1. A course is designed to increase mathematical comprehension. In order to evaluate the effectiveness of the course, students are given a test before and after the course. Does the course help the students comprehend math better? Student 1 2 3 4 Test score before course 75 67 82 70 Test score after course 87 68 80 69

2. Difference Data: (test score after course – test score before course) 87-75=12; 68-67=1; 80-82=-2; 69-70=-1 Difference Data:{12, 1, -2, -1} (Subscript: d = difference) H o :µ d ≤ 0 (no improvement in comprehension) H a : µ d > 0 (improvement in comprehension)

3. = average of the differences between the scores Distribution for the Test: Student-t: t 3 df = 4 – 1 = 3

4. Test statistic: 0.77 Standardized score for the sample mean (2.5) of the difference data. p-value: 0.7525 Use a TTest.

5. Decision: DO NOT REJECT H o. Conclusion: There is NOT sufficient evidence to conclude that the course helps the students to comprehend math better.