Certified Six Sigma Black Belt Hypothesis Testing Applications 1 Flashcards
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A Black Belt suspects that cycle time has increased from a historical mean of 8 minutes, and believes any change would only be an increase. Which type of hypothesis test should be used?
Answer: Right-tailed (upper-tail) test
When the team has a directional suspicion (increase only), a right-tailed (upper-tail) test is appropriate. It places all of α in the upper tail, giving more power to detect a shift in the specified direction versus splitting α across both tails.
A Black Belt sets the significance level α = 0.05 before running a hypothesis test. Which statement correctly interprets this value?
Answer: There is a 5% probability of rejecting a true null hypothesis
α (alpha) defines the Type I error rate — the probability of incorrectly rejecting a true null hypothesis. It does not describe the probability that H₀ is true, nor is it the same as power (which is 1 − β).
Cycle time data from two independent production lines fails a normality test. A Black Belt wants to compare central tendency between the two lines. Which test is most appropriate?
Answer: Mann-Whitney U test
The Mann-Whitney U test is the nonparametric equivalent of the two-sample t-test for independent groups. It compares medians and does not require the normality assumption, making it appropriate when data violates normality.
A CSSBB wants to test whether observed defect counts across five product categories follow a historically expected distribution. Which test should be applied?
Answer: Chi-square goodness-of-fit test
The chi-square goodness-of-fit test compares observed frequencies to expected frequencies derived from a theoretical or historical distribution. It is designed specifically for this use case, unlike the t-test or ANOVA which compare means.
A Black Belt increases sample size from n = 25 to n = 100 while keeping α = 0.05 fixed. What is the most likely result?
Answer: The power of the test increases
Power (1 − β) increases with larger sample sizes because larger samples reduce standard error, making it easier to detect a true effect. The Type I error rate (α) remains fixed by the researcher's choice and is not affected by sample size.
In a simple linear regression model, a Black Belt tests H₀: β₁ = 0 and obtains a p-value of 0.002 at α = 0.05. What is the correct conclusion?
Answer: Reject H₀; the slope coefficient is statistically significant
Since the p-value (0.002) is less than α (0.05), the null hypothesis H₀: β₁ = 0 is rejected. This means the predictor variable has a statistically significant linear relationship with the response variable. The p-value does not equal R², and the conclusion about β₁ says nothing about the intercept.