Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Hypothesis Testing Questions and Answers 2 — Questions and Answers
Question 1: In hypothesis testing, what does a Type II error represent?
- Rejecting a true null hypothesis
- Failing to reject a false null hypothesis (Correct answer)
- Accepting the alternative hypothesis correctly
- Rejecting the alternative hypothesis correctly
Correct answer: Failing to reject a false null hypothesis
A Type II error (beta error) occurs when the test fails to reject a null hypothesis that is actually false.
Question 2: A Black Belt sets alpha at 0.05 and obtains a p-value of 0.03. What is the correct conclusion?
- Fail to reject the null hypothesis
- Reject the null hypothesis (Correct answer)
- Accept the null hypothesis
- The test is inconclusive
Correct answer: Reject the null hypothesis
Since the p-value (0.03) is less than alpha (0.05), there is sufficient evidence to reject the null hypothesis.
Question 3: Which hypothesis test is most appropriate for comparing the means of three or more independent groups?
- Paired t-test
- Two-sample t-test
- One-way ANOVA (Correct answer)
- Chi-square test
Correct answer: One-way ANOVA
One-way ANOVA is designed to test whether there are statistically significant differences among the means of three or more independent groups.
Question 4: What is the primary purpose of calculating statistical power in a hypothesis test?
- To determine the sample size needed (Correct answer)
- To calculate the confidence interval width
- To verify data normality
- To measure process capability
Correct answer: To determine the sample size needed
Statistical power analysis is primarily used to determine the minimum sample size required to detect a meaningful effect at a given significance level.
Question 5: When conducting a two-proportion test, which assumption must be satisfied?
- Both samples must come from the same population
- The data must follow a normal distribution exactly
- The expected number of successes and failures in each sample should be at least five (Correct answer)
- The two sample sizes must be exactly equal
Correct answer: The expected number of successes and failures in each sample should be at least five
The two-proportion z-test requires that np and n(1-p) are each at least five in both samples to ensure the normal approximation is valid.
Question 6: In a paired t-test, what characteristic of the data distinguishes it from an independent two-sample t-test?
- The data must be non-normal
- Each observation in one group is matched to a specific observation in the other group (Correct answer)
- The variances of both groups must be equal
- The sample sizes must differ between groups
Correct answer: Each observation in one group is matched to a specific observation in the other group
A paired t-test is used when observations are naturally matched or paired, such as before-and-after measurements on the same subjects.
Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Hypothesis Testing Questions and Answers 2
In hypothesis testing, what does a Type II error represent?