AP STATISTICS LESSON COMPARING TWO PROPORTIONS

ESSENTIAL QUESTION: What are the procedures that are used in finding confidence interval and significance tests for two sample proportions? Objectives: To find confidence intervals for two sample proportions. To find the probability of a situation involving two sample proportions by using significance test. To use both two proportion significance tests and confidence intervals to make inferences.

Comparing Two Proportions In a two-sample problem, we want to compare two proportions or the response to two treatments based on two independent samples. We compare the population by doing inference about the difference p 1 – p 2 between the population proportions. The statistic that estimates this difference is the difference between the two sample proportions p 1 – p 2. ^^

Variables and Notation Population Proportion Sample Size Sample Proportion 1p1p1 n1n1 p1p1 2p2p2 n2n2 p2p2 ^ ^

Example Page 702 Does Preschool Help? Preschool group: 62 attended preschool & 38 needed social services Control group: 61 students, 49 required social services. 80% of control group needed social services vs. 61% of the preschool group.

The Sampling Distribution p 1 – p 2 The statistic p 1 – p 2, is the difference between these two variables. The mean of p 1 – p 2 μ = μ – μ = p – p ^ ^ ^^