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

Levene's test (robust to non-normality) or Bartlett's test is used to assess equality of variances between two or more groups. This is a prerequisite check before deciding whether to use a pooled or Welch's t-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

Power = 1 − β, where β is the probability of a Type II error (failing to reject a false null hypothesis). A power of 0.72 means β = 0.28, so there is a 28% chance the test misses a real 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

The Kruskal-Wallis test is the non-parametric equivalent of one-way ANOVA and compares medians across three or more independent groups when normality cannot be assumed. The Mann-Whitney is limited to two groups.

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

When the null hypothesis is actually true and the test fails to reject it, the result is a correct decision called a true negative. Type I error occurs when a true null is rejected; Type II error occurs when a false null is not rejected.

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

The chi-square goodness-of-fit test compares observed frequencies against expected frequencies derived from a known or hypothesized distribution. It is the correct choice when testing whether categorical count data matches a specified proportion pattern.

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Practice Test

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