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.
Read the first 7 Advanced Hypothesis Testing flashcards as text
A Black Belt uses a Z-test rather than a t-test. The primary justification for this choice is:
Answer: The population standard deviation is known
The Z-test is appropriate when the population standard deviation (σ) is known, which allows use of the standard normal distribution.
Which nonparametric test is equivalent to the two-sample independent t-test?
Answer: Mann-Whitney U test
The Mann-Whitney U test compares central tendencies of two independent samples without assuming normality, serving as the nonparametric alternative to the two-sample t-test.
A confidence interval and a hypothesis test at the same significance level will:
Answer: Produce equivalent conclusions — if H₀ value is outside the CI, reject H₀
A two-sided CI at (1 − α) confidence corresponds exactly to a two-sided hypothesis test at level α; exclusion of H₀ value from the CI equals rejection of H₀.
In hypothesis testing, which factor does NOT directly affect the width of the required sample size calculation?
Answer: The color of the measurement instrument
Sample size is mathematically determined by α, β (power), effect size, and variance — physical attributes of measuring tools are irrelevant to the formula.
The Anderson-Darling test is used in the context of hypothesis testing to:
Answer: Assess whether sample data follow a specified distribution
The Anderson-Darling test is a goodness-of-fit test that assesses how well sample data conform to a hypothesized distribution (commonly normality).
When using Tukey's HSD for post-hoc analysis after ANOVA, the primary purpose is to:
Answer: Identify which specific group pairs have significantly different means
Tukey's HSD controls the family-wise error rate while making all pairwise mean comparisons to pinpoint which groups differ after a significant ANOVA result.
A Black Belt observes that the test statistic falls exactly in the critical region boundary (t_calc = t_critical). The correct action is to:
Answer: Reject H₀, because the statistic meets the rejection criterion
By convention, when the test statistic equals the critical value the null hypothesis is rejected, as the p-value equals α exactly.