Six Sigma Green Belt Certification Practice Exam

What hypothesis test is designed to detect differences in three or more population means?

1. F test

2. ANOVA

3. Z test

4. Paired t test

The correct answer is: ANOVA

The hypothesis test designed specifically for detecting differences among three or more population means is known as ANOVA, which stands for Analysis of Variance. This statistical method examines the variances within and between groups to determine if at least one of the group means is statistically different from the others. ANOVA is particularly useful because it allows comparisons across multiple groups simultaneously, reducing the risk of Type I errors that could occur if multiple pairwise comparisons were conducted instead. While the F test is involved in the ANOVA process as part of the calculations used to derive the test statistic, it does not stand alone as a method for comparing population means. The Z test is typically used for comparing the means of two populations or in situations where the sample size is large and population variances are known. The paired t test is used for comparing the means of two related groups, making it unsuitable for situations involving three or more groups. Thus, the most appropriate method for testing the differences among three or more population means is ANOVA.