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

Two-sample t-test for means

Answer

F-test for comparing two means

Answer

One-sample z-test

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

Concluding a process improved when it actually did not

Answer

Selecting the wrong statistical test for the data

Answer

Using an insufficient sample size for the experiment

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

Kruskal-Wallis test

Answer

Wilcoxon signed-rank test

Answer

Friedman test

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

Lower the significance level from 0.05 to 0.01

Answer

Reduce the number of replications in the experiment

Answer

Switch from a two-tailed to a one-tailed test only if justified

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

To increase the power of individual hypothesis tests

Answer

To correct for non-normality in the data distribution

Answer

To adjust sample sizes for unequal group variances

Question 6

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?

Accepted Answer

The result is statistically significant but likely not practically significant given the tolerance

Answer

The process requires immediate corrective action

Answer

The test was conducted incorrectly and should be repeated

Answer

The paired t-test is invalid for this type of data