Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Hypothesis Testing 1 — Questions and Answers
Question 1: A Black Belt wants to test whether the variance of a process has changed after an improvement. Which test is most appropriate?
- Two-sample t-test
- Chi-square test for variance (Correct answer)
- Mann-Whitney U test
- One-proportion z-test
Correct answer: Chi-square test for variance
The chi-square test is used to compare a sample variance against a known or hypothesized population variance, making it the correct choice for testing whether process variance has changed.
Question 2: Which of the following statements best describes the null hypothesis in hypothesis testing?
- It states that a significant difference or effect exists
- It represents the research hypothesis the experimenter wants to prove
- It asserts that there is no effect or difference between groups (Correct answer)
- It is rejected whenever the sample size is large enough
Correct answer: It asserts that there is no effect or difference between groups
The null hypothesis (H₀) always represents the default claim of no difference, no effect, or no change. The goal of hypothesis testing is to determine whether evidence is sufficient to reject this baseline assumption.
Question 3: A Black Belt collects data and calculates a p-value of 0.12 with alpha set at 0.05. What is the correct action?
- Reject the null hypothesis because 0.12 is close to 0.05
- Fail to reject the null hypothesis due to insufficient evidence (Correct answer)
- Accept the alternative hypothesis since the p-value is less than 0.15
- Increase alpha to 0.15 to achieve significance
Correct answer: Fail to reject the null hypothesis due to insufficient evidence
When the p-value (0.12) exceeds alpha (0.05), there is insufficient statistical evidence to reject the null hypothesis. 'Failing to reject' is not the same as proving the null true — it simply means the data does not support rejection at the chosen significance level.
Question 4: What effect does increasing sample size have on a hypothesis test, assuming all other factors remain constant?
- It increases the probability of a Type I error
- It decreases statistical power
- It increases the ability to detect a true difference (power) (Correct answer)
- It widens the confidence interval
Correct answer: It increases the ability to detect a true difference (power)
Larger sample sizes reduce standard error, making it easier to detect true differences between groups. This directly increases statistical power (1 − β), reducing the likelihood of a Type II error.
Question 5: A paired t-test is preferred over a two-sample t-test when:
- The two groups have unequal variances
- Each observation in one group is naturally matched to an observation in the other group (Correct answer)
- The population standard deviation is known
- The data follows a non-normal distribution
Correct answer: Each observation in one group is naturally matched to an observation in the other group
Paired t-tests are used when observations are matched or related (e.g., before-and-after measurements on the same subject). Pairing controls for individual variation, increasing sensitivity to detect real differences.
Question 6: In a two-tailed hypothesis test with alpha = 0.05, the critical region is defined as:
- The area where p > 0.05 in one tail only
- The combined area of 2.5% in each tail of the distribution (Correct answer)
- The central 95% of the distribution
- The area beyond z = 1.645 in the right tail
Correct answer: The combined area of 2.5% in each tail of the distribution
A two-tailed test splits alpha equally between both tails. With alpha = 0.05, each tail contains 0.025 (2.5%), corresponding to critical z-values of approximately ±1.96. The null hypothesis is rejected if the test statistic falls in either tail.
Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Hypothesis Testing 1
A Black Belt wants to test whether the variance of a process has changed after an improvement.
Which test is most appropriate?