Question

A company that sponsors LSAT prep courses would like to be able to claim that their courses improve scores. To test this, they take a sample of 8 people, have each take an initial diagnostic test, then take the prep course, and then take a post-test after the course. The test results are below (scores are out of 100%):

Person Post-Test Initial Test

1 64 66

2 56 60

3 71 58

4 83 74

5 73 70

6 79 76

7 81 78

8 64 65

Is there evidence, at an ?=0.015?=0.015 level of significance, to conclude that the prep course improves scores? Carry out an appropriate hypothesis test, filling in the information requested. (Arrange your data so that the standardized test statistic is for the change from the initial test to the post-test.)

A. The value of the standardized test statistic:

Note: For the next part, your answer should use interval notation. An answer of the form (??,a)(??,a) is expressed (-infty, a), an answer of the form (b,?)(b,?) is expressed (b, infty), and an answer of the form (??,a)?(b,?)(??,a)?(b,?) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is:

Answer 1

H0: The prep course is not improves scores
H1: The prep course is improves scores
Let the los be alpha = 0.015

From the given data

Post-Test	Initial Test	Difference
64	66	-2
56	60	-4
71	58	13
83	74	9
73	70	3
79	76	3
81	78	3
64	65	-1

Critical t: 2.7146
P-Value: 0.0895

Here t value is less than t critical value and P-value > alpha 0.015 so we accept H0

Thus we conclude that  the prep course is not improves scores