Chapter 10 - Comparing two means and two proportions. After mastering the material in this chapter, you will be able to: Compare two population means when the samples are independent, recognize when data come from independent samples and when they are paired, compare two population means when the data are paired, compare two population proportions using large independent samples. | Chapter 10 Comparing Two Means and Two Proportions Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Statistical Inferences Based on Two Samples Comparing Two Population Means by Using Independent Samples Paired Difference Experiments Comparing Two Population Proportions by Using Large, Independent Samples 10- Comparing Two Population Means by Using Independent Samples Suppose a random sample has been taken from each of two different populations Suppose that the populations are independent of each other Then the random samples are independent of each other Then the sampling distribution of the difference in sample means is normally distributed LO10-1: Compare two population means when the samples are independent. 10- Sampling Distribution of the Difference of Two Sample Means #1 Suppose population 1 has mean µ1 and variance σ12 From population 1, a random sample of size n1 is selected which has mean 1 . | Chapter 10 Comparing Two Means and Two Proportions Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Statistical Inferences Based on Two Samples Comparing Two Population Means by Using Independent Samples Paired Difference Experiments Comparing Two Population Proportions by Using Large, Independent Samples 10- Comparing Two Population Means by Using Independent Samples Suppose a random sample has been taken from each of two different populations Suppose that the populations are independent of each other Then the random samples are independent of each other Then the sampling distribution of the difference in sample means is normally distributed LO10-1: Compare two population means when the samples are independent. 10- Sampling Distribution of the Difference of Two Sample Means #1 Suppose population 1 has mean µ1 and variance σ12 From population 1, a random sample of size n1 is selected which has mean 1 and variance s12 Suppose population 2 has mean µ2 and variance σ22 From population 2, a random sample of size n2 is selected which has mean 2 and variance s22 Then the sample distribution of the difference of two sample means LO10-1 10- Sampling Distribution of the Difference of Two Sample Means #2 Is normal, if each of the sampled populations is normal Approximately normal if the sample sizes n1 and n2 are large Has mean µx1–x2 = µ1 – µ2 Has standard deviation LO10-1 10- t-Based Confidence Interval for the Difference in Means: Equal Variances LO10-1 10- t-Based Test About the Difference in Means: Equal Variance LO10-1 10- Paired Difference Experiments Before, drew random samples from two different populations Now, have two different processes (or methods) Draw one random sample of units and use those units to obtain the results of each process LO10-2: Recognize when data come from independent samples and when they are paired. 10- Paired .
