Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Hypothesis Testing 1

Question 1

A Black Belt wants to test whether the variance of a process has changed after an improvement. Which test is most appropriate?

Accepted Answer

Chi-square test for variance

Answer

The chi-square test is used to compare a sample variance against a known or hypothesized population variance, making it the correct choice for testing whether process variance has changed.

Question 2

Which of the following statements best describes the null hypothesis in hypothesis testing?

Accepted Answer

It asserts that there is no effect or difference between groups

Answer

The null hypothesis (H₀) always represents the default claim of no difference, no effect, or no change. The goal of hypothesis testing is to determine whether evidence is sufficient to reject this baseline assumption.

Question 3

A Black Belt collects data and calculates a p-value of 0.12 with alpha set at 0.05. What is the correct action?

Accepted Answer

Fail to reject the null hypothesis due to insufficient evidence

Answer

When the p-value (0.12) exceeds alpha (0.05), there is insufficient statistical evidence to reject the null hypothesis. 'Failing to reject' is not the same as proving the null true — it simply means the data does not support rejection at the chosen significance level.

Question 4

What effect does increasing sample size have on a hypothesis test, assuming all other factors remain constant?

Accepted Answer

It increases the ability to detect a true difference (power)

Answer

Larger sample sizes reduce standard error, making it easier to detect true differences between groups. This directly increases statistical power (1 − β), reducing the likelihood of a Type II error.

Question 5

A paired t-test is preferred over a two-sample t-test when:

Accepted Answer

Each observation in one group is naturally matched to an observation in the other group

Answer

Paired t-tests are used when observations are matched or related (e.g., before-and-after measurements on the same subject). Pairing controls for individual variation, increasing sensitivity to detect real differences.

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 Hypothesis Testing 1