Certified Six Sigma Black Belt Advanced Hypothesis Testing Questions and Answers

Question 1

A Six Sigma Black Belt is analyzing customer satisfaction scores (on a 1-10 scale) for three different service centers (A, B, C).
The data is not normally distributed, and a test for equal variances has failed.
Which non-parametric test is most appropriate to determine if there is a statistically significant difference in the median satisfaction scores among the three centers?

Accepted Answer

Kruskal-Wallis Test

Answer

ANOVA

Answer

Mann-Whitney U Test

Answer

1-sample Sign Test

Question 2

A project team is investigating the relationship between the type of raw material supplier (four suppliers, a categorical variable) and the occurrence of a specific defect (present/absent, a categorical variable). Which statistical test should be used to determine if there is a significant association between the supplier and the defect rate?

Accepted Answer

Chi-Square Test of Independence

Answer

2-sample t-test

Answer

Mood's Median Test

Answer

Simple Linear Regression

Question 3

When performing an Analysis of Variance (ANOVA), a key assumption is the homogeneity of variances. If a Black Belt suspects the data may not be normally distributed, which test is more robust for verifying the equality of variances among the groups?

Accepted Answer

Levene's Test

Answer

Bartlett's Test

Answer

Anderson-Darling Test

Answer

Shapiro-Wilk Test

Question 4

A Black Belt wants to analyze the effect of a new training program (a categorical factor with two levels: 'New' and 'Old') on employee productivity (a continuous variable). However, they know that an employee's prior experience (a continuous variable, measured in months) also significantly impacts productivity. To isolate the effect of the training program while accounting for the influence of prior experience, which statistical technique is most appropriate?

Accepted Answer

Analysis of Covariance (ANCOVA)

Answer

Multiple Regression

Answer

Two-Way ANOVA

Answer

Mann-Whitney U Test

Question 5

In a multiple regression analysis, a Six Sigma team is concerned about multicollinearity. Which of the following is the BEST indicator that multicollinearity is a problem in their model?

Accepted Answer

High Variance Inflation Factor (VIF) values for predictor variables.

Answer

A low R-squared value.

Answer

A high p-value for the overall F-test.

Answer

Residuals that are not normally distributed.

Question 6

Which of the following scenarios is the most appropriate application for a non-parametric hypothesis test?

Accepted Answer

Comparing the median cycle times of three production lines where the data for each line is highly skewed.

Answer

Comparing the means of two large, normally distributed samples with equal variances.

Answer

Analyzing the relationship between two continuous variables that show a strong linear pattern.

Answer

Testing if the variance of a normally distributed process output is equal to a target value.