Certified Six Sigma Black Belt Exam Hypothesis Testing Applications 5

Question 1

A Black Belt applies Tukey's HSD post-hoc test after a significant ANOVA. What is its primary purpose?

Accepted Answer

To identify which specific pairs of group means differ significantly

Answer

Tukey's HSD controls family-wise error rate while identifying which specific mean pairs are statistically different.

Question 2

For a hypothesis test on proportions with n = 200 and p̂ = 0.12, which condition justifies using the normal approximation?

Accepted Answer

np̂ ≥ 5 and n(1−p̂) ≥ 5

Answer

The normal approximation for proportions is valid when both np̂ and n(1−p̂) are at least 5.

Question 3

What does a Bartlett's test evaluate, and when is it preferred over Levene's test?

Accepted Answer

It tests equality of variances and is preferred when data are normally distributed

Answer

Bartlett's test is more powerful than Levene's for normally distributed data but is sensitive to non-normality.

Question 4

A Six Sigma project measures cycle time before and after improvement for the same 25 units. Which test is most appropriate?

Accepted Answer

Paired t-test

Answer

When the same units are measured twice (before/after), a paired t-test is appropriate as it accounts for within-unit correlation.

Question 5

Which statement correctly describes the relationship between confidence level and significance level?

Accepted Answer

Confidence level = 1 − α

Answer

A 95% confidence interval corresponds to α = 0.05, so confidence level = 1 − α.

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