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 results are not statistically significant, and the team fails to reject the null hypothesis.

Answer

The results are inconclusive, and the sample size needs to be increased.

Answer

A Type II error has occurred, and the team should accept the null hypothesis.

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

Chi-Square Test

Answer

2-Sample t-test

Answer

Paired t-test

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 change or effect the project team is trying to prove.

Answer

The probability of a Type I error.

Answer

The statistical power of the test.

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

They fail to detect a real process improvement that has occurred.

Answer

They conclude there is no change when, in fact, there has been a significant change.

Answer

They correctly accept a false alternative hypothesis.

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

ANOVA

Answer

1-Sample t-test

Answer

Regression Analysis

Question 6

When conducting a hypothesis test, the 'alpha risk' (α), or significance level, is set by the practitioner before the analysis. What does this value represent?

Accepted Answer

The maximum acceptable probability of rejecting a true null hypothesis (Type I Error).

Answer

The probability of finding a statistically significant result.

Answer

The maximum acceptable probability of failing to reject a false null hypothesis (Type II Error).

Answer

The practical significance of the results.