Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Hypothesis Testing Applications 1

Question 1

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?

Accepted Answer

Right-tailed (upper-tail) test

Answer

Two-tailed test

Answer

Left-tailed (lower-tail) test

Answer

Chi-square goodness-of-fit test

Question 2

A Black Belt sets the significance level α = 0.05 before running a hypothesis test. Which statement correctly interprets this value?

Accepted Answer

There is a 5% probability of rejecting a true null hypothesis

Answer

There is a 5% chance the null hypothesis is true

Answer

The test will correctly detect a real effect 95% of the time

Answer

The alternative hypothesis has a 95% probability of being correct

Question 3

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?

Accepted Answer

Mann-Whitney U test

Answer

Paired t-test

Answer

Two-sample (independent) t-test

Answer

Levene's test

Question 4

A CSSBB wants to test whether observed defect counts across five product categories follow a historically expected distribution. Which test should be applied?

Accepted Answer

Chi-square goodness-of-fit test

Answer

One-sample t-test

Answer

Kruskal-Wallis test

Answer

One-way ANOVA

Question 5

A Black Belt increases sample size from n = 25 to n = 100 while keeping α = 0.05 fixed. What is the most likely result?

Accepted Answer

The power of the test increases

Answer

The Type I error rate increases

Answer

The significance level automatically adjusts downward

Answer

The null hypothesis becomes more likely to be accepted

Question 6

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?

Accepted Answer

Reject H₀; the slope coefficient is statistically significant

Answer

Fail to reject H₀; the predictor has no significant effect

Answer

The model explains 99.8% of the variation in the response

Answer

The regression intercept is also significantly different from zero