Certified Six Sigma Black Belt Exam Advanced Hypothesis Testing 2 — Questions and Answers
Question 1: A Six Sigma team wants to compare the variances of two independent populations. Which test is most appropriate?
- Levene's test
- Bartlett's test
- F-test (Snedecor's F) (Correct answer)
- Mann-Whitney U test
Correct answer: F-test (Snedecor's F)
The F-test (Snedecor's F) is the classical test for comparing two population variances using the ratio of sample variances.
Question 2: When the p-value equals 0.049 and alpha is 0.05, a Black Belt should:
- Fail to reject H₀ because the result is borderline
- Reject H₀ and consider practical significance before acting (Correct answer)
- Automatically accept H₁ as proven
- Increase the sample size and retest
Correct answer: Reject H₀ and consider practical significance before acting
A p-value below alpha leads to rejecting H₀, but statistical significance must always be weighed against practical/economic significance.
Question 3: Which assumption is NOT required for a standard two-sample t-test?
- Both populations are normally distributed
- The samples are independent
- The populations have equal variances (for pooled form)
- The sample means follow a chi-square distribution (Correct answer)
Correct answer: The sample means follow a chi-square distribution
Sample means follow a t-distribution (not chi-square) under normality assumptions; chi-square applies to variance tests.
Question 4: A Kruskal-Wallis test is the nonparametric alternative to which parametric test?
- Two-sample t-test
- One-way ANOVA (Correct answer)
- Paired t-test
- Chi-square goodness-of-fit
Correct answer: One-way ANOVA
The Kruskal-Wallis test compares medians across three or more independent groups, serving as the nonparametric equivalent of one-way ANOVA.
Question 5: In hypothesis testing, the power of a test is defined as:
- The probability of correctly rejecting a true null hypothesis
- 1 minus the probability of a Type II error (Correct answer)
- The probability of accepting H₀ when H₀ is false
- The significance level alpha
Correct answer: 1 minus the probability of a Type II error
Power = 1 − β, where β is the probability of a Type II error (failing to reject a false H₀).
Question 6: A Black Belt uses a one-tailed test instead of a two-tailed test. Compared to two-tailed at the same alpha, the one-tailed test:
- Has less power to detect the specified directional effect
- Has greater power to detect effects in the hypothesized direction (Correct answer)
- Always produces a smaller p-value regardless of direction
- Requires a larger sample size
Correct answer: Has greater power to detect effects in the hypothesized direction
By concentrating all of alpha in one tail, a one-tailed test has greater power to detect effects in the predicted direction.
Question 7: Which scenario correctly describes a Type I error in a manufacturing hypothesis test?
- Concluding a process is out of control when it actually is in control (Correct answer)
- Concluding a process is in control when it is actually out of control
- Failing to collect enough data
- Using the wrong test statistic
Correct answer: Concluding a process is out of control when it actually is in control
A Type I error (false positive) occurs when H₀ is true but is incorrectly rejected — concluding a problem exists when there is none.
Certified Six Sigma Black Belt Exam Advanced Hypothesis Testing 2
A Six Sigma team wants to compare the variances of two independent populations.
Which test is most appropriate?