Certified Six Sigma Black Belt Advanced Hypothesis Testing Questions and Answers Flashcards
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When conducting a two-sample t-test, what assumption must be evaluated if sample sizes are unequal and population variances are unknown?
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.
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?
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.
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?
Answer: One-proportion z-test
A one-proportion z-test compares an observed sample proportion against a known historical population proportion.
What is the primary risk of conducting multiple pairwise comparisons without adjusting the significance level?
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.
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?
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.
Which method is used to control the family-wise error rate when performing all pairwise comparisons after a significant one-way ANOVA result?
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.