Construct GPAs for three or more sets of student pairs (six or more students). Make the students' GPAs similar but not exactly the same.
Put all of the low-scoring students in Set A and all of the high-scoring students in Set B.
Create the numbers such that a two-sample t-test will not show a significant difference in the mean GPAs of the low scorers of each pair and the mean GPAs of the high scorers of each pair, but the paired t-test does show a significant difference.
(Hint: Make one of the pairs score the highest, one of the pairs score the lowest, and one of the pairs in-between.)
Report all the numbers and the t- and p-values for the tests. Explain why the paired t-test shows a difference and the two-sample t-test does not show a difference.