Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Analyze Phase: Hypothesis Testing Questions and Answers 2 — Questions and Answers
Question 1: In a two-sample t-test comparing process means, what does a p-value of 0.03 indicate at a significance level of 0.05?
- Reject the null hypothesis; the means are statistically different (Correct answer)
- Fail to reject the null hypothesis; the means are equal
- The test is inconclusive
- The sample size is too small
Correct answer: Reject the null hypothesis; the means are statistically different
A p-value of 0.03 is less than the significance level of 0.05, so we reject the null hypothesis and conclude the means differ significantly.
Question 2: Which hypothesis test is most appropriate for comparing the variance of a single sample against a known population variance?
- Chi-square test (Correct answer)
- F-test
- Paired t-test
- Mann-Whitney U test
Correct answer: Chi-square test
The chi-square test is used to compare a single sample variance to a specified population variance.
Question 3: What is a Type II error in the context of hypothesis testing?
- Failing to reject a false null hypothesis (Correct answer)
- Rejecting a true null hypothesis
- Accepting the alternative hypothesis correctly
- Setting an incorrect significance level
Correct answer: Failing to reject a false null hypothesis
A Type II error occurs when we fail to reject the null hypothesis even though it is actually false.
Question 4: When conducting an ANOVA test across four process groups, what does a statistically significant F-statistic tell you?
- At least one group mean differs from the others (Correct answer)
- All group means are different from each other
- The variances across groups are unequal
- The data is not normally distributed
Correct answer: At least one group mean differs from the others
A significant F-statistic in ANOVA indicates that at least one group mean is significantly different, but not which specific ones differ.
Question 5: What is the primary purpose of a paired t-test in the Analyze phase?
- To compare means of two related measurements from the same subjects (Correct answer)
- To compare means of two independent groups
- To test whether data follows a normal distribution
- To determine the correlation between two variables
Correct answer: To compare means of two related measurements from the same subjects
A paired t-test compares two related measurements taken from the same subjects, such as before-and-after a process change.
Question 6: Which assumption must be verified before performing a one-sample t-test on process cycle time data?
- The data is approximately normally distributed or the sample size is large enough (Correct answer)
- The data must have zero skewness
- The population standard deviation must be known
- The sample must contain at least 100 observations
Correct answer: The data is approximately normally distributed or the sample size is large enough
The one-sample t-test assumes approximately normal data, though the Central Limit Theorem makes it robust with larger samples.
Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Analyze Phase: Hypothesis Testing Questions and Answers 2
In a two-sample t-test comparing process means, what does a p-value of 0.03 indicate at a significance level of 0.05?