Certified Six Sigma Black Belt Exam Hypothesis Testing 2 — Questions and Answers
Question 1: A Six Sigma team sets α = 0.05. If the p-value from their test is 0.03, what is the correct conclusion?
- Fail to reject H₀ because p < α
- Reject H₀ because p < α (Correct answer)
- Accept H₀ because p < α
- Reject H₁ because p < α
Correct answer: Reject H₀ because p < α
When the p-value is less than the significance level α, you reject the null hypothesis.
Question 2: Which type of error occurs when you reject a true null hypothesis?
- Type II error
- Type III error
- Type I error (Correct answer)
- Power error
Correct answer: Type I error
A Type I error (false positive) is rejecting H₀ when it is actually true, and its probability equals α.
Question 3: A Black Belt wants to compare the means of three process lines simultaneously. Which test is most appropriate?
- Paired t-test
- One-sample t-test
- Chi-square test
- One-way ANOVA (Correct answer)
Correct answer: One-way ANOVA
One-way ANOVA is used to compare means across three or more groups simultaneously while controlling Type I error.
Question 4: Beta (β) in hypothesis testing represents which of the following?
- Probability of a Type I error
- The significance level
- Probability of a Type II error (Correct answer)
- The effect size
Correct answer: Probability of a Type II error
Beta (β) is the probability of a Type II error — failing to reject a false null hypothesis.
Question 5: A process engineer tests whether a new supplier's material hardness (continuous, normal) differs from a target of 60 HRC. Which test should be used?
- Two-sample t-test
- One-sample t-test (Correct answer)
- F-test
- Mann-Whitney U test
Correct answer: One-sample t-test
A one-sample t-test compares a sample mean to a known or specified target value.
Question 6: When the sample data is not normally distributed and the sample size is small, which non-parametric test replaces the one-sample t-test?
- 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 non-parametric alternative to the one-sample (or paired) t-test.
Question 7: Increasing sample size in a hypothesis test primarily affects which of the following?
- Significance level α
- Type I error rate
- Statistical power (Correct answer)
- The null hypothesis
Correct answer: Statistical power
Larger sample sizes increase statistical power by reducing the standard error, making it easier to detect true effects.
Certified Six Sigma Black Belt Exam Hypothesis Testing 2
A Six Sigma team sets α = 0.05.
If the p-value from their test is 0.03, what is the correct conclusion?