Certified Six Sigma Black Belt Exam Hypothesis Testing Applications 3

Question 1

A quality engineer compares process variance before and after a change using an F-test. The p-value is 0.08 with α = 0.05. What should be concluded?

Accepted Answer

Fail to reject H₀; insufficient evidence that variances differ

Answer

p = 0.08 > α = 0.05, so there is insufficient evidence to conclude the variances are different.

Question 2

Which nonparametric test is the appropriate alternative to the one-sample t-test when normality cannot be assumed?

Accepted Answer

Wilcoxon signed-rank test

Answer

The Wilcoxon signed-rank test is the nonparametric equivalent of the one-sample (or paired) t-test.

Question 3

A Black Belt selects α = 0.01 instead of α = 0.05. What is the direct effect on the hypothesis test?

Accepted Answer

The probability of a Type I error decreases

Answer

Lowering α reduces the acceptable probability of a Type I error (false rejection of H₀).

Question 4

When conducting a two-proportion z-test, what is the null hypothesis typically stated as?

Accepted Answer

p₁ = p₂

Answer

The null hypothesis for a two-proportion z-test states that the two population proportions are equal.

Question 5

Levene's test is used in hypothesis testing to evaluate which property of data?

Accepted Answer

Equality of variances across groups

Answer

Levene's test assesses whether group variances are equal, a key assumption for ANOVA and t-tests.

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