To compare jail time sentenced for bank robbers and car thieves, which test compares two independent means?

To compare jail time sentenced for bank robbers and car thieves, which test compares two independent means?

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

Answer: (B)

When you want to compare the average jail time between two separate groups, you use a two-sample t-test. The bank robbers and the car thieves form two independent samples, meaning the individuals in one group aren’t linked to individuals in the other. The two-sample t-test looks at the difference between the two sample means and asks whether that observed difference is large enough to conclude a real difference in the population means, considering sampling variability and the usual assumptions (approximate normality or sufficiently large samples, and whether you assume equal variances or not). This is different from a matched pairs t-test, which is for dependent or paired data (like measurements before and after on the same subjects). It’s also different from a one-sample t-test, which compares a single group’s mean to a known value, and from a two-proportion z-test, which compares proportions rather than means.

When you want to compare the average jail time between two separate groups, you use a two-sample t-test. The bank robbers and the car thieves form two independent samples, meaning the individuals in one group aren’t linked to individuals in the other. The two-sample t-test looks at the difference between the two sample means and asks whether that observed difference is large enough to conclude a real difference in the population means, considering sampling variability and the usual assumptions (approximate normality or sufficiently large samples, and whether you assume equal variances or not).

This is different from a matched pairs t-test, which is for dependent or paired data (like measurements before and after on the same subjects). It’s also different from a one-sample t-test, which compares a single group’s mean to a known value, and from a two-proportion z-test, which compares proportions rather than means.