Hypothesis Testing Applications Flashcards
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A Black Belt applies Tukey's HSD post-hoc test after a significant ANOVA. What is its primary purpose?
Answer: To identify which specific pairs of group means differ significantly
Tukey's HSD controls family-wise error rate while identifying which specific mean pairs are statistically different.
For a hypothesis test on proportions with n = 200 and p̂ = 0.12, which condition justifies using the normal approximation?
Answer: np̂ ≥ 5 and n(1−p̂) ≥ 5
The normal approximation for proportions is valid when both np̂ and n(1−p̂) are at least 5.
What does a Bartlett's test evaluate, and when is it preferred over Levene's test?
Answer: It tests equality of variances and is preferred when data are normally distributed
Bartlett's test is more powerful than Levene's for normally distributed data but is sensitive to non-normality.
A Six Sigma project measures cycle time before and after improvement for the same 25 units. Which test is most appropriate?
Answer: Paired t-test
When the same units are measured twice (before/after), a paired t-test is appropriate as it accounts for within-unit correlation.
Which statement correctly describes the relationship between confidence level and significance level?
Answer: Confidence level = 1 − α
A 95% confidence interval corresponds to α = 0.05, so confidence level = 1 − α.
During a hypothesis test, the p-value is best interpreted as:
Answer: The probability of observing results at least as extreme as those obtained, assuming H₀ is true
The p-value is the conditional probability of the observed (or more extreme) data given that H₀ is true.
A process team observes that their hypothesis test produces a statistically significant result, but the practical effect size is negligible. What does this most likely indicate?
Answer: The sample size was very large, making even trivial differences detectable
With very large samples, even practically meaningless differences can achieve statistical significance; effect size must also be evaluated.