Hypothesis Testing Applications Flashcards
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A quality engineer compares process variance before and after a change using an F-test. The p-value is 0.08 with α = 0.05. What should be concluded?
Answer: Fail to reject H₀; insufficient evidence that variances differ
p = 0.08 > α = 0.05, so there is insufficient evidence to conclude the variances are different.
Which nonparametric test is the appropriate alternative to the one-sample t-test when normality cannot be assumed?
Answer: Wilcoxon signed-rank test
The Wilcoxon signed-rank test is the nonparametric equivalent of the one-sample (or paired) t-test.
A Black Belt selects α = 0.01 instead of α = 0.05. What is the direct effect on the hypothesis test?
Answer: The probability of a Type I error decreases
Lowering α reduces the acceptable probability of a Type I error (false rejection of H₀).
When conducting a two-proportion z-test, what is the null hypothesis typically stated as?
Answer: p₁ = p₂
The null hypothesis for a two-proportion z-test states that the two population proportions are equal.
Levene's test is used in hypothesis testing to evaluate which property of data?
Answer: Equality of variances across groups
Levene's test assesses whether group variances are equal, a key assumption for ANOVA and t-tests.
A Six Sigma team performs 10 separate hypothesis tests at α = 0.05. Approximately what is the probability of at least one Type I error occurring?
Answer: 0.40
The family-wise error rate is 1 − (1 − 0.05)^10 ≈ 0.40, highlighting the risk of multiple comparisons.
In an equivalence test used in Six Sigma, the goal is to demonstrate that:
Answer: Two processes are practically equivalent within a defined margin
Equivalence testing (e.g., TOST) is designed to prove two processes are equivalent within a predefined acceptable margin.