Certified Six Sigma Black Belt Exam Advanced Hypothesis Testing 2

Question 1

A Six Sigma team wants to compare the variances of two independent populations. Which test is most appropriate?

Accepted Answer

F-test (Snedecor's F)

Answer

The F-test (Snedecor's F) is the classical test for comparing two population variances using the ratio of sample variances.

Question 2

When the p-value equals 0.049 and alpha is 0.05, a Black Belt should:

Accepted Answer

Reject H₀ and consider practical significance before acting

Answer

A p-value below alpha leads to rejecting H₀, but statistical significance must always be weighed against practical/economic significance.

Question 3

Which assumption is NOT required for a standard two-sample t-test?

Accepted Answer

The sample means follow a chi-square distribution

Answer

Sample means follow a t-distribution (not chi-square) under normality assumptions; chi-square applies to variance tests.

Question 4

A Kruskal-Wallis test is the nonparametric alternative to which parametric test?

Accepted Answer

One-way ANOVA

Answer

The Kruskal-Wallis test compares medians across three or more independent groups, serving as the nonparametric equivalent of one-way ANOVA.

Question 5

In hypothesis testing, the power of a test is defined as:

Accepted Answer

1 minus the probability of a Type II error

Answer

Power = 1 − β, where β is the probability of a Type II error (failing to reject a false H₀).

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