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 4Test score before course 75 67 82 70Test score after course 87 68 80 69

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)

Ho: µd ≤ 0(no improvement in comprehension)

Ha: µd > 0(improvement in comprehension)

= average of the differences between the scores

Distribution for the Test: Student-t: t3

df = 4 – 1 = 3

dX

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

Use a TTest.

Decision:

DO NOT REJECT Ho.

Conclusion: There is NOT sufficient evidence to conclude that the course helps the students to comprehend math better.

0.05 ( )p value