Two body shops' repair costs are compared using random samples of ten bills from each shop. Is there a significant difference in costs?

Two body shops' repair costs are compared using random samples of ten bills from each shop. Is there a significant difference in costs?

• A. ANOVA
• B. Paired t-test
• C. Chi-square test
• D. 2-sample t-test

Answer: (D)

This question tests comparing the average repair costs between two independent groups. When you want to know if the mean cost from one shop differs from the mean cost from another shop, the two-sample t-test is the standard approach. It uses the two sets of bills to see whether the observed difference in sample means is larger than what we'd expect if both shops had the same true average cost. The samples are independent (bills from one shop aren’t paired with bills from the other), and the outcome is a numeric cost, so a t-test for two independent samples fits best. If variances might differ, you can use Welch’s version, which adjusts for unequal variances. ANOVA is for more than two groups (and while equivalent to a t-test with two groups, the two-sample t-test is the typical choice here). The paired t-test is for matched or repeated measurements, which isn’t the case, and the chi-square test is for categorical data. So the two-sample t-test is the right method to determine if there’s a significant difference.

This question tests comparing the average repair costs between two independent groups. When you want to know if the mean cost from one shop differs from the mean cost from another shop, the two-sample t-test is the standard approach. It uses the two sets of bills to see whether the observed difference in sample means is larger than what we'd expect if both shops had the same true average cost. The samples are independent (bills from one shop aren’t paired with bills from the other), and the outcome is a numeric cost, so a t-test for two independent samples fits best. If variances might differ, you can use Welch’s version, which adjusts for unequal variances. ANOVA is for more than two groups (and while equivalent to a t-test with two groups, the two-sample t-test is the typical choice here). The paired t-test is for matched or repeated measurements, which isn’t the case, and the chi-square test is for categorical data. So the two-sample t-test is the right method to determine if there’s a significant difference.