During a trial with 18 employees, the average product packed increases by more than 10 cases per day per employee. The appropriate test is which of the following?

During a trial with 18 employees, the average product packed increases by more than 10 cases per day per employee. The appropriate test is which of the following?

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

Answer: (C)

When data come from paired observations—each employee has a before and an after measurement—the analysis should focus on the differences within each pair. In this scenario, you want to know if the average increase per employee is greater than 10 cases per day, so you compute the change for each employee and test whether the mean of these differences exceeds 10. That makes a matched pairs test the right choice, because it accounts for the linkage within each employee and compares the average difference directly. The test uses the differences for the 18 employees, with the statistic t = (mean_diff − 10) / (sd_diff / sqrt(18)), and degrees of freedom 17. This approach reduces between-subject variability and provides more power than treating the before and after measurements as independent samples. A 1-sample t-test would only be appropriate if you were testing a single sample against a fixed value without pairing. A 2-sample t-test assumes independent groups, which isn’t correct for before-versus-after data on the same individuals. A 1-proportion z-test is for proportions, not average changes in a continuous outcome.

When data come from paired observations—each employee has a before and an after measurement—the analysis should focus on the differences within each pair. In this scenario, you want to know if the average increase per employee is greater than 10 cases per day, so you compute the change for each employee and test whether the mean of these differences exceeds 10. That makes a matched pairs test the right choice, because it accounts for the linkage within each employee and compares the average difference directly.

The test uses the differences for the 18 employees, with the statistic t = (mean_diff − 10) / (sd_diff / sqrt(18)), and degrees of freedom 17. This approach reduces between-subject variability and provides more power than treating the before and after measurements as independent samples.

A 1-sample t-test would only be appropriate if you were testing a single sample against a fixed value without pairing. A 2-sample t-test assumes independent groups, which isn’t correct for before-versus-after data on the same individuals. A 1-proportion z-test is for proportions, not average changes in a continuous outcome.