company that sponsors LSAT prep courses would like to be able to claim that thei

Question

company that sponsors LSAT prep courses would like to be able to claim that their courses improve scores by at least 3 points. 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):

We want to know if there is evidence, at an =0.05=0.05 level of significance, to conclude that the prep course improves scores by at least 3 percentage points. Consider taking

Post-test score - Initial test score

for each person (so the value is >0 if they improved). Let dd be the mean of all such values in the population of all people who take the prep course.

1. Assume that a histogram of the score differences is approximately bell-shaped. The p-value is ____? (USE CALCULATOR VALUE)

person initial test Post test 1 74 87 2 66 76 3 72 83 4 72 73 5 77 77 6 70 78 7 69 68 8 75 85

Explanation / Answer

The statistical software output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Post test and initial test
H0 : D = 3
HA : D > 3
Hypothesis test results:

Hence,

1. p - Value = 0.0597

Difference Mean Std. Err. DF T-Stat P-value Post test - initial test 6.5 1.9730325 7 1.7739191 0.0597

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