Question

A student wants to prove that a GMAT prep company's claim that attending its 10-session prep course raises students' scores on the GMAT by an average of at least 50 points is false. In order to test the claim, they take eight students who have previously taken the GMAT and have them complete the 10 sessions. After completion, the students retake the GMAT and their scores are recorded. Test the theory at a 1% level of significance, using the paired difference test. You may assume that the differences in scores are normally distributed.

Student	Before	After
1	580	652
2	565	585
3	521	543
4	512	567
5	563	564
6	544	592
7	604	665
8	693	684
9	631	654

Answer 1

Solution:

Here, we have to use paired t test.

The null and alternative hypotheses for this test are given as below:

H0: µd ≥ 50 versus Ha: µd < 50

This is a lower tailed test.

Test statistic for paired t test is given as below:

t = (Dbar - µd)/[Sd/sqrt(n)]

From given data, we have

Dbar = 32.5556

Sd = 27.8169

n = 9

df = n – 1 = 8

α = 0.01

t = (Dbar - µd)/[Sd/sqrt(n)]

t = (32.5556 – 50)/[ 27.8169/sqrt(9)]

t = -1.8814

The p-value by using t-table is given as below:

P-value = 0.0484

P-value > α = 0.01

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that attending its 10-session prep course raises students' scores on the GMAT by an average of at least 50 points is not false.