FREE Certified Six Sigma Black Belt Hypothesis Testing Applications Questions and Answers Flashcards
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A Six Sigma team needs to determine if there is a relationship between operator experience level (low, medium, high) and product pass/fail rate. Which test should they use?
Answer: Chi-square test of independence
A chi-square test of independence assesses whether two categorical variables are related.
After a process change, a Black Belt collects yield data from two independent production lines to see if their mean yields differ. Which assumption is critical for a two-sample t-test?
Answer: Data should be approximately normally distributed
The two-sample t-test assumes that the underlying populations are approximately normally distributed, especially for small samples.
A Black Belt sets alpha at 0.05 and beta at 0.10 for a hypothesis test. What does a beta of 0.10 represent?
Answer: 10% chance of failing to reject a false null hypothesis
Beta is the probability of a Type II error, which is failing to reject the null hypothesis when it is actually false.
Which hypothesis testing method is most appropriate for determining whether the median cycle time has changed when the data is highly skewed and non-normal?
Answer: Mann-Whitney U test
The Mann-Whitney U test is a nonparametric alternative that does not require normality and compares medians or distributions.
A Black Belt performs a one-way ANOVA and obtains a significant result. What should be the next step to identify which specific groups differ?
Answer: Perform a post-hoc comparison test such as Tukey's HSD
A post-hoc test like Tukey's HSD identifies which specific group pairs have significantly different means after ANOVA.
A team tests whether a new inspection method yields the same proportion of detected defects as the old method using 200 samples from each. Which test applies?
Answer: Two-proportion z-test
A two-proportion z-test compares proportions from two independent groups to determine if they differ significantly.