Six Sigma practice questions, with answers.

Question 1Which statement best represents the three connected views of Six Sigma taught in this course?

1. It is a philosophy, an improvement method, and a family of process-performance measures.
2. It is an inspection plan, an accounting system, and a supplier-ranking program.
3. It is a software package, an organizational chart, and a fixed set of specification limits.
4. It is a statistical table, a maintenance schedule, and a customer survey.

Question 2A team has defined a chronic delay and established a trustworthy baseline. Which DMAIC phase should next validate the causes of the delay?

1. Control
2. Analyze
3. Improve
4. Define

Question 3In the process relationship Y = f(X), what does the lowercase f represent?

1. The final inspection frequency
2. The number of failed units
3. The relationship or rule connecting inputs X to output Y
4. The financial value of the output

Question 4Which statement best captures the practical reason for “The Define phase and its tollgate”?

1. A charter creates shared authorization and prevents different participants from pursuing different problems, goals, boundaries, or decision rules.
2. A project should not consume measurement and analysis resources until leaders agree that the problem, customer, boundaries, ownership, and expected value are sufficiently clear.
3. Weak statements bias the analysis, obscure the actual gap, and make success impossible to judge consistently.
4. A worthwhile project can still fail if its boundaries, value, dependencies, or uncertainty are not made explicit before work begins.

Question 5Which statement best captures the practical reason for “The project charter as a governing agreement”?

1. Weak statements bias the analysis, obscure the actual gap, and make success impossible to judge consistently.
2. A worthwhile project can still fail if its boundaries, value, dependencies, or uncertainty are not made explicit before work begins.
3. A charter creates shared authorization and prevents different participants from pursuing different problems, goals, boundaries, or decision rules.
4. Technically sound work can fail when people who control resources, own the process, supply knowledge, or absorb the change are ignored.

Question 6Which statement best captures the practical reason for “Problem statements and SMART goals”?

1. A worthwhile project can still fail if its boundaries, value, dependencies, or uncertainty are not made explicit before work begins.
2. Technically sound work can fail when people who control resources, own the process, supply knowledge, or absorb the change are ignored.
3. Improvement is cross-functional work; a collection of experts will not reliably become an effective team without operating agreements and deliberate leadership.
4. Weak statements bias the analysis, obscure the actual gap, and make success impossible to judge consistently.

Question 7Which statement best captures the practical reason for “Population, sample, parameter, and statistic”?

1. Mean, median, mode, quartiles, and percentiles summarize different features and can tell conflicting stories in skewed or mixed data.
2. Processes with the same center can have very different consistency, risk, capability, and customer experience.
3. A graph can reveal distribution, sequence, relationship, or category concentration, but no single graph preserves all four.
4. Responsible interpretation depends on knowing whether a number describes observed data or estimates a broader target with sampling uncertainty.

Question 8Which statement best captures the practical reason for “Measures of center and position”?

1. Mean, median, mode, quartiles, and percentiles summarize different features and can tell conflicting stories in skewed or mixed data.
2. Processes with the same center can have very different consistency, risk, capability, and customer experience.
3. A graph can reveal distribution, sequence, relationship, or category concentration, but no single graph preserves all four.
4. Probability errors commonly arise from adding overlapping events, multiplying dependent events, or confusing a conditional rate with its reverse.

Question 9Which statement best captures the practical reason for “Spread, shape, and robust summaries”?

1. A graph can reveal distribution, sequence, relationship, or category concentration, but no single graph preserves all four.
2. Processes with the same center can have very different consistency, risk, capability, and customer experience.
3. Probability errors commonly arise from adding overlapping events, multiplying dependent events, or confusing a conditional rate with its reverse.
4. A familiar distribution name does not make an interval, probability, or test valid when its support and assumptions do not match the process.

Question 10Which statement best captures the practical reason for “Begin inference with the decision and estimand”?

1. A test decision balances false-positive and false-negative risks; the p-value alone does not quantify either consequence or the probability a hypothesis is true.
2. A binary reject or fail-to-reject label discards information about effect direction, magnitude, precision, and operational relevance.
3. Choosing a test from a software menu before defining the population, parameter, effect, and decision creates technically polished answers to the wrong question.
4. Independent, paired, and one-sample questions have different error structures and cannot be selected from the number of columns alone.

Question 11A test has β = 0.20. What is its statistical power?

1. 0.20
2. 0.40
3. 0.80
4. 1.20

Question 12Which statement best captures the practical reason for “Confidence intervals and practical decisions”?

1. A binary reject or fail-to-reject label discards information about effect direction, magnitude, precision, and operational relevance.
2. Independent, paired, and one-sample questions have different error structures and cannot be selected from the number of columns alone.
3. Binary outcomes, defect counts, and contingency tables require models based on opportunities, independence, and expected frequencies rather than mean-test formulas.
4. Testing every pair separately inflates the chance of at least one false positive across the family of comparisons.