Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Assessment 1

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?

Accepted Answer

The process exhibits special cause variation

Answer

The process is in statistical control with common cause variation only

Answer

The control limits are set too wide and should be recalculated

Answer

The sample size is insufficient to draw any conclusion

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?

Accepted Answer

Project charter

Answer

SIPOC diagram

Answer

Fishbone (Ishikawa) diagram

Answer

Process capability report

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?

Accepted Answer

Type II error (β error)

Answer

Type I error (α error)

Answer

The test was executed correctly; no error occurred

Answer

The significance level was set too high

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?

Accepted Answer

82% of the variation in the response variable is explained by the predictors in the model

Answer

The model is statistically significant at the 82% confidence level

Answer

The average correlation between each predictor and the response is 0.82

Answer

82% of observed data points fall within the model's prediction interval

Question 5

A process is measured and found to produce 250 defects per million opportunities (DPMO). Approximately what sigma level does this represent?

Accepted Answer

5 sigma

Answer

4 sigma

Answer

6 sigma

Answer

3 sigma

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?

Accepted Answer

Two-sample t-test

Answer

Paired t-test

Answer

Chi-square test for independence

Answer

One-proportion z-test