Which takes less time to travel to work - car or train? A random sample of 45 businessmen is used to compare travel times for both types of commute.

Which takes less time to travel to work - car or train? A random sample of 45 businessmen is used to compare travel times for both types of commute.

• A. Matched Pairs T-Test
• B. 1-Proportion Z-Test
• C. 2-Sample T-Test
• D. ANOVA

Answer: (A)

The key idea here is comparing two related measurements from the same people. Each businessman has a car travel time and a train travel time, so the data are paired. The best way to compare these two related sets of times is the matched pairs (paired) t-test. How it works: form the difference for each person (car time minus train time). If, on average, that difference is not zero, one mode tends to be faster. The test uses the mean and variability of these differences: t = (mean difference) / (standard deviation of differences / sqrt(n)), where n is the number of pairs (45 in this case). The conclusion comes from this t-statistic with n−1 degrees of freedom. This approach is preferred here over other tests because it directly accounts for the pairing. A 1-proportion z-test is for proportions, not average times. A two-sample t-test treats the two samples as independent, which isn’t true when the same individuals provide both measurements. ANOVA is for comparing means across three or more groups (or complex designs), whereas here there are only two related measurements.

The key idea here is comparing two related measurements from the same people. Each businessman has a car travel time and a train travel time, so the data are paired. The best way to compare these two related sets of times is the matched pairs (paired) t-test.

How it works: form the difference for each person (car time minus train time). If, on average, that difference is not zero, one mode tends to be faster. The test uses the mean and variability of these differences: t = (mean difference) / (standard deviation of differences / sqrt(n)), where n is the number of pairs (45 in this case). The conclusion comes from this t-statistic with n−1 degrees of freedom.

This approach is preferred here over other tests because it directly accounts for the pairing. A 1-proportion z-test is for proportions, not average times. A two-sample t-test treats the two samples as independent, which isn’t true when the same individuals provide both measurements. ANOVA is for comparing means across three or more groups (or complex designs), whereas here there are only two related measurements.