Certified Six Sigma Black Belt Exam Hypothesis Testing Applications 4

Question 1

A process engineer tests whether mean fill volume equals 500 mL using a one-sample t-test. The 95% confidence interval is (498.2, 501.8). What is the correct conclusion at α = 0.05?

Accepted Answer

Fail to reject H₀ because 500 is contained in the interval

Answer

A two-sided confidence interval that contains the hypothesized value corresponds to failing to reject H₀.

Question 2

Which of the following best describes statistical power in hypothesis testing?

Accepted Answer

The probability of correctly rejecting a false null hypothesis

Answer

Power = 1 − β, representing the probability of correctly detecting a real effect when one exists.

Question 3

A Black Belt wants to detect a shift of 1.5σ with 90% power and α = 0.05 (two-tailed). Which action most effectively increases power without changing α?

Accepted Answer

Increase the sample size

Answer

Increasing sample size is the primary lever to increase power while holding α constant.

Question 4

The Mann-Whitney U test is the nonparametric alternative to which parametric test?

Accepted Answer

Independent two-sample t-test

Answer

The Mann-Whitney U test compares two independent groups without assuming normality, replacing the two-sample t-test.

Question 5

A team uses a chi-square test of independence to analyze a 3×4 contingency table. What are the degrees of freedom?

Accepted Answer

6

Answer

Degrees of freedom for a chi-square test of independence = (rows − 1)(columns − 1) = (3−1)(4−1) = 6.

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Hypothesis Testing Applications 4