Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Advanced Hypothesis Testing Questions and Answers 2 — Questions and Answers
Question 1: When conducting a two-sample t-test, what assumption must be evaluated if sample sizes are unequal and population variances are unknown?
- Equal variances assumption using an F-test or Levene's test (Correct answer)
- Normal distribution of the population means
- Independence of the sample standard deviations
- Homogeneity of sample sizes
Correct answer: Equal variances assumption using an F-test or Levene's test
When sample sizes differ and variances are unknown, you must test for equal variances to determine whether to use a pooled or Welch's t-test.
Question 2: In a hypothesis test, a Six Sigma Black Belt obtains a p-value of 0.03 with a significance level of 0.05. What is the correct interpretation?
- Reject the null hypothesis; there is sufficient evidence of a statistically significant effect (Correct answer)
- Accept the alternative hypothesis as proven true
- The probability that the null hypothesis is true is 3%
- The effect size is practically significant
Correct answer: Reject the null hypothesis; there is sufficient evidence of a statistically significant effect
Since the p-value (0.03) is less than alpha (0.05), we reject the null hypothesis and conclude there is statistically significant evidence.
Question 3: A Black Belt wants to determine if a process change reduced the defect rate from a known historical proportion. Which hypothesis test is most appropriate?
- One-proportion z-test (Correct answer)
- Two-sample t-test
- Chi-square goodness-of-fit test
- Paired t-test
Correct answer: One-proportion z-test
A one-proportion z-test compares an observed sample proportion against a known historical population proportion.
Question 4: What is the primary risk of conducting multiple pairwise comparisons without adjusting the significance level?
- Inflated family-wise Type I error rate (Correct answer)
- Decreased statistical power for each test
- Increased Type II error for the overall analysis
- Violation of the normality assumption
Correct answer: Inflated family-wise Type I error rate
Performing multiple comparisons without correction inflates the overall probability of committing at least one Type I error across all tests.
Question 5: A Black Belt uses an Anderson-Darling test before performing a one-sample t-test and obtains a p-value of 0.15. What should be concluded about the normality assumption?
- Fail to reject normality; the data does not significantly deviate from a normal distribution (Correct answer)
- The data is confirmed to be perfectly normally distributed
- The t-test results will definitely be valid
- Normality is rejected and a nonparametric test must be used
Correct answer: Fail to reject normality; the data does not significantly deviate from a normal distribution
A p-value of 0.15 exceeds the typical alpha of 0.05, so we fail to reject the null hypothesis that the data follows a normal distribution.
Question 6: Which method is used to control the family-wise error rate when performing all pairwise comparisons after a significant one-way ANOVA result?
- Tukey's Honestly Significant Difference (HSD) test (Correct answer)
- Increasing the sample size for each group
- Repeating the ANOVA with different factor levels
- Using a higher significance level for each comparison
Correct answer: Tukey's Honestly Significant Difference (HSD) test
Tukey's HSD controls the family-wise error rate by adjusting critical values for all pairwise comparisons simultaneously.
Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Advanced Hypothesis Testing Questions and Answers 2
When conducting a two-sample t-test, what assumption must be evaluated if sample sizes are unequal and population variances are unknown?