Certified Six Sigma Black Belt Exam Hypothesis Testing Applications 4 — Questions and Answers
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?
- Reject H₀ because the interval is wide
- Fail to reject H₀ because 500 is contained in the interval (Correct answer)
- Reject H₀ because the interval does not contain zero
- Accept H₁ because sample mean differs from 500
Correct answer: Fail to reject H₀ because 500 is contained in the interval
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?
- The probability of correctly rejecting a false null hypothesis (Correct answer)
- The probability of failing to reject a true null hypothesis
- The probability that the null hypothesis is true
- The significance level used in the test
Correct answer: The probability of correctly rejecting a false null hypothesis
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?
- Decrease the sample size
- Increase the sample size (Correct answer)
- Change to a one-tailed test only
- Reduce the measurement resolution
Correct answer: Increase the sample size
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?
- Paired t-test
- One-sample t-test
- Independent two-sample t-test (Correct answer)
- One-way ANOVA
Correct answer: Independent two-sample t-test
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?
- 6 (Correct answer)
- 12
- 7
- 11
Correct answer: 6
Degrees of freedom for a chi-square test of independence = (rows − 1)(columns − 1) = (3−1)(4−1) = 6.
Question 6: Which scenario correctly calls for a one-tailed hypothesis test rather than a two-tailed test?
- Checking if a process mean changed in either direction
- Testing whether a new material is stronger than the current material (Correct answer)
- Comparing two suppliers' defect rates for any difference
- Verifying whether measurement system bias is zero
Correct answer: Testing whether a new material is stronger than the current material
When the research question specifies a direction (e.g., stronger), a one-tailed test is appropriate.
Question 7: In a hypothesis test, the region where the test statistic leads to rejecting H₀ is called:
- Confidence region
- Acceptance region
- Critical region (rejection region) (Correct answer)
- Power region
Correct answer: Critical region (rejection region)
The critical region is the set of test statistic values that fall beyond the critical value, leading to rejection of H₀.
Certified Six Sigma Black Belt Exam Hypothesis Testing Applications 4
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?