Many states mandate tests that have to be passed for graduation. A tutor works with 15 students for a month before the plan to implement an after-school tutoring program. The tutoring program will be implemented if student scores increase by more than 20 points. Which test should be used to analyze the before/after scores?

Many states mandate tests that have to be passed for graduation. A tutor works with 15 students for a month before the plan to implement an after-school tutoring program. The tutoring program will be implemented if student scores increase by more than 20 points. Which test should be used to analyze the before/after scores?

• A. 2-proportion z-test
• B. ANOVA
• C. Matched Pairs t-test
• D. 1-sample t-test

Answer: (C)

The situation involves two related measurements from the same students—before and after scores. When data are paired like this, you use a matched pairs (paired) t-test because it focuses on the differences within each individual rather than treating the two sets of scores as independent groups. By computing each student’s score change (after minus before) and analyzing those differences, you account for how each student’s own starting level affects the outcome, which gives you a more precise estimate of the average change. If you want to know whether the average change exceeds 20 points, you test whether the mean of those differences is greater than 20 (a one‑sided test). With 15 students, the test uses the differences’ mean and standard deviation, and the degrees of freedom are 14. Why not the other options? A 2-proportion z-test compares proportions, not mean scores. ANOVA is for comparing means across three or more groups or factors, not just two related measurements. A 1-sample t-test would compare a single sample to a fixed population mean, not pairwise differences within the same individuals.

The situation involves two related measurements from the same students—before and after scores. When data are paired like this, you use a matched pairs (paired) t-test because it focuses on the differences within each individual rather than treating the two sets of scores as independent groups. By computing each student’s score change (after minus before) and analyzing those differences, you account for how each student’s own starting level affects the outcome, which gives you a more precise estimate of the average change.

If you want to know whether the average change exceeds 20 points, you test whether the mean of those differences is greater than 20 (a one‑sided test). With 15 students, the test uses the differences’ mean and standard deviation, and the degrees of freedom are 14.

Why not the other options? A 2-proportion z-test compares proportions, not mean scores. ANOVA is for comparing means across three or more groups or factors, not just two related measurements. A 1-sample t-test would compare a single sample to a fixed population mean, not pairwise differences within the same individuals.