Question

A company that sponsors LSAT prep courses would like to be able to claim that their courses improve scores by more than 3 percentage 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%): Person Initial Test Post-Test 1 62 59 2 78 89 3 79 84 4 67 64 5 76 75 6 70 85 7 72 84 8 65 65 Is there evidence, at an a = 0.025 level of significance, to conclude that the prep course improves scores by more than 3 percentage points? Carry out an appropriate hypothesis test, filling in the information requested. (Do post-test minus initial test.) A. The value of the standardized test statistic: .622171016701 Note: For the next part, your answer should use interval notation. An answer of the form (-0, a) is expressed (-infty, a), an answer of the form (b, 00) is expressed (b, infty), and an answer of the form (-0, a) U (b,00) is expressed (-infty, a)U(b, infty). B. The rejection region for the standardized test statistic: (2.364624252, infty) C. The p-value is 0.276773338 D. Your decision for the hypothesis test:

Answer 1

The statistical software output for this problem is:

Paired T hypothesis test: Po=H-H: Mean of the difference between Post and Initial HA HDP3 Hypothesis test results: Difference Mean Std. Err. DF T-Stat P-value Post-Initial 4.5 2.5773741 7 0.5819877 0.2894

From above output:

a) Test statistic = 0.58199

c) p - Value = 0.2894