Lean Six Sigma Black Belt Certification Measure Phase: Data Analysis 3 — Questions and Answers
Question 1: A Gauge R&R study reveals that %Gauge R&R is 28%. How should this measurement system be classified?
- Acceptable for all uses
- Marginal—acceptable depending on application and customer approval (Correct answer)
- Excellent measurement system
- Completely unacceptable and must be scrapped
Correct answer: Marginal—acceptable depending on application and customer approval
A %Gauge R&R between 10% and 30% is considered marginal; it may be acceptable depending on the importance of the application and cost of repair.
Question 2: What is the relationship between Type I error (alpha) and Type II error (beta) when sample size is fixed?
- Reducing alpha automatically reduces beta
- Reducing alpha increases beta (they have an inverse relationship) (Correct answer)
- Alpha and beta are always equal
- Beta is independent of alpha
Correct answer: Reducing alpha increases beta (they have an inverse relationship)
With a fixed sample size, decreasing alpha (the risk of a false positive) increases beta (the risk of a false negative) because the decision boundary shifts.
Question 3: In a Box-Cox transformation, what is the goal?
- To calculate process capability for attribute data
- To stabilize variance and make non-normal data approximately normal (Correct answer)
- To remove outliers from the dataset
- To convert continuous data to discrete categories
Correct answer: To stabilize variance and make non-normal data approximately normal
The Box-Cox transformation applies a power function to non-normal data to stabilize variance and achieve approximate normality for parametric analysis.
Question 4: Which statistic is used to assess the overall adequacy of a multiple regression model?
- Individual p-values of coefficients
- Adjusted R-squared (Correct answer)
- The y-intercept value
- The standard error of a single predictor
Correct answer: Adjusted R-squared
Adjusted R-squared measures the proportion of variance explained by the model while penalizing for adding unnecessary predictors, making it suitable for comparing models.
Question 5: A process produces 340 defects per million opportunities (DPMO). What sigma level does this correspond to approximately?
- 3 sigma
- 4 sigma
- 5 sigma (Correct answer)
- 6 sigma
Correct answer: 5 sigma
A DPMO of approximately 233 corresponds to 5 sigma; 340 DPMO is very close to the 5-sigma level using the 1.5-sigma shift convention.
Question 6: What does the Anderson-Darling test evaluate in data analysis?
- The equality of two population means
- Whether a dataset follows a specified distribution (typically normal) (Correct answer)
- The correlation between two variables
- The homogeneity of variances across groups
Correct answer: Whether a dataset follows a specified distribution (typically normal)
The Anderson-Darling test is a goodness-of-fit test that assesses whether sample data come from a specified distribution such as the normal distribution.
Question 7: In a time-series analysis, which component represents the long-term upward or downward movement in data?
- Seasonality
- Cyclical variation
- Trend (Correct answer)
- Irregular variation
Correct answer: Trend
The trend component in time-series analysis represents the long-term, sustained upward or downward movement in a dataset over time.
Lean Six Sigma Black Belt Certification Measure Phase: Data Analysis 3
A Gauge R&R study reveals that %Gauge R&R is 28%.
How should this measurement system be classified?