Certified Six Sigma Black Belt Exam Hypothesis Testing 3 — Questions and Answers
Question 1: A Black Belt needs to test whether the variances of two process streams are equal before running a two-sample t-test. Which test is appropriate?
- Bartlett's test
- Chi-square goodness-of-fit
- Anderson-Darling test
- Levene's test or F-test (Correct answer)
Correct answer: Levene's test or F-test
Levene's test or the F-test (variance ratio test) are used to compare variances of two groups.
Question 2: In a hypothesis test, statistical power is defined as:
- 1 − α
- α + β
- 1 − β (Correct answer)
- β / α
Correct answer: 1 − β
Power equals 1 − β, representing the probability of correctly rejecting a false null hypothesis.
Question 3: A team performs a chi-square test of independence on a contingency table. What is the null hypothesis?
- The two variables are dependent
- The two variables are independent (Correct answer)
- The means of the groups are equal
- The variances of the groups are equal
Correct answer: The two variables are independent
For a chi-square test of independence, H₀ states that the two categorical variables are independent (no association).
Question 4: A manufacturer tests a new coating process and finds p = 0.048 with α = 0.05. A colleague argues the result is 'practically significant.' What is wrong with this reasoning?
- Statistical significance always implies practical significance
- p < 0.05 means the effect is large
- Statistical significance does not guarantee practical significance (Correct answer)
- The test should have used α = 0.01
Correct answer: Statistical significance does not guarantee practical significance
Statistical significance only indicates that an effect is unlikely due to chance; practical significance depends on the magnitude (effect size) of the difference.
Question 5: When performing multiple hypothesis tests simultaneously, which risk increases?
- Type II error rate
- Beta
- Familywise Type I error rate (Correct answer)
- Statistical power
Correct answer: Familywise Type I error rate
Running multiple tests inflates the familywise Type I error rate; corrections like Bonferroni are used to control it.
Question 6: A Six Sigma team compares defect counts (discrete data) across four machine types. Which test is most appropriate?
- Two-sample t-test
- One-way ANOVA
- Chi-square test of independence (Correct answer)
- Paired t-test
Correct answer: Chi-square test of independence
Chi-square tests are used for categorical/count data to assess independence or differences across groups.
Question 7: A Black Belt calculates a 95% confidence interval for the mean that does not include the hypothesized value μ₀. What does this imply?
- Fail to reject H₀ at α = 0.05
- Reject H₀ at α = 0.05 (Correct answer)
- Accept H₁ at α = 0.01
- The test is inconclusive
Correct answer: Reject H₀ at α = 0.05
If the hypothesized value falls outside the 95% confidence interval, the two-sided hypothesis test rejects H₀ at α = 0.05.
Certified Six Sigma Black Belt Exam Hypothesis Testing 3
A Black Belt needs to test whether the variances of two process streams are equal before running a two-sample t-test.
Which test is appropriate?