A nutrition program aims to determine whether the mean change in cholesterol after the program differs from zero, using paired measurements on the same individuals. Which test?

A nutrition program aims to determine whether the mean change in cholesterol after the program differs from zero, using paired measurements on the same individuals. Which test?

• A. One-Sample T-Test
• B. Matched-Pairs T-Test
• C. Two-Sample T-Test
• D. One-Proportion Z-Test

Answer: (B)

When measurements are taken on the same individuals before and after an intervention, you look at how each person’s value changed and ask whether the average change across all individuals is different from zero. This uses the differences within each person, which is why it’s a paired design. Compute the change for every person (final minus initial), then test whether the mean of these changes is zero. In practice, you’d calculate the average change and its variability, and use a t-statistic that compares that average change to zero, adjusting for how much change varies and how many people you have. The test statistic is based on the mean difference and the standard deviation of those differences, with degrees of freedom equal to the number of paired observations minus one. This approach directly addresses whether the program produced a systematic increase or decrease in cholesterol across individuals. It relies on the assumption that the differences are roughly normally distributed (or that you have a sufficiently large sample for the Central Limit Theorem to help). If the differences don’t look normal and the sample is small, a nonparametric alternative like the Wilcoxon signed-rank test can be used. The reason this fits better than other tests is that it honors the pairing: you’re not comparing two independent groups, and you’re not testing a population proportion. You’re testing a mean change in a continuous measurement within the same subjects, which is precisely what the paired t-test (also seen as testing the mean difference on the differences) is designed to do.

When measurements are taken on the same individuals before and after an intervention, you look at how each person’s value changed and ask whether the average change across all individuals is different from zero. This uses the differences within each person, which is why it’s a paired design.

Compute the change for every person (final minus initial), then test whether the mean of these changes is zero. In practice, you’d calculate the average change and its variability, and use a t-statistic that compares that average change to zero, adjusting for how much change varies and how many people you have. The test statistic is based on the mean difference and the standard deviation of those differences, with degrees of freedom equal to the number of paired observations minus one.

This approach directly addresses whether the program produced a systematic increase or decrease in cholesterol across individuals. It relies on the assumption that the differences are roughly normally distributed (or that you have a sufficiently large sample for the Central Limit Theorem to help). If the differences don’t look normal and the sample is small, a nonparametric alternative like the Wilcoxon signed-rank test can be used.

The reason this fits better than other tests is that it honors the pairing: you’re not comparing two independent groups, and you’re not testing a population proportion. You’re testing a mean change in a continuous measurement within the same subjects, which is precisely what the paired t-test (also seen as testing the mean difference on the differences) is designed to do.