A black belt plans to test the performance of workers before and after training. Which of the following hypothesis tests should be used to determine whether the training actually improved the workers' performance?

• A. 2-sample z test
• B. 2-sample t test
• C. Paired t test
• D. F test

Answer: (C)

The paired t test is appropriate for this scenario because it is specifically designed to compare two related samples. In this case, the black belt is interested in the performance of the same group of workers before and after training, making the data inherently related. The paired t test analyzes the differences between the two sets of measurements (pre-training and post-training) for each worker and assesses whether the mean difference is statistically significant.

This method is advantageous in such situations because it accounts for individual variability by looking at the changes in performance within the same subjects, rather than comparing two separate groups. It helps determine if the training intervention had a tangible effect on worker performance by focusing on how each individual’s performance changed as a result of the training.

In contrast, the other options do not fit this specific scenario. For example, the 2-sample z test and the 2-sample t test are meant for comparing the means of two independent groups, which is not applicable here since the same workers’ performances are being measured at two different times. The F test, often used in ANOVA, assesses variances among groups rather than directly testing for improvements within a single group across two time points. Hence, the paired t test is the most suitable choice for evaluating the effectiveness