Certified Six Sigma Black Belt Exam Advanced Hypothesis Testing 5

Question 1

A Black Belt uses a Z-test rather than a t-test. The primary justification for this choice is:

Accepted Answer

The population standard deviation is known

Answer

The Z-test is appropriate when the population standard deviation (σ) is known, which allows use of the standard normal distribution.

Question 2

Which nonparametric test is equivalent to the two-sample independent t-test?

Accepted Answer

Mann-Whitney U test

Answer

The Mann-Whitney U test compares central tendencies of two independent samples without assuming normality, serving as the nonparametric alternative to the two-sample t-test.

Question 3

A confidence interval and a hypothesis test at the same significance level will:

Accepted Answer

Produce equivalent conclusions — if H₀ value is outside the CI, reject H₀

Answer

A two-sided CI at (1 − α) confidence corresponds exactly to a two-sided hypothesis test at level α; exclusion of H₀ value from the CI equals rejection of H₀.

Question 4

In hypothesis testing, which factor does NOT directly affect the width of the required sample size calculation?

Accepted Answer

The color of the measurement instrument

Answer

Sample size is mathematically determined by α, β (power), effect size, and variance — physical attributes of measuring tools are irrelevant to the formula.

Question 5

The Anderson-Darling test is used in the context of hypothesis testing to:

Accepted Answer

Assess whether sample data follow a specified distribution

Answer

The Anderson-Darling test is a goodness-of-fit test that assesses how well sample data conform to a hypothesized distribution (commonly normality).

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Advanced Hypothesis Testing 5