Lean Six Sigma Green Belt Certification Basic Statistical Tools 4 — Questions and Answers
Question 1: When constructing a histogram, the recommended number of bins for a dataset of 64 observations using the square-root rule is approximately:
- 4
- 6
- 8 (Correct answer)
- 10
Correct answer: 8
The square-root rule recommends √n bins; √64 = 8 bins.
Question 2: In regression analysis, an R² value of 0.85 means:
- There is an 85% chance the model is correct
- 85% of the variation in Y is explained by the model (Correct answer)
- The slope of the regression line is 0.85
- The correlation coefficient is 0.85
Correct answer: 85% of the variation in Y is explained by the model
R² (coefficient of determination) represents the proportion of variation in the response variable explained by the predictor(s).
Question 3: A process average is 100 units with σ = 4. The upper specification limit is 112. What is the Cpu?
- 1.00 (Correct answer)
- 1.33
- 1.50
- 2.00
Correct answer: 1.00
Cpu = (USL − mean) / 3σ = (112 − 100) / (3 × 4) = 12 / 12 = 1.00.
Question 4: What is the primary purpose of a run chart in Six Sigma?
- To display the distribution shape of process data
- To monitor a process over time and detect trends or shifts (Correct answer)
- To compare the means of multiple groups
- To identify the most frequent defect categories
Correct answer: To monitor a process over time and detect trends or shifts
A run chart plots data in time sequence to reveal trends, cycles, or shifts in a process over time.
Question 5: Which level of measurement allows calculation of ratios and has a true zero point?
- Nominal
- Ordinal
- Interval
- Ratio (Correct answer)
Correct answer: Ratio
Ratio scale has a true zero point, making ratios meaningful (e.g., 20 kg is twice 10 kg).
Question 6: In a normal probability plot, data that follow a straight line indicate:
- The data have significant outliers
- The data are approximately normally distributed (Correct answer)
- The process is out of statistical control
- The data exhibit a bimodal distribution
Correct answer: The data are approximately normally distributed
If points on a normal probability plot fall approximately on a straight line, the data are consistent with a normal distribution.
Question 7: A Lean Six Sigma team calculates a correlation coefficient (r) of −0.92 between machine temperature and defect rate. What can they conclude?
- Higher temperature causes fewer defects
- There is a strong negative linear relationship between temperature and defect rate (Correct answer)
- Temperature explains 92% of defect variation
- There is no practical relationship between the two variables
Correct answer: There is a strong negative linear relationship between temperature and defect rate
r = −0.92 indicates a strong negative linear association; correlation does not prove causation.
Lean Six Sigma Green Belt Certification Basic Statistical Tools 4
When constructing a histogram, the recommended number of bins for a dataset of 64 observations using the square-root rule is approximately: