Question

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=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course). Use a significance level of α=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. Student 1 2 3 4 5 6 7 Score on first SAT 560 490 400 350 360 470 560 Score on second SAT 590 540 470 460 380 510 620 Step 1 of 5: State the null and alternative hypotheses for the test.

Answer 1

Claim: The SAT prep course improves the students' verbal SAT scores.

The null and alternative hypothesis is

Before	After	Difference
560	590	-30
490	540	-50
400	470	-70
350	460	-110
360	380	-20
470	510	-40
560	620	-60
	Total	-380

Level of significance = 0.01

Sample size = n = 7

Sample mean of difference = = - 54.29

Sample standard deviation of difference = = 29.9205

Test statistic is

Degrees of freedom = n - 1 = 7 - 1 = 6

Critical value = 3.143 ( Using t table)

Test statistic | t | > critical value we reject null hypothesis.

Conclusion:

The SAT prep course improves the students' verbal SAT scores.