Certified Six Sigma Black Belt Exam Hypothesis Testing Applications 3 — Questions and Answers
Question 1: A quality engineer compares process variance before and after a change using an F-test. The p-value is 0.08 with α = 0.05. What should be concluded?
- Reject H₀; variances are significantly different
- Fail to reject H₀; insufficient evidence that variances differ (Correct answer)
- Accept H₁; the new process has lower variance
- Reject H₀; the sample size was too small
Correct answer: Fail to reject H₀; insufficient evidence that variances differ
p = 0.08 > α = 0.05, so there is insufficient evidence to conclude the variances are different.
Question 2: Which nonparametric test is the appropriate alternative to the one-sample t-test when normality cannot be assumed?
- Kruskal-Wallis test
- Wilcoxon signed-rank test (Correct answer)
- Mann-Whitney U test
- Mood's median test
Correct answer: Wilcoxon signed-rank test
The Wilcoxon signed-rank test is the nonparametric equivalent of the one-sample (or paired) t-test.
Question 3: A Black Belt selects α = 0.01 instead of α = 0.05. What is the direct effect on the hypothesis test?
- The probability of a Type I error decreases (Correct answer)
- The probability of a Type II error decreases
- Power of the test increases
- The critical value decreases
Correct answer: The probability of a Type I error decreases
Lowering α reduces the acceptable probability of a Type I error (false rejection of H₀).
Question 4: When conducting a two-proportion z-test, what is the null hypothesis typically stated as?
- p₁ > p₂
- p₁ = p₂ (Correct answer)
- p₁ ≠ p₂
- p₁ + p₂ = 1
Correct answer: p₁ = p₂
The null hypothesis for a two-proportion z-test states that the two population proportions are equal.
Question 5: Levene's test is used in hypothesis testing to evaluate which property of data?
- Normality of residuals
- Equality of variances across groups (Correct answer)
- Independence of observations
- Linearity of regression relationship
Correct answer: Equality of variances across groups
Levene's test assesses whether group variances are equal, a key assumption for ANOVA and t-tests.
Question 6: A Six Sigma team performs 10 separate hypothesis tests at α = 0.05. Approximately what is the probability of at least one Type I error occurring?
- 0.05
- 0.40 (Correct answer)
- 0.50
- 0.10
Correct answer: 0.40
The family-wise error rate is 1 − (1 − 0.05)^10 ≈ 0.40, highlighting the risk of multiple comparisons.
Question 7: In an equivalence test used in Six Sigma, the goal is to demonstrate that:
- The process mean is significantly different from the target
- Two processes are practically equivalent within a defined margin (Correct answer)
- The null hypothesis should be rejected at α = 0.10
- Process variance exceeds the specification limit
Correct answer: Two processes are practically equivalent within a defined margin
Equivalence testing (e.g., TOST) is designed to prove two processes are equivalent within a predefined acceptable margin.
Certified Six Sigma Black Belt Exam Hypothesis Testing Applications 3
A quality engineer compares process variance before and after a change using an F-test.
The p-value is 0.08 with α = 0.05.
What should be concluded?