A car company has made an adjustment to improve gas mileage. Random samples of cars measured before and after the adjustment. Which test should be used to determine if the mean difference is zero?

A car company has made an adjustment to improve gas mileage. Random samples of cars measured before and after the adjustment. Which test should be used to determine if the mean difference is zero?

• A. 1-sample t-test
• B. Matched Pairs t-test
• C. 2-sample t-test
• D. Chi-square test

Answer: (B)

When measurements are taken on the same cars before and after the adjustment, the data are paired. The goal is to see if the adjustment changes the mean mileage, which is best answered by looking at the average difference in each pair (after minus before) and testing whether that average difference is zero. This is exactly what the matched-pairs (paired) t-test does. It forms the differences for each car, then tests if the mean of these differences is zero, using the t statistic t = (d̄) / (s_d/√n), with n pairs. This approach has the advantage of removing between-car variability, giving more precise inference about the adjustment’s effect than treating pre and post as two independent groups. The other tests aren’t appropriate here: a 1-sample t-test would compare a single sample to a fixed value rather than differences within pairs; a 2-sample t-test assumes the two groups are independent; a chi-square test applies to categorical data, not to averages of numerical measurements.

When measurements are taken on the same cars before and after the adjustment, the data are paired. The goal is to see if the adjustment changes the mean mileage, which is best answered by looking at the average difference in each pair (after minus before) and testing whether that average difference is zero. This is exactly what the matched-pairs (paired) t-test does. It forms the differences for each car, then tests if the mean of these differences is zero, using the t statistic t = (d̄) / (s_d/√n), with n pairs.

This approach has the advantage of removing between-car variability, giving more precise inference about the adjustment’s effect than treating pre and post as two independent groups. The other tests aren’t appropriate here: a 1-sample t-test would compare a single sample to a fixed value rather than differences within pairs; a 2-sample t-test assumes the two groups are independent; a chi-square test applies to categorical data, not to averages of numerical measurements.