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
The Wilcoxon signed-rank test is the nonparametric equivalent of:
Answer: One-sample or paired t-test
The Wilcoxon signed-rank test handles one-sample or paired data, making it the nonparametric counterpart of the one-sample and paired t-tests.
A Black Belt finds a statistically significant difference but the effect size (Cohen's d) is 0.08. This result is best described as:
Answer: Statistically significant but practically trivial
Cohen's d of 0.08 is far below the conventional small-effect threshold of 0.2, indicating the detected difference is unlikely to be practically meaningful.
In a two-proportion z-test, the pooled proportion p̂ is used because:
Answer: Under H₀ the two populations share a common proportion
Under the null hypothesis of equal proportions, both samples estimate the same population proportion, so a pooled estimate is the best single estimate to use in the standard error.
Which test statistic is used in a chi-square goodness-of-fit test?
Answer: Σ (O − E)² / E
The chi-square statistic sums the squared differences between observed (O) and expected (E) frequencies, divided by expected frequency, across all categories.
A Black Belt sets α = 0.01 instead of α = 0.05. This decision:
Answer: Reduces power and reduces Type I error risk
Tightening alpha reduces the chance of a false positive (Type I error) but makes it harder to detect real effects, thereby reducing power.
Which of the following correctly describes a two-sided (two-tailed) alternative hypothesis?
Answer: H₁: μ ≠ μ₀
A two-sided alternative hypothesis states that the parameter differs from the null value in either direction, using the ≠ symbol.
In an ANOVA F-test, what does a large F-statistic indicate?
Answer: The between-group variance is large relative to within-group variance
F = MSbetween / MSwithin; a large F means treatment effects explain much more variability than random error, suggesting group means differ.