Certified Six Sigma Black Belt Exam Advanced Hypothesis Testing 3

Question 1

A paired t-test is preferred over a two-sample t-test when:

Accepted Answer

Measurements are taken on the same subject under two conditions

Answer

Pairing on the same subject removes between-subject variability, making the paired t-test more powerful when natural pairs exist.

Question 2

Bartlett's test is preferred over Levene's test when:

Accepted Answer

Data are approximately normally distributed

Answer

Bartlett's test assumes normality and is more powerful than Levene's test when that assumption holds.

Question 3

In a chi-square test of independence, the degrees of freedom are calculated as:

Accepted Answer

(number of rows − 1) × (number of columns − 1)

Answer

Degrees of freedom for a chi-square test of independence = (r − 1)(c − 1), where r = rows and c = columns.

Question 4

A Black Belt conducts 20 simultaneous hypothesis tests each at α = 0.05. The probability of at least one false positive (family-wise error) is approximately:

Accepted Answer

0.64

Answer

Family-wise error rate = 1 − (1 − 0.05)²⁰ ≈ 0.64, meaning there is about a 64% chance of at least one spurious rejection.

Question 5

Which correction is commonly applied to control the family-wise error rate when performing multiple comparisons?

Accepted Answer

Bonferroni correction

Answer

The Bonferroni correction divides alpha by the number of tests (α/k), maintaining the family-wise error rate at the desired level.

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Advanced Hypothesis Testing 3