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Green Belt · Review

Lesson 10: Green Belt review and sitting the practice certification exam

Covers IASSC Green Belt Body of Knowledge 3.1 through 5.2 · 20 review questions · plus the practice certification exam

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Nine lessons have carried this course from Yellow Belt's awareness level into the Green Belt Body of Knowledge's Analyze and Improve statistics: inferential statistics and sampling, hypothesis testing, tests for normal and non-normal data, proportion and chi-square tests, correlation and regression, and statistical process control. The IASSC Certified Lean Six Sigma Green Belt exam itself is 100 questions, multiple choice and true/false, closed book, with a 3 hour time limit and a 70 percent score required to pass, distributed at roughly 20 questions per major Body of Knowledge section. This lesson does not introduce new statistical methods. Instead it lays the nine lessons side by side as one decision path, walks through the mix-ups that account for most missed exam questions, and explains how the practice exam that follows is built and scored.

The Analyze-Improve-Control tool roadmap across Green Belt Lessons 1-9 Analyze tools from Lessons 1 through 6 (patterns of variation, inference, hypothesis testing, tests for normal and non-normal data, proportion and chi-square tests) feed into Improve tools from Lessons 7 and 8 (correlation, regression, residuals), which feed into the Control tool from Lesson 9, statistical process control, and finally into the Green Belt practice certification exam. Analyze Lessons 1-6 Variation, inference, hypothesis tests, proportions, chi-square Improve Lessons 7-8 Correlation, regression, residuals, transformation Control Lesson 9 Statistical process control charts Practice Exam Every question on the Analyze path is really asking: what kind of data do I have, and what claim am I testing? Improve then asks whether X actually predicts Y, and by how much. Control asks whether the process is stable now. Black Belt, next, adds designed experiments: instead of only observing X and Y, the team deliberately changes X.
The Analyze-Improve-Control roadmap: Lessons 1-6 build the Analyze tool set, Lessons 7-8 build Improve's correlation and regression tools, and Lesson 9 builds the Control chart tool set, all feeding into the Green Belt practice certification exam.

Which tool when: a one-page synthesis

Almost every Green Belt scenario question is really asking two things at once: what type of data do you have, and what question are you asking of it. The table below collapses nine lessons into that lookup.

Question you are askingData typeTool
Does one sample's mean differ from a target?Continuous, normal1-sample t-test
Do two independent groups' means differ?Continuous, normal2-sample t-test
Did before/after measurements on the same units change?Continuous, normal, pairedPaired t-test
Do three or more group means differ?Continuous, normalOne-way ANOVA
Do two groups' medians differ, data not normal?Continuous, non-normalMann-Whitney
Do three or more groups' medians differ, not normal?Continuous, non-normalKruskal-Wallis or Mood's median
Does one proportion differ from a target?Attribute (pass/fail)1-sample proportion test
Do two proportions differ?Attribute (pass/fail)2-sample proportion test
Are two categorical variables associated?Attribute, counts in a tableChi-square test of independence
Are two continuous variables related, and how strongly?Continuous, continuousCorrelation, then simple linear regression
Does more than one X predict Y, and is the relationship curved?Continuous, several X'sMultiple or non-linear regression
Is the process stable over time, individual readings?Continuous, subgroup of 1I-MR chart
Is the process stable over time, subgroups of readings?Continuous, subgroups >1Xbar-R or Xbar-S chart
Is a defect rate or count stable over time?Attribute countsP, NP, U, or C chart

Trap one: fail to reject is not accept

A test that comes back with p greater than alpha means the data did not give enough evidence to reject the null hypothesis. It never means the null hypothesis has been proven true, and it is a core principle of hypothesis testing (Body of Knowledge 3.3). If a GCHS team runs a 2-sample t-test comparing two subcontractors' punch-list closure times and gets p = 0.31 against alpha = 0.05, the correct conclusion is "we failed to reject the null hypothesis of no difference," not "we proved the two subcontractors perform identically." A larger sample, or a real but small difference the test was underpowered to detect, could still be hiding in that result.

Why this matters

Any answer choice that says "accept the null" or "proves no difference exists" is wrong on sight, regardless of the rest of the question.

Trap two: statistical significance versus practical significance

A large enough sample size can make a genuinely tiny, meaningless difference come back statistically significant, because the standard error that p-values depend on shrinks as sample size grows. A hypothesis test answers "is this difference likely real, and not just noise." It does not answer "is this difference big enough to justify a change." Suppose a regression on 4,000 completed work orders finds a statistically significant relationship (p = 0.002) between crew size and cycle time, but the effect is 0.03 days per additional crew member. That result can be statistically real and still not be worth reorganizing crews over. Practical significance is a business judgment laid on top of a statistical one, not a replacement for it.

