A study comparing jail time for black and white offenders with 25 cases in each group. Which test best determines if there is a difference in average jail time between the two groups?

A study comparing jail time for black and white offenders with 25 cases in each group. Which test best determines if there is a difference in average jail time between the two groups?

• A. Welch's T-Test
• B. Paired T-Test
• C. One-Sample T-Test
• D. Two-Sample T-Test

Answer: (D)

Two independent samples are being compared to see if their average jail times differ. When you have two separate groups and want to know whether their means are different, the two-sample t-test is the standard method. It tests whether the difference between the two group means is significantly different from zero. Here, jail times for black offenders and white offenders come from separate groups, each with 25 cases, so this test directly addresses the question of whether the average jail time differs between the groups. The paired t-test would be for matched or dependent observations, which isn’t the case here. The one-sample t-test would compare a single group to a known value, not two groups. If you were concerned about unequal variances between the groups, the Welch version of the two-sample t-test is an alternative, but the basic two-sample t-test is the appropriate choice for comparing two independent means.

Two independent samples are being compared to see if their average jail times differ. When you have two separate groups and want to know whether their means are different, the two-sample t-test is the standard method. It tests whether the difference between the two group means is significantly different from zero. Here, jail times for black offenders and white offenders come from separate groups, each with 25 cases, so this test directly addresses the question of whether the average jail time differs between the groups. The paired t-test would be for matched or dependent observations, which isn’t the case here. The one-sample t-test would compare a single group to a known value, not two groups. If you were concerned about unequal variances between the groups, the Welch version of the two-sample t-test is an alternative, but the basic two-sample t-test is the appropriate choice for comparing two independent means.