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

Two-sample t-test

Answer

Mann-Whitney U test

Answer

One-proportion z-test

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

It states that a significant difference or effect exists

Answer

It represents the research hypothesis the experimenter wants to prove

Answer

It is rejected whenever the sample size is large enough

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

Reject the null hypothesis because 0.12 is close to 0.05

Answer

Accept the alternative hypothesis since the p-value is less than 0.15

Answer

Increase alpha to 0.15 to achieve significance

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

It increases the probability of a Type I error

Answer

It decreases statistical power

Answer

It widens the confidence interval

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

The two groups have unequal variances

Answer

The population standard deviation is known

Answer

The data follows a non-normal distribution

Question 6

In a two-tailed hypothesis test with alpha = 0.05, the critical region is defined as:

Accepted Answer

The combined area of 2.5% in each tail of the distribution

Answer

The area where p > 0.05 in one tail only

Answer

The central 95% of the distribution

Answer

The area beyond z = 1.645 in the right tail