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

Fail to reject the null hypothesis; there is not enough evidence to conclude the mean time has been reduced.

Answer

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

Answer

The p-value is greater than the significance level, so the alternative hypothesis is accepted.

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

Correctly concluding that the process has not improved.

Answer

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

Answer

Incorrectly failing to reject a false null hypothesis.

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

Paired t-test

Answer

2-Sample t-test

Answer

Chi-Square test

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

F-test for variances

Answer

One-way ANOVA

Answer

2-Sample t-test

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

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

Answer

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

Answer

Sample size has no direct effect on power or the risk of a Type II error.

Question 6

A quality manager wants to verify a machine manufacturer's claim that the variance of their machine's output is no more than 0.5 mm². The manager will conduct a hypothesis test to challenge this claim. What is the correct formulation for the null (H₀) and alternative (H₁) hypotheses?

Accepted Answer

H₀: σ² ≤ 0.5, H₁: σ² > 0.5

Answer

H₀: μ ≤ 0.5, H₁: μ > 0.5

Answer

H₀: σ² = 0.5, H₁: σ² ≠ 0.5

Answer

H₀: σ² > 0.5, H₁: σ² ≤ 0.5