A sample of five third graders took a reading test. They then participated in a reading improvement program, and took the test again to determine whether their reading ability had improved. Following are the test scores for each of the students both before and after the program. Can you conclude that the mean reading score increased after the program?

a. Let μd denote the population mean difference After − Before. State the appropriate null and alternate hypotheses about μd.

b. Compute the differences After−Before.

c. Compute the value of the test statistic.

d. Compute the P-value.

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

f. State a conclusion.

1 2 3 4 5 After 67 68 78 75 84 Before 59 63 81 74 78