Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Advanced Hypothesis Testing Questions and Answers 3

Question 1

A Black Belt is testing whether the variance of a critical dimension has changed after a process improvement. Which hypothesis test should be used?

Accepted Answer

Chi-square test for a single variance

Answer

The chi-square test for a single variance compares a sample variance against a known or hypothesized population variance.

Question 2

In the context of hypothesis testing, what does a Type II error represent in a Six Sigma project?

Accepted Answer

Failing to detect a real process shift or improvement that actually exists

Answer

A Type II error (beta) occurs when the test fails to reject a false null hypothesis, meaning a real effect goes undetected.

Question 3

When the normality assumption is violated for comparing two independent groups, which nonparametric alternative to the two-sample t-test is most appropriate?

Accepted Answer

Mann-Whitney U test

Answer

The Mann-Whitney U test is the nonparametric equivalent of the independent two-sample t-test, comparing distributions of two independent groups.

Question 4

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?

Accepted Answer

Increase the sample size to raise power to at least 0.80

Answer

Increasing sample size is the most straightforward and reliable method to increase statistical power above the commonly accepted threshold of 0.80.

Question 5

What is the purpose of the Bonferroni correction in hypothesis testing?

Accepted Answer

To adjust the significance level downward when performing multiple simultaneous tests

Answer

The Bonferroni correction divides the desired alpha by the number of tests to control the overall Type I error rate across multiple comparisons.

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Advanced Hypothesis Testing Questions and Answers 3