Certified Six Sigma Black Belt Exam Hypothesis Testing 5 — Questions and Answers
Question 1: A CSSBB candidate must determine sample size for a hypothesis test. Which factor, if increased, will REDUCE the required sample size?
- Smaller effect size (δ)
- Higher desired power (1−β)
- Larger acceptable α level (Correct answer)
- Lower population variability (σ)
Correct answer: Larger acceptable α level
A larger α (less stringent significance level) reduces the sample size needed because a wider rejection region is accepted.
Question 2: Which hypothesis testing approach is most appropriate when testing whether a process proportion defective exceeds 2%?
- One-sample t-test
- One-proportion z-test (Correct answer)
- Chi-square goodness-of-fit
- F-test
Correct answer: One-proportion z-test
The one-proportion z-test compares an observed proportion to a specified target proportion.
Question 3: After completing ANOVA and finding a significant F-statistic, which step is required to identify which specific group means differ?
- Run a second ANOVA with fewer groups
- Perform post-hoc pairwise comparisons (e.g., Tukey's HSD) (Correct answer)
- Re-run the test with a smaller α
- Calculate the pooled standard deviation
Correct answer: Perform post-hoc pairwise comparisons (e.g., Tukey's HSD)
Post-hoc tests like Tukey's HSD identify which specific pairs of group means are significantly different after a significant ANOVA.
Question 4: A Black Belt is analyzing whether a new machine reduces defect rate compared to the old machine. This is best framed as:
- Two-tailed test: H₁: μ_new ≠ μ_old
- One-tailed test: H₁: μ_new < μ_old (Correct answer)
- One-tailed test: H₁: μ_new > μ_old
- A goodness-of-fit test
Correct answer: One-tailed test: H₁: μ_new < μ_old
When testing for a specific directional improvement (reduction), a one-tailed test in the direction of interest is appropriate.
Question 5: The Mann-Whitney U test is the non-parametric equivalent of which test?
- Paired t-test
- One-way ANOVA
- Two-sample independent t-test (Correct answer)
- One-sample t-test
Correct answer: Two-sample independent t-test
Mann-Whitney U compares medians of two independent groups and is used when normality assumptions for the two-sample t-test are violated.
Question 6: A Black Belt reports that their hypothesis test had 'low power.' Which of the following is a likely consequence?
- Increased risk of Type I error
- Increased risk of Type II error (missing a real effect) (Correct answer)
- Smaller required sample size
- More stringent significance level
Correct answer: Increased risk of Type II error (missing a real effect)
Low power (high β) means the test is unlikely to detect a true effect, increasing the risk of a Type II error.
Question 7: A Six Sigma project team uses a significance level of α = 0.01 instead of α = 0.05. What is the trade-off?
- Higher power and fewer Type II errors
- Lower Type I error rate but higher Type II error rate (Correct answer)
- Higher Type I and Type II error rates
- No change in error rates; only the interval changes
Correct answer: Lower Type I error rate but higher Type II error rate
Lowering α makes it harder to reject H₀, reducing Type I errors but increasing the chance of Type II errors (missing real effects).
Certified Six Sigma Black Belt Exam Hypothesis Testing 5
A CSSBB candidate must determine sample size for a hypothesis test.
Which factor, if increased, will REDUCE the required sample size?