Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Advanced Hypothesis Testing 1

Question 1

A Six Sigma Black Belt is comparing the variance of two independent processes to determine if they differ significantly before running a two-sample t-test. Which hypothesis test should be used?

Accepted Answer

Levene's test or Bartlett's test for equal variances

Answer

Chi-square goodness-of-fit test

Answer

Paired t-test

Answer

One-proportion z-test

Question 2

A Black Belt sets alpha = 0.05 and calculates a power of 0.72 for a hypothesis test. What does this mean?

Accepted Answer

The test has a 28% probability of failing to detect a true effect (Type II error rate)

Answer

There is a 72% chance the null hypothesis is true

Answer

There is a 28% probability of committing a Type I error

Answer

The test will reject the null hypothesis 72% of the time regardless of the true effect

Question 3

Which non-parametric test is the most appropriate alternative to a one-way ANOVA when the assumption of normality is severely violated?

Accepted Answer

Kruskal-Wallis test

Answer

Mood's Median test

Answer

Mann-Whitney U test

Answer

Friedman test

Question 4

A Black Belt conducts a hypothesis test and correctly fails to reject a true null hypothesis. Which outcome does this represent?

Accepted Answer

Correct decision — true negative

Answer

Type I error

Answer

Type II error

Answer

Correct decision — true positive

Question 5

A Six Sigma team wants to test whether defect counts across four production shifts follow the expected distribution based on historical proportions. Which test is most appropriate?

Accepted Answer

Chi-square goodness-of-fit test

Answer

Two-sample t-test

Answer

One-way ANOVA

Answer

F-test for equal variances

Question 6

When increasing sample size in a hypothesis test while holding alpha constant, what is the direct effect on the power of the test?

Accepted Answer

Power increases because the standard error decreases and effect detection improves

Answer

Power decreases because there is more sampling variability

Answer

Power remains unchanged because alpha is fixed

Answer

Power decreases because the critical value increases