Certified Six Sigma Black Belt Advanced Hypothesis Testing Questions and Answers Flashcards
6 cards from real Certified Six Sigma Black Belt Exam practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 6 Certified Six Sigma Black Belt Advanced Hypothesis Testing Questions and Answers flashcards as text
A Black Belt is testing whether the variance of a critical dimension has changed after a process improvement. Which hypothesis test should be used?
Answer: Chi-square test for a single variance
The chi-square test for a single variance compares a sample variance against a known or hypothesized population variance.
In the context of hypothesis testing, what does a Type II error represent in a Six Sigma project?
Answer: Failing to detect a real process shift or improvement that actually exists
A Type II error (beta) occurs when the test fails to reject a false null hypothesis, meaning a real effect goes undetected.
When the normality assumption is violated for comparing two independent groups, which nonparametric alternative to the two-sample t-test is most appropriate?
Answer: Mann-Whitney U test
The Mann-Whitney U test is the nonparametric equivalent of the independent two-sample t-test, comparing distributions of two independent groups.
A Black Belt calculates a power of 0.70 for a planned hypothesis test. What action should be taken to improve the test's ability to detect a meaningful difference?
Answer: Increase the sample size to raise power to at least 0.80
Increasing sample size is the most straightforward and reliable method to increase statistical power above the commonly accepted threshold of 0.80.
What is the purpose of the Bonferroni correction in hypothesis testing?
Answer: To adjust the significance level downward when performing multiple simultaneous tests
The Bonferroni correction divides the desired alpha by the number of tests to control the overall Type I error rate across multiple comparisons.
A paired t-test yields a statistically significant result, but the mean difference is only 0.002 units on a tolerance of 5 units. What should the Black Belt conclude?
Answer: The result is statistically significant but likely not practically significant given the tolerance
Statistical significance does not imply practical significance; a difference of 0.002 on a 5-unit tolerance is negligible from an engineering standpoint.