Assume the standard deviation is $\sigma = 46$ 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 $P$ -value. ive

A) 0.0496
B) 0.0248
C) 0.0992
D) 1.2861