Six Sigma Black Belt Certified Practice Exam

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

1. 2-sample z test

2. 2-sample t test

3. Paired t test

4. F test

The correct answer is: Paired t test

When evaluating the performance of workers before and after training, it's essential to understand that the two sets of data (before and after training) are not independent of each other. The paired t-test is specifically designed for situations where you have two related samples, such as measurements taken from the same subjects at different times. In this context, the same workers are being assessed at two different points in time, making their performances correlated. Using the paired t-test allows the analysis to account for the inherent pairing of the pre-training and post-training data, providing a more accurate measure of whether there is a statistically significant difference in performance due to the training. This test essentially works by calculating the difference in performance for each individual worker and then analyzing those differences to see if there is a notable improvement overall. The other options do not apply correctly to this scenario. The 2-sample z test and the 2-sample t test are used for comparing two independent groups, which is not the case here since the same workers' performances are being compared. The F test is typically used for comparing variances among groups or for analysis of variance (ANOVA), and it is not suited for direct comparison of two related samples like this training scenario.