Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Advanced Hypothesis Testing Questions and Answers 2

Question 1

When conducting a two-sample t-test, what assumption must be evaluated if sample sizes are unequal and population variances are unknown?

Accepted Answer

Equal variances assumption using an F-test or Levene's test

Answer

Normal distribution of the population means

Answer

Independence of the sample standard deviations

Answer

Homogeneity of sample sizes

Question 2

In a hypothesis test, a Six Sigma Black Belt obtains a p-value of 0.03 with a significance level of 0.05. What is the correct interpretation?

Accepted Answer

Reject the null hypothesis; there is sufficient evidence of a statistically significant effect

Answer

Accept the alternative hypothesis as proven true

Answer

The probability that the null hypothesis is true is 3%

Answer

The effect size is practically significant

Question 3

A Black Belt wants to determine if a process change reduced the defect rate from a known historical proportion. Which hypothesis test is most appropriate?

Accepted Answer

One-proportion z-test

Answer

Two-sample t-test

Answer

Chi-square goodness-of-fit test

Answer

Paired t-test

Question 4

What is the primary risk of conducting multiple pairwise comparisons without adjusting the significance level?

Accepted Answer

Inflated family-wise Type I error rate

Answer

Decreased statistical power for each test

Answer

Increased Type II error for the overall analysis

Answer

Violation of the normality assumption

Question 5

A Black Belt uses an Anderson-Darling test before performing a one-sample t-test and obtains a p-value of 0.15. What should be concluded about the normality assumption?

Accepted Answer

Fail to reject normality; the data does not significantly deviate from a normal distribution

Answer

The data is confirmed to be perfectly normally distributed

Answer

The t-test results will definitely be valid

Answer

Normality is rejected and a nonparametric test must be used

Question 6

Which method is used to control the family-wise error rate when performing all pairwise comparisons after a significant one-way ANOVA result?

Accepted Answer

Tukey's Honestly Significant Difference (HSD) test

Answer

Increasing the sample size for each group

Answer

Repeating the ANOVA with different factor levels

Answer

Using a higher significance level for each comparison