Lean Six Sigma Green Belt Certification Basic Statistical Tools 5 — Questions and Answers
Question 1: Which central limit theorem property allows the use of normal-distribution-based control charts even when the underlying data are non-normal?
- Individual measurements are always normally distributed in manufacturing
- Sample means approach a normal distribution as sample size increases (Correct answer)
- The median is always equal to the mean for large samples
- Variance decreases proportionally to sample size
Correct answer: Sample means approach a normal distribution as sample size increases
The Central Limit Theorem states that the distribution of sample means becomes approximately normal as n increases, regardless of the population distribution.
Question 2: A Gauge R&R study reveals that measurement system variation accounts for 28% of total observed variation. What action is most appropriate?
- Accept the measurement system as capable
- Improve or replace the measurement system before collecting process data (Correct answer)
- Increase the sample size to compensate
- Recalculate using a different formula
Correct answer: Improve or replace the measurement system before collecting process data
A %GR&R above 30% is unacceptable; 28% is in the marginal zone and improvement is strongly recommended before analysis.
Question 3: What does the standard error of the mean (SEM) measure?
- The variability of individual data points around the mean
- How much sample means vary from the population mean across repeated samples (Correct answer)
- The difference between the largest and smallest sample means
- The total error in a measurement system
Correct answer: How much sample means vary from the population mean across repeated samples
SEM = σ / √n, representing how much the sample mean is expected to vary from the true population mean.
Question 4: A process has Cp = 1.50 and Cpk = 0.80. What does this tell you?
- The process is both capable and centered
- The process has adequate spread but is significantly off-center (Correct answer)
- The process is not capable and is perfectly centered
- Both indices indicate a defect-free process
Correct answer: The process has adequate spread but is significantly off-center
High Cp with low Cpk indicates the process spread fits within specs but the mean is shifted toward or beyond one limit.
Question 5: When should a nonparametric statistical test be used instead of a parametric test?
- When the sample size is greater than 30
- When the data are normally distributed
- When the data are ordinal or clearly non-normal with small sample sizes (Correct answer)
- When you need a more powerful test
Correct answer: When the data are ordinal or clearly non-normal with small sample sizes
Nonparametric tests make no normality assumption and are appropriate for ordinal data or non-normal distributions, especially with small samples.
Question 6: In the context of control charts, what is the purpose of control limits set at ±3σ?
- To define the engineering specification boundaries
- To identify when process variation is likely due to special causes (Correct answer)
- To show the target value for the process
- To set customer acceptance criteria
Correct answer: To identify when process variation is likely due to special causes
±3σ control limits represent the range of expected common-cause variation; points beyond them signal likely special causes.
Question 7: A team finds that their process data exhibit positive skewness. Which statement best describes this distribution?
- The left tail is longer and the majority of data falls on the right
- The right tail is longer and the majority of data falls on the left (Correct answer)
- The mean equals the median and mode
- The data are symmetrically distributed around the center
Correct answer: The right tail is longer and the majority of data falls on the left
Positive (right) skewness means the distribution has a longer right tail, with most data concentrated on the left side.
Lean Six Sigma Green Belt Certification Basic Statistical Tools 5
Which central limit theorem property allows the use of normal-distribution-based control charts even when the underlying data are non-normal?