Analyze Phase: Hypothesis Testing Flashcards
6 cards from real Lean Six Sigma Black Belt Certification practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
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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?
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.
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?
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.
In the context of hypothesis testing, what does the null hypothesis (H₀) typically represent?
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.
A project team commits a Type I error during hypothesis testing. What is the consequence of this error?
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.
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?
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.
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?
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.