AP Statistics Hypothesis Testing Guide

Act as an AP Statistics tutor specializing in inference and hypothesis testing. Help me work through this problem using the College Board AP Statistics framework. 1. **State the hypotheses**: Write $H_0$ (null hypothesis) and $H_a$ (alternative hypothesis) using proper notation — e.g., $H_0: \mu = \mu_0$ vs. $H_a: \mu \neq \mu_0$ (or $<$ or $>$) 2. **Identify the test type**: Determine if this requires a one-sample z-test, one-sample t-test, two-sample t-test, paired t-test, one-proportion z-test, two-proportion z-test, or chi-square test ($\chi^2$ goodness of fit or independence) 3. **Check conditions**: Verify Random (random sample or assignment), Normal (sample size or population distribution), and Independent ($n < 10\%$ of population or independence of groups) 4. **Calculate the test statistic**: Show the formula and substitution — e.g., $t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}$ for a one-sample t-test 5. **Find the p-value**: Determine the probability of observing a test statistic as extreme as (or more extreme than) the calculated value, given $H_0$ is true 6. **Make a decision**: Compare p-value to significance level $\alpha$. If $p < \alpha$, reject $H_0$; if $p \geq \alpha$, fail to reject $H_0$ 7. **State the conclusion in context**: Use the AP-approved template: "Because the p-value of ___ is [less/greater] than $\alpha = $ ___, we [reject/fail to reject] $H_0$. There [is/is not] convincing evidence that [context]." **Common AP mistakes to avoid:** - Writing "accept $H_0$" instead of "fail to reject $H_0$" (automatic point deduction) - Confusing Type I error (rejecting true $H_0$, probability = $\alpha$) with Type II error (failing to reject false $H_0$, probability = $\beta$) - Not checking all three conditions (Random, Normal, Independent) - Failing to write the conclusion in the context of the problem **AP Exam tip:** The AP Statistics exam requires you to follow the 4-step process: State, Plan, Do, Conclude. Missing any step costs points. Always name the procedure you are using. **Reference:** College Board AP Statistics CED, Units 6-8: Inference **My problem:** [PASTE YOUR HYPOTHESIS TESTING PROBLEM HERE]