Certified Six Sigma Black Belt Exam FREE Certified Six Sigma Black Belt Hypothesis Testing Applications Questions and Answers 2 — Questions and Answers
Question 1: A Black Belt wants to determine if a new supplier's material thickness differs from the current supplier's specification of 2.5 mm. Which hypothesis test is most appropriate?
- One-sample t-test (Correct answer)
- Two-sample t-test
- Paired t-test
- Chi-square test
Correct answer: One-sample t-test
A one-sample t-test compares a sample mean against a known or specified population value.
Question 2: When conducting a hypothesis test comparing defect rates across three production shifts, which test should be applied?
- One-way ANOVA
- Two-sample t-test
- Chi-square test of independence (Correct answer)
- Paired t-test
Correct answer: Chi-square test of independence
A chi-square test of independence evaluates whether categorical outcomes like defect rates differ across multiple groups.
Question 3: A team suspects that calibrating equipment before each run reduces measurement variation. They measure variation before and after calibration on the same instruments. Which test applies?
- Two-sample t-test
- One-sample z-test
- F-test for equality of variances
- Paired t-test (Correct answer)
Correct answer: Paired t-test
A paired t-test is used when comparing two related measurements taken on the same subjects.
Question 4: In a hypothesis test, a Black Belt obtains a p-value of 0.03 with a significance level of 0.05. What is the correct conclusion?
- Fail to reject the null hypothesis
- Reject the null hypothesis (Correct answer)
- Accept the alternative hypothesis unconditionally
- The test is inconclusive
Correct answer: Reject the null hypothesis
When the p-value is less than the significance level, the null hypothesis is rejected.
Question 5: A process improvement team wants to verify whether the variance of fill weights has been reduced after implementing a new filling nozzle. Which test is most appropriate?
- Two-sample t-test
- F-test (or Levene's test) (Correct answer)
- One-sample z-test
- Chi-square goodness-of-fit test
Correct answer: F-test (or Levene's test)
An F-test or Levene's test compares variances between two samples to determine if they differ significantly.
Question 6: A Black Belt increases sample size from 30 to 120 while keeping significance level constant. What is the primary effect on the hypothesis test?
- Type I error increases
- Power of the test increases (Correct answer)
- The p-value automatically decreases
- The significance level changes
Correct answer: Power of the test increases
Increasing sample size reduces standard error, making it easier to detect a true difference and thus increasing statistical power.
Certified Six Sigma Black Belt Exam FREE Certified Six Sigma Black Belt Hypothesis Testing Applications Questions and Answers 2
A Black Belt wants to determine if a new supplier's material thickness differs from the current supplier's specification of 2.5 mm.
Which hypothesis test is most appropriate?