Practice Paired t-Test in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A hypothesis test for the mean difference in a paired (matched) data design, where each subject provides two related measurements. The test analyzes the differences d_i = x_{1i} - x_{2i} as a single sample.
You want to know if a tutoring program improves math scores. Instead of comparing two separate groups, you test the SAME students before and after tutoring. Each student is their own control. By looking at the difference (after - before) for each student, you eliminate individual variation and focus purely on the change.
Example 1
mediumStudents' scores before and after tutoring: Before: \{70, 65, 80, 75, 60\}, After: \{75, 70, 85, 80, 70\}. Conduct a paired t-test at \alpha=0.05 to test if tutoring improved scores.
Example 2
hardExplain when to use a paired t-test vs. a two-sample t-test. If shoe comfort is measured on the same subjects wearing Brand A and Brand B, which test is appropriate and why?
Example 3
easyFive paired differences are: \{2, -1, 3, 0, 4\}. Calculate \bar{d} and s_d, then set up the t-test statistic formula.
Example 4
hardA paired t-test for blood pressure before and after medication: \bar{d}=-8 mmHg, s_d=5 mmHg, n=16. Construct a 95% CI for the true mean difference and interpret.