Lean Six Sigma Black Belt Analyze Phase: Hypothesis Testing Questions and Answers

Question 1

A Six Sigma team is investigating the cycle time of a claims process. They believe a new software update has reduced the average time. The null hypothesis (H₀) states that the mean cycle time is unchanged, while the alternative hypothesis (Hₐ) states it has decreased. After analysis, they calculate a p-value of 0.04. Using a standard alpha (α) level of 0.05, what is the correct conclusion?

Accepted Answer

The results are statistically significant, and the team rejects the null hypothesis.

Answer

The p-value (0.04) is less than the alpha level (0.05), which indicates that the observed result is statistically significant. Therefore, the team should reject the null hypothesis, which stated there was no change. This provides statistical evidence supporting the alternative hypothesis that the new software update has indeed reduced the average cycle time.

Question 2

A Black Belt wants to determine if there is a statistically significant difference in the average defect rates across four different production lines. The data collected is continuous. Which hypothesis test is most appropriate for this scenario?

Accepted Answer

Analysis of Variance (ANOVA)

Answer

Analysis of Variance (ANOVA) is the correct statistical test to use when comparing the means of three or more groups. A 2-Sample t-test is only used for comparing the means of two groups. A Chi-Square test is used for analyzing categorical data, not continuous data. A Paired t-test is used when the data points are linked in pairs, which is not the case here.

Question 3

In the context of hypothesis testing, what does the null hypothesis (H₀) typically represent?

Accepted Answer

The assumption of no effect, no difference, or no relationship.

Answer

The null hypothesis (H₀) is the default assumption or statement of the status quo. It posits that there is no statistically significant effect, difference, or relationship between the variables being tested. The goal of the hypothesis test is to gather enough statistical evidence to be able to reject this null hypothesis in favor of the alternative hypothesis.

Question 4

A project team commits a Type I error during hypothesis testing. What is the consequence of this error?

Accepted Answer

They incorrectly reject a true null hypothesis.

Answer

A Type I error, also known as alpha (α) error or a 'false positive,' occurs when the null hypothesis is rejected even though it is actually true. In practical terms, this means the team concludes that a significant effect exists (e.g., an improvement was made) when it does not. This can lead to implementing unnecessary changes based on a false finding.

Question 5

A Black Belt is analyzing survey data to determine if customer satisfaction levels (categorized as 'Satisfied', 'Neutral', 'Dissatisfied') are independent of the service region ('North', 'South', 'East', 'West'). Which of the following statistical tools should be used to test this hypothesis?

Accepted Answer

Chi-Square Test of Independence

Answer

The Chi-Square Test of Independence is used to determine whether there is a significant association between two categorical variables. In this scenario, both 'customer satisfaction level' and 'service region' are categorical variables, making the Chi-Square test the appropriate choice to see if they are related or independent.

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Analyze Phase: Hypothesis Testing Questions and Answers