Free Certified Six Sigma Black Belt Hypothesis Testing Applications Questions and Answers

Question 1

A Six Sigma team wants to determine if there is a statistically significant difference in the average processing time (a continuous variable) among three different operational shifts.
Which of the following hypothesis tests is the most appropriate to use?

Accepted Answer

ANOVA (Analysis of Variance)

Answer

2-sample t-test

Answer

Paired t-test

Answer

Chi-Square Test

Question 2

A project team implemented a process change to reduce the proportion of defective products. A 2-proportion test was conducted, yielding a p-value of 0.025. Using a standard significance level (alpha) of 0.05, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; the change resulted in a statistically significant reduction in defects.

Answer

Fail to reject the null hypothesis; there is no evidence of a change in the defect rate.

Answer

The results are inconclusive and require a larger sample size.

Answer

Accept the null hypothesis; the process change had no effect on the defect rate.

Question 3

A Black Belt is preparing to compare the mean performance of two independent groups using a 2-sample t-test. For the results of this parametric test to be valid, which of the following is a critical assumption?

Accepted Answer

The data from both populations should be approximately normally distributed.

Answer

The data in both samples must be attribute data.

Answer

The two samples must have exactly the same number of data points.

Answer

The variances of the two populations must be unequal.

Question 4

A quality manager wants to determine if there is a statistically significant association between the type of paint defect (e.g., 'Cracking', 'Peeling', 'Blistering') and the production line ('Line A', 'Line B', 'Line C') on which the product was painted. What is the most appropriate statistical test for this analysis?

Accepted Answer

Chi-Square Test of Independence

Answer

ANOVA

Answer

1-proportion test

Answer

Pearson Correlation

Question 5

A team is testing a new manufacturing process to see if it reduces the average cycle time, which has historically been 45 minutes. Which of the following represents the correct null hypothesis (H0) for a one-tailed test to determine if the new process is an improvement?

Accepted Answer

H0: μ ≥ 45 minutes

Answer

H0: μ < 45 minutes

Answer

H0: μ ≠ 45 minutes

Answer

Ha: μ < 45 minutes

Question 6

Before conducting a 2-sample t-test, a Black Belt wants to check the assumption of equal variances between the two independent samples. Which statistical test is specifically designed to compare the variances of two populations?

Accepted Answer

F-test

Answer

Paired t-test

Answer

ANOVA

Answer

Goodness-of-Fit Test