Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Assessment 1 — Questions and Answers
Question 1: A control chart for a packaging line shows 8 consecutive data points all falling above the centerline, yet none exceed the upper or lower control limits. What should the Black Belt conclude?
- The process exhibits special cause variation (Correct answer)
- The process is in statistical control with common cause variation only
- The control limits are set too wide and should be recalculated
- The sample size is insufficient to draw any conclusion
Correct answer: The process exhibits special cause variation
A run of 8 or more consecutive points on the same side of the centerline is a recognized non-random pattern (per Nelson/Western Electric rules), signaling special cause variation even when no individual point breaches the control limits. The Black Belt should investigate the assignable cause.
Question 2: Which document, created during the Define phase of DMAIC, formally authorizes a Six Sigma project by establishing the business case, scope, goals, timeline, and team roles?
- Project charter (Correct answer)
- SIPOC diagram
- Fishbone (Ishikawa) diagram
- Process capability report
Correct answer: Project charter
The project charter is the governing document of the Define phase. It provides the team's formal mandate, sets scope boundaries to prevent scope creep, and aligns stakeholders before data collection begins. SIPOC and fishbone diagrams are analytical tools used later in the project.
Question 3: A Black Belt sets α = 0.05 and runs a hypothesis test. The null hypothesis is not rejected — but the null hypothesis is actually false. What statistical error has been committed?
- Type II error (β error) (Correct answer)
- Type I error (α error)
- The test was executed correctly; no error occurred
- The significance level was set too high
Correct answer: Type II error (β error)
A Type II error (beta error) occurs when the test fails to reject a null hypothesis that is in fact false — the analyst misses a real effect. Type I error is the opposite: rejecting a true null. Reducing β requires increasing sample size or raising α.
Question 4: A multiple regression model built in the Analyze phase yields an R² of 0.82. How should the Black Belt interpret this value?
- 82% of the variation in the response variable is explained by the predictors in the model (Correct answer)
- The model is statistically significant at the 82% confidence level
- The average correlation between each predictor and the response is 0.82
- 82% of observed data points fall within the model's prediction interval
Correct answer: 82% of the variation in the response variable is explained by the predictors in the model
R² (coefficient of determination) quantifies the proportion of total variability in the dependent variable (Y) that is accounted for by the independent variables in the model. An R² of 0.82 means the model explains 82% of Y's variation; the remaining 18% is unexplained noise or unmodeled factors.
Question 5: A process is measured and found to produce 250 defects per million opportunities (DPMO). Approximately what sigma level does this represent?
- 5 sigma (Correct answer)
- 4 sigma
- 6 sigma
- 3 sigma
Correct answer: 5 sigma
Using the standard sigma conversion table (which incorporates the 1.5-sigma long-term shift), approximately 233 DPMO corresponds to 5 sigma, while 6,210 DPMO corresponds to 4 sigma. A DPMO of 250 falls closest to the 5-sigma level. For reference, 6 sigma = 3.4 DPMO.
Question 6: After implementing a process improvement, a Black Belt collects two independent data sets — one from before the change and one from after — and wants to statistically confirm that the process mean has shifted. Which hypothesis test is most appropriate?
- Two-sample t-test (Correct answer)
- Paired t-test
- Chi-square test for independence
- One-proportion z-test
Correct answer: Two-sample t-test
A two-sample t-test compares the means of two independent groups. Because the before and after samples are drawn from different (independent) process runs, this is the correct choice. A paired t-test applies when the same units are measured twice; chi-square and proportion z-tests are used for categorical or count data, not continuous means.
Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Assessment 1
A control chart for a packaging line shows 8 consecutive data points all falling above the centerline, yet none exceed the upper or lower control limits.
What should the Black Belt conclude?