Certified Six Sigma Black Belt Exam Advanced Hypothesis Testing 5 — Questions and Answers
Question 1: A Black Belt uses a Z-test rather than a t-test. The primary justification for this choice is:
- The sample is non-normal and large (n > 100)
- The population standard deviation is known (Correct answer)
- The sample size is less than 30
- The data are categorical
Correct answer: The population standard deviation is known
The Z-test is appropriate when the population standard deviation (σ) is known, which allows use of the standard normal distribution.
Question 2: Which nonparametric test is equivalent to the two-sample independent t-test?
- Wilcoxon signed-rank test
- Mann-Whitney U test (Correct answer)
- Kruskal-Wallis test
- Friedman test
Correct answer: Mann-Whitney U test
The Mann-Whitney U test compares central tendencies of two independent samples without assuming normality, serving as the nonparametric alternative to the two-sample t-test.
Question 3: A confidence interval and a hypothesis test at the same significance level will:
- Always produce contradictory conclusions
- Produce equivalent conclusions — if H₀ value is outside the CI, reject H₀ (Correct answer)
- Only agree when sample sizes exceed 30
- Only agree for two-tailed tests, not one-tailed
Correct answer: Produce equivalent conclusions — if H₀ value is outside the CI, reject H₀
A two-sided CI at (1 − α) confidence corresponds exactly to a two-sided hypothesis test at level α; exclusion of H₀ value from the CI equals rejection of H₀.
Question 4: In hypothesis testing, which factor does NOT directly affect the width of the required sample size calculation?
- Desired power (1 − β)
- The significance level α
- The minimum detectable effect size (δ)
- The color of the measurement instrument (Correct answer)
Correct answer: The color of the measurement instrument
Sample size is mathematically determined by α, β (power), effect size, and variance — physical attributes of measuring tools are irrelevant to the formula.
Question 5: The Anderson-Darling test is used in the context of hypothesis testing to:
- Compare two population means
- Assess whether sample data follow a specified distribution (Correct answer)
- Test for equal variances across groups
- Determine the minimum detectable effect
Correct answer: Assess whether sample data follow a specified distribution
The Anderson-Darling test is a goodness-of-fit test that assesses how well sample data conform to a hypothesized distribution (commonly normality).
Question 6: When using Tukey's HSD for post-hoc analysis after ANOVA, the primary purpose is to:
- Test whether group variances are equal
- Identify which specific group pairs have significantly different means (Correct answer)
- Determine the overall F-statistic
- Check the normality of residuals
Correct answer: Identify which specific group pairs have significantly different means
Tukey's HSD controls the family-wise error rate while making all pairwise mean comparisons to pinpoint which groups differ after a significant ANOVA result.
Question 7: A Black Belt observes that the test statistic falls exactly in the critical region boundary (t_calc = t_critical). The correct action is to:
- Reject H₀, because the statistic meets the rejection criterion (Correct answer)
- Fail to reject H₀, because the statistic is not strictly beyond the boundary
- Collect more data before deciding
- Report the result as inconclusive and take no action
Correct answer: Reject H₀, because the statistic meets the rejection criterion
By convention, when the test statistic equals the critical value the null hypothesis is rejected, as the p-value equals α exactly.
Certified Six Sigma Black Belt Exam Advanced Hypothesis Testing 5
A Black Belt uses a Z-test rather than a t-test.
The primary justification for this choice is: