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

Question 1

A Black Belt suspects that cycle time has increased from a historical mean of 8 minutes, and believes any change would only be an increase. Which type of hypothesis test should be used?

Accepted Answer

Right-tailed (upper-tail) test

Answer

When the team has a directional suspicion (increase only), a right-tailed (upper-tail) test is appropriate. It places all of α in the upper tail, giving more power to detect a shift in the specified direction versus splitting α across both tails.

Question 2

A Black Belt sets the significance level α = 0.05 before running a hypothesis test. Which statement correctly interprets this value?

Accepted Answer

There is a 5% probability of rejecting a true null hypothesis

Answer

α (alpha) defines the Type I error rate — the probability of incorrectly rejecting a true null hypothesis. It does not describe the probability that H₀ is true, nor is it the same as power (which is 1 − β).

Question 3

Cycle time data from two independent production lines fails a normality test. A Black Belt wants to compare central tendency between the two lines. Which test is most appropriate?

Accepted Answer

Mann-Whitney U test

Answer

The Mann-Whitney U test is the nonparametric equivalent of the two-sample t-test for independent groups. It compares medians and does not require the normality assumption, making it appropriate when data violates normality.

Question 4

A CSSBB wants to test whether observed defect counts across five product categories follow a historically expected distribution. Which test should be applied?

Accepted Answer

Chi-square goodness-of-fit test

Answer

The chi-square goodness-of-fit test compares observed frequencies to expected frequencies derived from a theoretical or historical distribution. It is designed specifically for this use case, unlike the t-test or ANOVA which compare means.

Question 5

A Black Belt increases sample size from n = 25 to n = 100 while keeping α = 0.05 fixed. What is the most likely result?

Accepted Answer

The power of the test increases

Answer

Power (1 − β) increases with larger sample sizes because larger samples reduce standard error, making it easier to detect a true effect. The Type I error rate (α) remains fixed by the researcher's choice and is not affected by sample size.

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 Applications 1