Lean Six Sigma Black Belt Analyze Phase: Hypothesis Testing Questions and Answers — 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?
- The results are not statistically significant, and the team fails to reject the null hypothesis.
- The results are statistically significant, and the team rejects the null hypothesis. (Correct answer)
- The results are inconclusive, and the sample size needs to be increased.
- A Type II error has occurred, and the team should accept the null hypothesis.
Correct answer: The results are statistically significant, and the team rejects the null hypothesis.
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?
- Chi-Square Test
- 2-Sample t-test
- Analysis of Variance (ANOVA) (Correct answer)
- Paired t-test
Correct answer: Analysis of Variance (ANOVA)
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?
- The change or effect the project team is trying to prove.
- The probability of a Type I error.
- The assumption of no effect, no difference, or no relationship. (Correct answer)
- The statistical power of the test.
Correct answer: The assumption of no effect, no difference, or no relationship.
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?
- They fail to detect a real process improvement that has occurred.
- They conclude there is no change when, in fact, there has been a significant change.
- They incorrectly reject a true null hypothesis. (Correct answer)
- They correctly accept a false alternative hypothesis.
Correct answer: They incorrectly reject a true null hypothesis.
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?
- ANOVA
- 1-Sample t-test
- Chi-Square Test of Independence (Correct answer)
- Regression Analysis
Correct answer: Chi-Square Test of Independence
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.
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?
- The probability of finding a statistically significant result.
- The maximum acceptable probability of failing to reject a false null hypothesis (Type II Error).
- The practical significance of the results.
- The maximum acceptable probability of rejecting a true null hypothesis (Type I Error). (Correct answer)
Correct answer: The maximum acceptable probability of rejecting a true null hypothesis (Type I Error).
The alpha risk (α), or significance level, is the threshold set before a hypothesis test. It represents the maximum risk the team is willing to take of making a Type I error. A Type I error is the incorrect rejection of a true null hypothesis. A common alpha level used in Six Sigma is 0.05, which corresponds to a 5% risk of concluding a difference exists when it actually doesn't.
Lean Six Sigma Black Belt Analyze Phase: Hypothesis Testing Questions and Answers
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?