Certified Six Sigma Black Belt Exam Advanced Hypothesis Testing 4 — Questions and Answers
Question 1: The Wilcoxon signed-rank test is the nonparametric equivalent of:
- One-sample or paired t-test (Correct answer)
- Two-sample independent t-test
- One-way ANOVA
- Chi-square test of independence
Correct answer: One-sample or paired t-test
The Wilcoxon signed-rank test handles one-sample or paired data, making it the nonparametric counterpart of the one-sample and paired t-tests.
Question 2: A Black Belt finds a statistically significant difference but the effect size (Cohen's d) is 0.08. This result is best described as:
- Practically significant and should drive immediate process changes
- Statistically significant but practically trivial (Correct answer)
- A Type I error that should be ignored
- Proof that the null hypothesis is false
Correct answer: Statistically significant but practically trivial
Cohen's d of 0.08 is far below the conventional small-effect threshold of 0.2, indicating the detected difference is unlikely to be practically meaningful.
Question 3: In a two-proportion z-test, the pooled proportion p̂ is used because:
- It increases test power by reducing variance
- Under H₀ the two populations share a common proportion (Correct answer)
- It corrects for small sample sizes
- It accounts for unequal group variances
Correct answer: Under H₀ the two populations share a common proportion
Under the null hypothesis of equal proportions, both samples estimate the same population proportion, so a pooled estimate is the best single estimate to use in the standard error.
Question 4: Which test statistic is used in a chi-square goodness-of-fit test?
- Σ (O − E)² / E (Correct answer)
- Σ |O − E| / E
- √[Σ (O − E)²]
- Σ (O − E) / √E
Correct answer: Σ (O − E)² / E
The chi-square statistic sums the squared differences between observed (O) and expected (E) frequencies, divided by expected frequency, across all categories.
Question 5: A Black Belt sets α = 0.01 instead of α = 0.05. This decision:
- Increases power and reduces Type I error risk
- Reduces power and reduces Type I error risk (Correct answer)
- Reduces power and increases Type I error risk
- Has no effect on power or error rates
Correct answer: Reduces power and reduces Type I error risk
Tightening alpha reduces the chance of a false positive (Type I error) but makes it harder to detect real effects, thereby reducing power.
Question 6: Which of the following correctly describes a two-sided (two-tailed) alternative hypothesis?
- H₁: μ > μ₀
- H₁: μ < μ₀
- H₁: μ ≠ μ₀ (Correct answer)
- H₁: μ = μ₀
Correct answer: H₁: μ ≠ μ₀
A two-sided alternative hypothesis states that the parameter differs from the null value in either direction, using the ≠ symbol.
Question 7: In an ANOVA F-test, what does a large F-statistic indicate?
- The within-group variance dominates the between-group variance
- The between-group variance is large relative to within-group variance (Correct answer)
- The data violate the normality assumption
- All group means are equal
Correct answer: The between-group variance is large relative to within-group variance
F = MSbetween / MSwithin; a large F means treatment effects explain much more variability than random error, suggesting group means differ.
Certified Six Sigma Black Belt Exam Advanced Hypothesis Testing 4
The Wilcoxon signed-rank test is the nonparametric equivalent of: