Certified Six Sigma Black Belt Exam Hypothesis Testing Applications 5 — Questions and Answers
Question 1: A Black Belt applies Tukey's HSD post-hoc test after a significant ANOVA. What is its primary purpose?
- To re-test whether variances are equal across groups
- To identify which specific pairs of group means differ significantly (Correct answer)
- To confirm the normality assumption before ANOVA
- To adjust the alpha level for the overall ANOVA test
Correct answer: To identify which specific pairs of group means differ significantly
Tukey's HSD controls family-wise error rate while identifying which specific mean pairs are statistically different.
Question 2: For a hypothesis test on proportions with n = 200 and p̂ = 0.12, which condition justifies using the normal approximation?
- np̂ ≥ 5 and n(1−p̂) ≥ 5 (Correct answer)
- n ≥ 30 regardless of p̂
- p̂ > 0.10 and n > 100
- The population must be normally distributed
Correct answer: np̂ ≥ 5 and n(1−p̂) ≥ 5
The normal approximation for proportions is valid when both np̂ and n(1−p̂) are at least 5.
Question 3: What does a Bartlett's test evaluate, and when is it preferred over Levene's test?
- It tests normality and is preferred for skewed data
- It tests equality of variances and is preferred when data are normally distributed (Correct answer)
- It tests independence and is preferred for categorical data
- It tests medians and is preferred for small samples
Correct answer: It tests equality of variances and is preferred when data are normally distributed
Bartlett's test is more powerful than Levene's for normally distributed data but is sensitive to non-normality.
Question 4: A Six Sigma project measures cycle time before and after improvement for the same 25 units. Which test is most appropriate?
- Two-sample t-test assuming equal variances
- Paired t-test (Correct answer)
- One-sample z-test
- Kruskal-Wallis test
Correct answer: Paired t-test
When the same units are measured twice (before/after), a paired t-test is appropriate as it accounts for within-unit correlation.
Question 5: Which statement correctly describes the relationship between confidence level and significance level?
- Confidence level = 1 − α (Correct answer)
- Confidence level = α
- Confidence level = 1 − β
- Confidence level = β/2
Correct answer: Confidence level = 1 − α
A 95% confidence interval corresponds to α = 0.05, so confidence level = 1 − α.
Question 6: During a hypothesis test, the p-value is best interpreted as:
- The probability that H₀ is true
- The probability of observing results at least as extreme as those obtained, assuming H₀ is true (Correct answer)
- The probability that H₁ is correct
- The proportion of the population that falls outside the confidence interval
Correct answer: The probability of observing results at least as extreme as those obtained, assuming H₀ is true
The p-value is the conditional probability of the observed (or more extreme) data given that H₀ is true.
Question 7: A process team observes that their hypothesis test produces a statistically significant result, but the practical effect size is negligible. What does this most likely indicate?
- The test had insufficient power
- The sample size was very large, making even trivial differences detectable (Correct answer)
- A Type II error occurred
- The null hypothesis was incorrectly formulated
Correct answer: The sample size was very large, making even trivial differences detectable
With very large samples, even practically meaningless differences can achieve statistical significance; effect size must also be evaluated.
Certified Six Sigma Black Belt Exam Hypothesis Testing Applications 5
A Black Belt applies Tukey's HSD post-hoc test after a significant ANOVA.
What is its primary purpose?