Hypothesis Testing Applications Flashcards
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Read the first 7 Hypothesis Testing Applications flashcards as text
A Six Sigma team runs a two-sample t-test and obtains a p-value of 0.03 with α = 0.05. What is the correct conclusion?
Answer: Reject H₀ because p < α
When p < α, there is sufficient evidence to reject the null hypothesis.
Which assumption must be verified before performing a paired t-test?
Answer: The differences between pairs are approximately normally distributed
A paired t-test requires that the within-pair differences are approximately normally distributed.
An engineer wants to test whether a new process reduces defect rates compared to the old process. Which hypothesis setup is correct?
Answer: H₀: μnew ≥ μold, H₁: μnew < μold
A one-tailed (lower-tail) test is appropriate when the goal is to show the new process has fewer defects.
What is the consequence of increasing sample size on hypothesis test power, assuming all else remains constant?
Answer: Power increases because the standard error decreases
Larger samples reduce standard error, making it easier to detect true effects and increasing statistical power.
When applying a chi-square goodness-of-fit test, which condition must be satisfied for valid results?
Answer: All expected cell frequencies must be at least 5
The chi-square approximation is unreliable when expected cell counts fall below 5; cells may need to be combined.
A Black Belt uses ANOVA to compare the means of four process lines. If the F-statistic is significant, what does this tell you?
Answer: At least one pair of means is significantly different
A significant ANOVA F-test indicates at least one group mean differs, but post-hoc tests are needed to identify which pairs.
In hypothesis testing, a Type II error occurs when:
Answer: H₀ is not rejected when it is actually false
A Type II error (β) is failing to reject a false null hypothesis, meaning a real effect goes undetected.