Lean Six Sigma Green Belt Certification Basic Statistical Tools 3 — Questions and Answers
Question 1: In hypothesis testing, what does the p-value represent?
- The probability that the null hypothesis is true
- The probability of observing results as extreme as the sample if the null hypothesis is true (Correct answer)
- The probability that the alternative hypothesis is true
- The significance level chosen by the analyst
Correct answer: The probability of observing results as extreme as the sample if the null hypothesis is true
The p-value is the probability of obtaining the observed data (or more extreme) assuming the null hypothesis is true.
Question 2: A Type II error in hypothesis testing occurs when you:
- Reject a true null hypothesis
- Fail to reject a false null hypothesis (Correct answer)
- Reject a false null hypothesis
- Fail to reject a true null hypothesis
Correct answer: Fail to reject a false null hypothesis
A Type II error (β) means failing to detect a real effect — accepting H₀ when it is actually false.
Question 3: What does a Cpk value of 1.33 indicate about a process?
- The process is centered but barely meets specifications
- The process is capable and has some margin relative to the nearest specification limit (Correct answer)
- The process is out of control
- The process is centered and has excess capability
Correct answer: The process is capable and has some margin relative to the nearest specification limit
Cpk = 1.33 is the traditional minimum target, indicating the process mean is at least 4σ from the nearest spec limit.
Question 4: Which statistical test compares the means of exactly two independent groups?
- One-way ANOVA
- Chi-square test
- Two-sample t-test (Correct answer)
- Paired t-test
Correct answer: Two-sample t-test
A two-sample t-test compares the means of two independent groups to determine if they differ significantly.
Question 5: What is the interquartile range (IQR) used to measure?
- The total spread of all data
- The spread of the middle 50% of data (Correct answer)
- The distance from the mean to each data point
- The average deviation from the median
Correct answer: The spread of the middle 50% of data
IQR = Q3 − Q1, capturing the spread of the central 50% of the data and resisting outlier influence.
Question 6: A box plot whisker extends to a data point that is 1.7 × IQR above Q3. How should this point be classified?
- A mild outlier
- An extreme outlier
- A normal data point within the whisker (Correct answer)
- The upper specification limit
Correct answer: A normal data point within the whisker
Box plot whiskers typically extend to 1.5 × IQR; 1.7 × IQR falls outside that but the point itself is still plotted at its actual value — it would actually be an outlier (mild) since 1.7 > 1.5.
Question 7: Which type of variation in a process is attributable to identifiable, non-random causes?
- Common cause variation
- Special cause variation (Correct answer)
- Natural variation
- Random variation
Correct answer: Special cause variation
Special cause variation is assignable to specific, identifiable factors and is not part of the normal process distribution.
Lean Six Sigma Green Belt Certification Basic Statistical Tools 3
In hypothesis testing, what does the p-value represent?