Certified Six Sigma Black Belt Hypothesis Testing Questions and Answers

Question 1

A Six Sigma Black Belt is analyzing a process improvement aimed at reducing the average processing time. The null hypothesis (H₀) is that the mean time is unchanged (μ = 30 minutes), and the alternative hypothesis (H₁) is that the mean time has been reduced (μ < 30 minutes). After conducting the test, the calculated p-value is 0.04. Using a significance level (α) of 0.05, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is sufficient evidence to conclude the mean time has been reduced.

Answer

The rule for making a decision using a p-value is: If the p-value is less than or equal to the significance level (α), we reject the null hypothesis (H₀). In this case, the p-value (0.04) is less than α (0.05), leading to the rejection of H₀ in favor of the alternative hypothesis (H₁), which states that the mean time has been reduced.

Question 2

In the context of a hypothesis test for a process improvement project, what is the consequence of committing a Type I error?

Accepted Answer

Concluding that the process has improved when, in fact, it has not.

Answer

A Type I error (also known as alpha risk or a false positive) occurs when we incorrectly reject a true null hypothesis. In a process improvement context, the null hypothesis often represents the 'status quo' or 'no change.' Therefore, rejecting a true null hypothesis means concluding there was an improvement or change when, in reality, no change occurred. This can lead to implementing an ineffective solution.

Question 3

A project team wants to determine if there is a statistically significant difference in the average customer satisfaction scores (measured on a continuous scale from 1 to 10) among four different service centers. Which of the following statistical tests is the most appropriate to use?

Accepted Answer

Analysis of Variance (ANOVA)

Answer

Analysis of Variance (ANOVA) is used to compare the means of three or more groups to determine if at least one group mean is statistically different from the others. A 2-Sample t-test is used for two groups, a paired t-test is for comparing two related samples, and a Chi-Square test is used for categorical data, not continuous data like satisfaction scores.

Question 4

A Black Belt is investigating a claim that a new supplier's raw material leads to a different proportion of defective products compared to the old supplier. To determine if there is a statistically significant difference in the defect rates between the two suppliers, which hypothesis test is most suitable?

Accepted Answer

2-Proportion test

Answer

The goal is to compare the proportions (or percentages) of defective products from two independent populations (old supplier vs. new supplier). The 2-Proportion test is specifically designed for this purpose. A 2-Sample t-test compares means of continuous data, an F-test compares variances, and ANOVA compares the means of more than two groups.

Question 5

Which of the following statements correctly describes the relationship between statistical power, sample size, and Type II error (beta risk)?

Accepted Answer

Increasing the sample size increases power and decreases the risk of a Type II error.

Answer

The power of a test (1 - β) is the probability of correctly detecting a real effect. A larger sample size provides more information and reduces sampling error, making it easier to detect a true effect. This increases the power of the test and, by definition, decreases the probability of a Type II error (β), which is the error of failing to detect a real effect.

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Hypothesis Testing Questions and Answers