A math teacher has developed a new program to help high school students prepare for the math SAT. A sample of 100 students enroll in the program. They take a math SAT exam before the program starts and again at the end to measure their improvement. The mean number of points improved was x̄ = 2.5. Assume the standard deviation is σ = 10.

Let μ be the population mean number of points improved. To determine whether the program is effective, a test is made of the hypotheses H0: μ = 0 versus H1: μ > 0.

a. Compute the value of the test statistic.

b. Compute the P-value.

c. Do you reject H0 at the α = 0.05 level?

d. Is the result of practical significance? Explain.