Certified Six Sigma Black Belt Exam Hypothesis Testing 5

Question 1

A CSSBB candidate must determine sample size for a hypothesis test. Which factor, if increased, will REDUCE the required sample size?

Accepted Answer

Larger acceptable α level

Answer

A larger α (less stringent significance level) reduces the sample size needed because a wider rejection region is accepted.

Question 2

Which hypothesis testing approach is most appropriate when testing whether a process proportion defective exceeds 2%?

Accepted Answer

One-proportion z-test

Answer

The one-proportion z-test compares an observed proportion to a specified target proportion.

Question 3

After completing ANOVA and finding a significant F-statistic, which step is required to identify which specific group means differ?

Accepted Answer

Perform post-hoc pairwise comparisons (e.g., Tukey's HSD)

Answer

Post-hoc tests like Tukey's HSD identify which specific pairs of group means are significantly different after a significant ANOVA.

Question 4

A Black Belt is analyzing whether a new machine reduces defect rate compared to the old machine. This is best framed as:

Accepted Answer

One-tailed test: H₁: μ_new < μ_old

Answer

When testing for a specific directional improvement (reduction), a one-tailed test in the direction of interest is appropriate.

Question 5

The Mann-Whitney U test is the non-parametric equivalent of which test?

Accepted Answer

Two-sample independent t-test

Answer

Mann-Whitney U compares medians of two independent groups and is used when normality assumptions for the two-sample t-test are violated.

Certified Six Sigma Black Belt Exam Practice Test