Advanced Hypothesis Testing Flashcards
7 cards from real Certified Six Sigma Black Belt Exam practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
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A paired t-test is preferred over a two-sample t-test when:
Answer: Measurements are taken on the same subject under two conditions
Pairing on the same subject removes between-subject variability, making the paired t-test more powerful when natural pairs exist.
Bartlett's test is preferred over Levene's test when:
Answer: Data are approximately normally distributed
Bartlett's test assumes normality and is more powerful than Levene's test when that assumption holds.
In a chi-square test of independence, the degrees of freedom are calculated as:
Answer: (number of rows − 1) × (number of columns − 1)
Degrees of freedom for a chi-square test of independence = (r − 1)(c − 1), where r = rows and c = columns.
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:
Answer: 0.64
Family-wise error rate = 1 − (1 − 0.05)²⁰ ≈ 0.64, meaning there is about a 64% chance of at least one spurious rejection.
Which correction is commonly applied to control the family-wise error rate when performing multiple comparisons?
Answer: Bonferroni correction
The Bonferroni correction divides alpha by the number of tests (α/k), maintaining the family-wise error rate at the desired level.
When sample size increases, holding alpha constant, what happens to the power of a hypothesis test?
Answer: Power increases because the standard error decreases
Larger samples reduce the standard error, shrink the confidence interval, and improve the test's ability to detect true differences.
A Mood's Median test is used to:
Answer: Test whether multiple population medians are equal
Mood's Median test is a nonparametric test for comparing medians across two or more independent groups.