An SAT prep course claims to improve the test score of students. The table below shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her verbal SAT scores. Do these results support the claim that the SAT prep course improves the students' verbal SAT scores?

Let d=(verbalSATscorespriortotakingtheprepcourse)(verbalSATscoresaftertakingtheprepcourse)

. Use a significance level of =0.01

for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.

Student1234567Score on first SAT470

440

560

390

510

370

560

Score on second SAT490

500

600

430

540

440

600

Step 1 of 5:

State the null and alternative hypotheses for the test.