# Choose and Explain a Classical Hypothesis Test Explain null and alternative hypotheses, significance level, p-value, Type I error, and Type II error. Then compare when a z-test, t-test, chi-square test, and F-test is appropriate. For each test, name the parameter or relationship being tested, its assumptions, and what a statistically significant result does and does not establish. ### Constraints & Assumptions - Use frequentist definitions for this question. - Distinguish a test statistic's reference distribution from the observed data distribution. - Address independence and distributional assumptions rather than selecting from sample size alone. - Do not interpret a p-value as the probability that the null hypothesis is true. ### Clarifying Questions to Ask - Is the outcome continuous, categorical, or a variance estimate? - Are samples paired, independent, or grouped? - Are normality and equal-variance assumptions plausible, and is the variance known? ```hint Start from the estimand Choose the test only after naming whether the target is a mean, proportion, independence relationship, or variance ratio. ``` ```hint State the reference world A p-value measures how extreme the statistic is under the null model and its assumptions. ``` ### What a Strong Answer Covers - Precise definitions and the relationship between alpha and Type I error under the null. - Power and Type II error as functions of effect size, variability, sample size, and test design. - Correct use cases and assumptions for all four named test families. - Interpretation that separates statistical significance, effect size, and practical importance. ### Follow-up Questions - How would multiple testing change the decision threshold? - What would you report alongside a p-value to communicate magnitude and uncertainty?