Hypothesis Testing Applications Flashcards
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A process engineer tests whether mean fill volume equals 500 mL using a one-sample t-test. The 95% confidence interval is (498.2, 501.8). What is the correct conclusion at α = 0.05?
Answer: Fail to reject H₀ because 500 is contained in the interval
A two-sided confidence interval that contains the hypothesized value corresponds to failing to reject H₀.
Which of the following best describes statistical power in hypothesis testing?
Answer: The probability of correctly rejecting a false null hypothesis
Power = 1 − β, representing the probability of correctly detecting a real effect when one exists.
A Black Belt wants to detect a shift of 1.5σ with 90% power and α = 0.05 (two-tailed). Which action most effectively increases power without changing α?
Answer: Increase the sample size
Increasing sample size is the primary lever to increase power while holding α constant.
The Mann-Whitney U test is the nonparametric alternative to which parametric test?
Answer: Independent two-sample t-test
The Mann-Whitney U test compares two independent groups without assuming normality, replacing the two-sample t-test.
A team uses a chi-square test of independence to analyze a 3×4 contingency table. What are the degrees of freedom?
Answer: 6
Degrees of freedom for a chi-square test of independence = (rows − 1)(columns − 1) = (3−1)(4−1) = 6.
Which scenario correctly calls for a one-tailed hypothesis test rather than a two-tailed test?
Answer: Testing whether a new material is stronger than the current material
When the research question specifies a direction (e.g., stronger), a one-tailed test is appropriate.
In a hypothesis test, the region where the test statistic leads to rejecting H₀ is called:
Answer: Critical region (rejection region)
The critical region is the set of test statistic values that fall beyond the critical value, leading to rejection of H₀.