Certified Six Sigma Black Belt Exam Hypothesis Testing Applications 2

Question 1

A Six Sigma team runs a two-sample t-test and obtains a p-value of 0.03 with α = 0.05. What is the correct conclusion?

Accepted Answer

Reject H₀ because p < α

Answer

When p < α, there is sufficient evidence to reject the null hypothesis.

Question 2

Which assumption must be verified before performing a paired t-test?

Accepted Answer

The differences between pairs are approximately normally distributed

Answer

A paired t-test requires that the within-pair differences are approximately normally distributed.

Question 3

An engineer wants to test whether a new process reduces defect rates compared to the old process. Which hypothesis setup is correct?

Accepted Answer

H₀: μnew ≥ μold, H₁: μnew < μold

Answer

A one-tailed (lower-tail) test is appropriate when the goal is to show the new process has fewer defects.

Question 4

What is the consequence of increasing sample size on hypothesis test power, assuming all else remains constant?

Accepted Answer

Power increases because the standard error decreases

Answer

Larger samples reduce standard error, making it easier to detect true effects and increasing statistical power.

Question 5

When applying a chi-square goodness-of-fit test, which condition must be satisfied for valid results?

Accepted Answer

All expected cell frequencies must be at least 5

Answer

The chi-square approximation is unreliable when expected cell counts fall below 5; cells may need to be combined.

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