Lean Six Sigma Exam
Hypothesis Testing & Statistics Practice Questions
160 practice questions with detailed explanations — aligned to the Lean Six Sigma Exam.
Master Hypothesis Testing & Statistics to boost your score on the Lean Six Sigma Exam. Each question below mirrors the style and difficulty of real exam questions, complete with detailed explanations so you understand the why behind every answer. Work through all 160 questions, review any that trip you up, and use the related topics below to round out your preparation.
Q1.In hypothesis testing, a Type I error (α error) is defined as:
A.Failing to reject H₀ when H₁ is trueB.Rejecting H₀ when H₀ is actually trueC.Accepting H₁ when H₀ is trueD.Setting too large a sample sizeB. Rejecting H₀ when H₀ is actually trueExplanation: A Type I error (false positive) occurs when you reject the null hypothesis (H₀) when it is actually true. The probability of a Type I error is α (significance level). A Type II error (β) is failing to reject H₀ when H₁ is actually true (false negative).
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Q2.Which test is used to compare the means of two independent groups when population variances are unknown?
A.F-testB.Chi-square testC.Two-sample t-testD.ANOVAC. Two-sample t-testExplanation: The two-sample (independent) t-test compares the means of two independent groups when population standard deviations are unknown. ANOVA is used for three or more groups. The F-test compares variances. Chi-square tests are for categorical (attribute) data.
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Q3.A p-value of 0.03 with α = 0.05 means:
A.There is a 3% chance the null hypothesis is trueB.There is a 3% chance of observing this result (or more extreme) if H₀ is true — reject H₀C.The practical effect size is largeD.You should increase α to 0.10 before concludingB. There is a 3% chance of observing this result (or more extreme) if H₀ is true — reject H₀Explanation: The p-value is the probability of observing a result as extreme or more extreme than the sample data, assuming H₀ is true. p = 0.03 < α = 0.05, so you reject H₀. A p-value does NOT equal the probability that H₀ is true — that is a common misinterpretation.
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Q4.What does a Gauge Repeatability & Reproducibility (Gauge R&R) study measure?
A.Whether the process is in controlB.The percentage of total process variation attributable to the measurement systemC.The capability of the process vs. specification limitsD.The reliability of a gauge over 1,000 cyclesB. The percentage of total process variation attributable to the measurement systemExplanation: Gauge R&R (Measurement System Analysis) quantifies how much of observed variation comes from the measurement system (gauge) vs. the actual process. Repeatability measures variation when one operator uses the same gauge multiple times; Reproducibility measures variation across different operators. A well-accepted benchmark: %GR&R < 10% is excellent; 10–30% may be acceptable; >30% is unacceptable.
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Q5.When is a chi-square test of independence appropriate?
A.Comparing means of two continuous datasetsB.Testing whether two categorical variables are relatedC.Comparing the variance of two groupsD.Testing normality of residuals in a regressionB. Testing whether two categorical variables are relatedExplanation: The chi-square test of independence tests whether two categorical (attribute) variables are associated. For example, testing whether defect type and shift are independent. It operates on count data in a contingency table. The chi-square goodness-of-fit test (different) tests whether observed frequencies match expected frequencies.
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