Trap three: control limits versus specification limits

Control limits, typically the process mean plus or minus three standard deviations of the plotted statistic, describe what the process itself is capable of producing when it is behaving consistently. Specification limits come from the customer or a contract and describe what output is acceptable. The two are calculated from entirely different inputs and have no required relationship to each other: a process can be perfectly stable, sitting comfortably inside its own control limits, while still producing output outside a tight specification. Confusing the two on the exam, for example treating a point outside a specification limit as automatically an "out of control" signal on a control chart, is one of the most common mistakes at this level.

Trap four: correlation is not causation

A strong correlation coefficient, or a high R-squared from a regression, shows that two variables move together. Neither shows that one causes the other. A GCHS example: months with more completed accessibility modifications might correlate with higher call center volume, not because the work causes calls but because both rise together with the size of that month's active caseload, a lurking third variable. Regression and correlation are Improve-phase tools for building and quantifying a relationship; establishing that the relationship is causal, rather than coincidental or driven by a confounder, is a separate step that usually needs a designed experiment, the subject Black Belt picks up next.

Trap five: prediction interval versus confidence interval

Both come out of a regression model, and both get confused on exam questions because they look almost identical in a printout. A confidence interval (CI) is a range for the mean response at a given X value, how precisely the model has pinned down the average. A prediction interval (PI) is a range for a single new observation at that X value, and it must be wider than the CI at the same X, because a single new data point carries both the uncertainty in the estimated mean and the ordinary scatter of individual points around that mean. If a regression predicts average inspection turnaround at a given crew size, the CI bounds the average turnaround; the PI bounds what one specific upcoming inspection is likely to take, and is always the wider of the two.

How the practice exam is built, and how to sit it

The practice exam below draws 100 questions from a larger pool covering the Yellow Belt and Green Belt lessons, with 20 from each of the five DMAIC phases (IASSC describes about 20 questions from each major section on the real exam), and it is timed and scored the same way: 3 hours, 70 percent to pass. Two honest differences from the real thing are worth naming plainly. First, this is a study tool, not a proctored credential: the real IASSC exam is administered under proctoring, and passing this practice run does not itself certify anyone. Second, because the questions are drawn from a shared pool, the exact 100 questions, and their order, will differ between attempts, which is useful for repeat practice but means two people's "exam" are not identical. Treat a low score as a map of which lessons to reread, not as a verdict, and retake it after reviewing any section that came back weak.

Practice questions

1. A 2-sample t-test comparing two crews' rework rates returns p = 0.18 against alpha = 0.05. What is the correct conclusion?

  1. Reject the null hypothesis
  2. The test is invalid because p exceeds 0.05
  3. Accept the null hypothesis; the crews perform identically, because p is greater than alpha
  4. Fail to reject the null hypothesis; not enough evidence of a difference

2. A regression on a very large data set finds a statistically significant but tiny effect size. What does this illustrate?

  1. The test must have been run incorrectly, because a real effect that small could never reach significance
  2. Statistical significance always implies practical significance, so any significant result justifies a change
  3. A large sample can make a practically meaningless difference statistically significant
  4. Regression cannot be used with large samples

3. Control limits on a control chart are calculated from which of the following?

  1. The Cp and Cpk from a separate capability study run against the customer's specification
  2. The desired pass rate set by leadership
  3. The process's own mean and standard deviation, typically plus or minus 3 sigma
  4. The customer's specification or contract requirements, expressed as an upper and lower limit

4. Months with more completed accessibility modifications also show higher call center volume. What is the most defensible conclusion?

  1. The two are correlated, but causation has not been established and a lurking variable such as caseload size may explain both
  2. Completing modifications directly causes more calls
  3. The correlation proves no third factor is involved
  4. Call volume causes modifications to be completed

5. At a given X value, which interval from a regression model is wider?

  1. They are always identical in width
  2. Neither has a defined width
  3. The confidence interval for the mean response, because it must cover the scatter of individual points
  4. The prediction interval for a single new observation

6. Which test compares the medians of three or more independent groups when the data is not normally distributed?

  1. Kruskal-Wallis
  2. Chi-square test of independence
  3. One-way ANOVA
  4. 2-sample t-test

7. Two categorical variables, such as inspector and pass/fail outcome, need to be tested for association. Which tool applies?

