Which test is used for comparing the first semester GPA to the third semester GPA for the same students?

Which test is used for comparing the first semester GPA to the third semester GPA for the same students?

• A. Independent samples T-Test
• B. Related samples T-Test
• C. Z-test for means
• D. ANOVA

Answer: (B)

When comparing two measurements that come from the same individuals, the data are paired because each student has two GPA scores. The question asks whether the average change from the first semester to the third semester is different from zero, which is exactly what a paired (related-samples) t-test examines. This test uses the difference for each student and tests whether the mean difference is zero, taking into account the within-person correlation. A significant result would indicate a real change in GPA over time, while a non-significant result suggests no evidence of change. The other tests aren’t as appropriate here: an independent samples t-test compares two unrelated groups, a Z-test relies on known population variance (rare in practice), and ANOVA is used for more than two groups or time points (or repeated measures with more than two levels).

When comparing two measurements that come from the same individuals, the data are paired because each student has two GPA scores. The question asks whether the average change from the first semester to the third semester is different from zero, which is exactly what a paired (related-samples) t-test examines. This test uses the difference for each student and tests whether the mean difference is zero, taking into account the within-person correlation. A significant result would indicate a real change in GPA over time, while a non-significant result suggests no evidence of change. The other tests aren’t as appropriate here: an independent samples t-test compares two unrelated groups, a Z-test relies on known population variance (rare in practice), and ANOVA is used for more than two groups or time points (or repeated measures with more than two levels).