Lean Six Sigma Black Belt Certification Measure Phase: Data Analysis 4 — Questions and Answers
Question 1: A Black Belt uses Minitab to run a one-way ANOVA and obtains a p-value of 0.032. With alpha = 0.05, what is the correct conclusion?
- Fail to reject H0; there is no significant difference among group means
- Reject H0; at least one group mean differs significantly from the others (Correct answer)
- Accept H0; all group means are equal
- The test is inconclusive because the p-value is too close to alpha
Correct answer: Reject H0; at least one group mean differs significantly from the others
Since p = 0.032 < alpha = 0.05, we reject the null hypothesis and conclude that at least one group mean is significantly different.
Question 2: What does the concept of 'rational subgrouping' mean in the context of control charts?
- Using the largest possible sample size for each subgroup
- Grouping samples collected under similar conditions to maximize within-subgroup variation
- Grouping samples so that special causes appear between subgroups rather than within them (Correct answer)
- Randomly assigning observations to subgroups regardless of time order
Correct answer: Grouping samples so that special causes appear between subgroups rather than within them
Rational subgrouping organizes data so within-subgroup variation reflects only common causes, maximizing the chance that special causes manifest as between-subgroup differences.
Question 3: Which non-parametric test is the equivalent of the paired t-test when normality cannot be assumed?
- Mann-Whitney U test
- Kruskal-Wallis test
- Wilcoxon signed-rank test (Correct answer)
- Mood's median test
Correct answer: Wilcoxon signed-rank test
The Wilcoxon signed-rank test is the non-parametric alternative to the paired t-test, comparing medians of two related samples when normality is violated.
Question 4: In a scatter diagram, a correlation coefficient (r) of -0.92 indicates:
- A weak positive linear relationship
- A strong negative linear relationship (Correct answer)
- No meaningful relationship between variables
- A perfect non-linear relationship
Correct answer: A strong negative linear relationship
A correlation coefficient of -0.92 indicates a strong negative linear relationship, meaning as one variable increases, the other decreases substantially.
Question 5: A process engineer finds that the Pp is 1.6 but the Ppk is 0.9. What does this imply?
- The process spread is adequate but the process is significantly off-center (Correct answer)
- Both the process spread and centering are inadequate
- The process is centered and capable
- The measurement system has high bias
Correct answer: The process spread is adequate but the process is significantly off-center
A high Pp with a low Ppk indicates the process has sufficient inherent capability (spread) but is poorly centered relative to the specification limits.
Question 6: Which data collection strategy best controls for the effect of time-related lurking variables?
- Convenience sampling
- Stratified random sampling by shift or time period (Correct answer)
- Systematic sampling from a fixed list
- Voluntary response sampling
Correct answer: Stratified random sampling by shift or time period
Stratified random sampling by shift or time period ensures representation across time-related strata, controlling for lurking temporal variables.
Question 7: What is 'attribute agreement analysis' used to assess?
- The bias in a continuous measurement instrument
- The consistency and accuracy of appraisers classifying categorical outcomes (Correct answer)
- The linearity of a gauge across its operating range
- The stability of a measurement system over time
Correct answer: The consistency and accuracy of appraisers classifying categorical outcomes
Attribute agreement analysis evaluates how consistently appraisers agree with each other and with a known standard when making pass/fail or categorical judgments.
Lean Six Sigma Black Belt Certification Measure Phase: Data Analysis 4
A Black Belt uses Minitab to run a one-way ANOVA and obtains a p-value of 0.032.
With alpha = 0.05, what is the correct conclusion?