Question

# An SAT prep course claims to improve the test score of students. The table below shows...

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=0.05 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 430 400 490 440 490 530 550 Score on second SAT 470 500 510 470 520 600 580

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places

. Step 5 of 5: Make the decision for the hypothesis test.

Ans:

 Before After d 1 430 470 -40 2 400 500 -100 3 490 510 -20 4 440 470 -30 5 490 520 -30 6 530 600 -70 7 550 580 -30 d-bar= -45.7143 sd= 28.785

Test statistic:

t=(-45.7143-0)/(28.785/SQRT(7))

t=-4.202

df=7-1=6

critical t value=-1.943

Decision rule:Reject H0,if t<-1.943

Reject Ho,as t<-1.943

There is sufficient evidence to support the claim that the SAT prep course improves the students' verbal SAT scores

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