  1. Xbar-R chart
  2. Chi-square test of independence
  3. Simple linear regression of pass/fail outcome against inspector name
  4. Paired t-test

8. Central Limit Theorem underlies which of the following practices?

  1. Calculating Cp and Cpk
  2. Deciding whether to use a p-chart or a u-chart
  3. Choosing between attribute and continuous data
  4. Treating a sample mean as approximately normally distributed even when the underlying population is not, for a large enough sample

9. A team wants to know if a single sample's variance matches a historical target. Which family of test applies?

  1. 2-sample proportion test
  2. Mann-Whitney test
  3. 1-sample variance test
  4. Friedman test

10. A process is being charted using subgroups of five continuous readings taken every hour. Which chart pair is appropriate?

  1. U and C charts
  2. Xbar-R chart
  3. P and NP charts
  4. I-MR chart

11. Which statement about a p-value is correct?

  1. A p-value above alpha proves the null hypothesis is true
  2. If p is less than alpha, reject the null hypothesis
  3. If p is less than alpha, accept the null hypothesis
  4. A p-value measures the size of the effect

12. A regression model's R-squared is 0.81. What does this tell a Green Belt?

  1. 81 percent of individual predictions will land within one standard error of the actual value
  2. 81 percent of the variation in Y is explained by the model's X's
  3. The relationship between X and Y is definitely causal, since a fit that close cannot come from a lurking variable
  4. The model has no residual error

13. Sampling technique and sample size both matter primarily because of which underlying idea?

  1. Inference from a sample to a population depends on the sample being representative and adequately sized to detect the effect of interest
  2. Sample size has no effect on a test's power
  3. Larger samples always eliminate the need for hypothesis testing
  4. Any convenience sample represents the population equally well

14. A Green Belt has one sample of non-normal, paired before/after data. Which test fits?

  1. 2-sample proportion test
  2. Chi-square test of independence
  3. 1-sample Wilcoxon signed-rank test
  4. One-way ANOVA comparing the before and after means as two independent groups

15. Why is a point outside a specification limit not automatically an "out of control" signal on a control chart?

  1. Because control limits and specification limits are calculated from different inputs and have no required relationship to each other
  2. Because control charts cannot be used with specification limits at all
  3. Because out-of-control signals only apply to attribute charts
  4. Because specification limits are always wider than control limits

16. A count of defects per inspected unit, where each unit has room for more than one defect, is best tracked on which chart?

  1. Xbar-S chart
  2. I-MR chart
  3. P chart
  4. U chart

17. What is the key difference between a designed experiment, the Black Belt topic coming next, and the regression covered in Green Belt?

  1. A designed experiment deliberately manipulates X, while regression typically analyzes X's as observed, which strengthens the case for causation
  2. There is no meaningful difference between the two
  3. Regression cannot use continuous data
  4. Designed experiments never use statistics

18. Two proportions, defect rates from two suppliers, need to be compared. Which test applies?

  1. Paired t-test
  2. 2-sample proportion test
  3. Simple linear regression
  4. 1-sample variance test

19. What is the real IASSC Green Belt exam's format?

  1. 60 questions, 2 hour limit, open book
  2. 150 questions, 4 hour limit, closed book, 70 percent required to pass
  3. 50 questions, 1 hour limit, no pass mark
  4. 100 questions, 3 hour limit, closed book, 70 percent required to pass

20. A Box-Cox transformation is applied to a data set before running a capability or regression analysis. What is it addressing?

  1. Missing data
  2. Measurement system error, by rescaling every reading to remove repeatability and gauge bias
  3. Non-normality, by transforming the data toward a more normal shape
  4. Sample size that is too small

Glossary

Fail to reject
The correct conclusion when p is greater than or equal to alpha; the data did not provide enough evidence against the null hypothesis, which is never described as "accepted" or "proven."
Practical significance
A business judgment about whether an effect is large enough to matter, layered on top of, and separate from, statistical significance.
Control limits
Boundaries, typically the process mean plus or minus three standard deviations of the plotted statistic, describing what a stable process itself produces; distinct from specification limits.
Confidence interval (CI)
A range for the mean response at a given X value from a regression model.
Prediction interval (PI)
A range for a single new observation at a given X value; always wider than the CI at the same X.
Lurking variable
An unmeasured third factor that drives both variables in an observed correlation, one reason correlation does not establish causation.
Rational subgroup
A sample grouped so that variation within it reflects only common-cause variation, letting a control chart correctly separate common from special cause.

Next

Sit the Green Belt practice certification exam

100 questions drawn from a larger pool, a 3 hour timer, 70 percent pass mark, closed note. It stays closed note and timed for a study session rather than the real exam's proctored, in-person or online-proctored setting, and passing it here does not itself certify anyone.

Start the practice exam

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