FREE Certified Six Sigma Black Belt Analyze Phase: Hypothesis Testing Questions and Answers

Question 1

A Six Sigma Black Belt is analyzing a process where the current defect rate is 5%.
The team hypothesizes that implementing a new training program will reduce this rate.
They want to test if the new training program leads to a statistically significant reduction in defects.
Which type of hypothesis test would be most appropriate for this scenario?

Accepted Answer

One-sample proportion test

Answer

Two-sample t-test

Answer

Chi-square test of independence

Answer

ANOVA (Analysis of Variance)

Question 2

In hypothesis testing, what is the primary risk associated with setting an alpha (α) level that is too high?

Accepted Answer

Increased probability of a Type I error (α error)

Answer

Increased probability of a Type II error (β error)

Answer

Failure to detect a true difference (power decreases)

Answer

Reduced sample size requirement

Question 3

A Black Belt is testing whether the mean tensile strength of a new material (Sample A) is significantly different from an existing material (Sample B). Both samples are independent, and it is assumed that their population variances are unequal. Which statistical test should the Black Belt use?

Accepted Answer

Two-sample t-test (Welch's t-test)

Answer

Paired t-test

Answer

One-sample Z-test

Answer

ANOVA

Question 4

Which of the following statements about the p-value in hypothesis testing is CORRECT?

Accepted Answer

A p-value less than alpha (α) indicates strong evidence to reject the null hypothesis.

Answer

The p-value represents the probability that the null hypothesis is true.

Answer

A higher p-value always implies a more significant result.

Answer

The p-value is the probability of a Type I error.

Question 5

A Six Sigma team is investigating if there is a relationship between the shift (Day, Evening, Night) and the type of defect (A, B, C) observed in a manufacturing process. The data consists of counts of defects for each shift and type. Which hypothesis test should the team employ?

Accepted Answer

Chi-square test of independence

Answer

Two-sample t-test

Answer

ANOVA

Answer

Regression analysis

Question 6

Before conducting a hypothesis test, a Black Belt must formulate both a null hypothesis (H0) and an alternative hypothesis (Ha). What is the fundamental principle guiding the formulation of the null hypothesis?

Accepted Answer

It represents the status quo or the absence of an effect/difference.

Answer

It always states that there is a significant difference or relationship.

Answer

It is what the Black Belt hopes to prove true through the analysis.

Answer

It must always be a two-tailed hypothesis.