Certified Six Sigma Black Belt Exam Hypothesis Testing 4 — Questions and Answers
Question 1: Which condition must be met to validly use a two-sample t-test with pooled variance?
- Sample sizes must be equal
- Data must be categorical
- Population variances must be assumed equal (Correct answer)
- Data must follow an exponential distribution
Correct answer: Population variances must be assumed equal
The pooled two-sample t-test assumes the two populations have equal variances; use Welch's t-test when this assumption fails.
Question 2: A team detects a statistically significant difference in cycle times but the improvement is only 0.5 seconds on a 10-minute process. Which concept explains why this finding may not matter?
- Type I error
- Lack of power
- Practical significance / effect size (Correct answer)
- Confidence interval width
Correct answer: Practical significance / effect size
Practical significance considers whether the detected effect is large enough to be meaningful in context, independent of statistical significance.
Question 3: The Kruskal-Wallis test is the non-parametric equivalent of which parametric test?
- Paired t-test
- One-way ANOVA (Correct answer)
- Two-sample t-test
- F-test for variances
Correct answer: One-way ANOVA
Kruskal-Wallis tests for differences in median ranks across three or more independent groups, analogous to one-way ANOVA.
Question 4: A Black Belt runs a hypothesis test and obtains p = 0.12 with α = 0.05. The correct conclusion is:
- Reject H₀; significant evidence exists
- Fail to reject H₀; insufficient evidence to conclude a difference (Correct answer)
- Accept H₀; no difference exists
- Increase α to 0.10 and re-run
Correct answer: Fail to reject H₀; insufficient evidence to conclude a difference
Failing to reject H₀ means there is insufficient evidence to support H₁; it does not prove H₀ is true.
Question 5: In a two-tailed hypothesis test with α = 0.05, the critical region is located:
- Entirely in the right tail
- Entirely in the left tail
- Split equally (2.5%) in each tail (Correct answer)
- At the center of the distribution
Correct answer: Split equally (2.5%) in each tail
A two-tailed test divides α equally between both tails, placing 2.5% in each tail for α = 0.05.
Question 6: Which of the following BEST describes the purpose of a paired t-test?
- Comparing means of two independent groups
- Comparing variances of two groups
- Comparing means of matched or before/after measurements (Correct answer)
- Comparing more than two group means
Correct answer: Comparing means of matched or before/after measurements
The paired t-test accounts for within-subject or matched-pair correlation, reducing variability and increasing test sensitivity.
Question 7: A process engineer finds the Anderson-Darling p-value is 0.021 for a dataset. What does this indicate?
- The data is normally distributed
- There is insufficient evidence to reject normality
- The data significantly deviates from a normal distribution (Correct answer)
- The sample size is too small
Correct answer: The data significantly deviates from a normal distribution
A low p-value in the Anderson-Darling test (below α) leads to rejecting the null hypothesis of normality.
Certified Six Sigma Black Belt Exam Hypothesis Testing 4
Which condition must be met to validly use a two-sample t-test with pooled variance?