Lesson 1: 9.1 Significance Tests: The Basics

1. What is the difference between a "null" hypothesis and an "alternative" hypothesis?

2. What does a P-value actually measure: the probability the null is true, or the probability of our data occurring if the null is true?

3. What are the consequences of being wrong in two different ways (Type I vs. Type II)?

AP Stats CED: SRE-1.A (Null/Alt Hypotheses), SRE-1.B (P-values), SRE-1.C (Type I/II Errors). Common Core: HSS-IC.B.5.

Description
This section introduces the logic of proof by contradiction. We assume a claim is true and see if our sample data is so unlikely (low P-value) that we must reject that claim in favor of a new one. It covers one-sided vs. two-sided tests and the formal definitions of Type I (false positive) and Type II (false negative) errors.

Purpose
To provide a standardized, objective way to weigh evidence. This is the "Judge and Jury" phase of statistics—determining if an observed effect is "statistically significant" or just a result of random chance.

DOK Level
Level 3 (Strategic Thinking): Students must evaluate the "cost" of Type I and Type II errors in real-world scenarios (like medical testing or legal trials) to decide which error is more dangerous and adjust alpha accordingly.

Struggling Learners: Use the "Courtroom Analogy." Ho is "Innocent until proven guilty." The P-value is the evidence. A small P-value is like finding a smoking gun—it's so unlikely to happen if the person were innocent that we must "Reject" innocence.

Advanced Learners: Have them explore the power of a test. Ask: "If we make alpha smaller to avoid a Type I error, what happens to our chance of a Type II error?" They should realize the inverse relationship between the two.

ELL Learners: Focus on the "Null" prefix. Explain that Null = No Change or No Difference. Use visual "Logic Signs":

Formative assessment; vocabulary checks in context