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

Question 1

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?

Accepted Answer

Chi-square test of independence

Answer

One-way ANOVA

Answer

Regression analysis

Answer

Two-sample t-test

Question 2

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?

Accepted Answer

Data should be approximately normally distributed

Answer

Samples must be paired

Answer

Population variances must be exactly equal

Answer

Sample sizes must be identical

Question 3

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?

Accepted Answer

10% chance of failing to reject a false null hypothesis

Answer

10% chance of rejecting a true null hypothesis

Answer

90% chance of a Type I error

Answer

10% significance level

Question 4

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?

Accepted Answer

Mann-Whitney U test

Answer

One-sample t-test

Answer

F-test

Answer

Linear regression

Question 5

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?

Accepted Answer

Perform a post-hoc comparison test such as Tukey's HSD

Answer

Increase the sample size and retest

Answer

Switch to a chi-square test

Answer

Report only that a difference exists without further analysis

Question 6

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?

Accepted Answer

Two-proportion z-test

Answer

Paired t-test

Answer

One-sample t-test

Answer

Kruskal-Wallis test