418 CHAPTER 8 Hypothesis Testing with Two Samples Testing the Difference Between Means (Independent Samples, s1 and s2 Known) 8.1 What You Should Learn How to determine whether two samples are independent or dependent An introduction to two-sample hypothesis testing for the difference between two population parameters How to perform a two-sample z-test for the difference between two means m1 and m2 using independent samples with s1 and s2 known Independent and Dependent Samples An Overview ofTwo-Sample Hypothesis Testing Two-Sample z-Test for the Difference Between Means Sample 1 Sample 2 Independent Samples Sample 1 Sample 2 Dependent Samples Independent and Dependent Samples In Chapter 7, you studied methods for testing a claim about the value of a population parameter. In this chapter, you will learn how to test a claim comparing parameters from two populations. Before learning how to test the difference between two parameters, you need to understand the distinction between independent samples and dependent samples. Two samples are independent when the sample selected from one population is not related to the sample selected from the second population (see top figure at the left). Two samples are dependent when each member of one sample corresponds to a member of the other sample (see bottom figure at the left). Dependent samples are also called paired samples or matched samples. DEFINITION Independent and Dependent Samples Classify each pair of samples as independent or dependent. 1. Sample 1: Triglyceride levels of 70 patients Sample 2: Triglyceride levels of the same 70 patients after using a triglyceride-lowering drug for 6 months 2. Sample 1: Scores for 38 adult males on a psychological screening test for attention-deficit/hyperactivity disorder Sample 2: Scores for 50 adult females on a psychological screening test for attention-deficit/hyperactivity disorder SOLUTION 1. These samples are dependent. Because the triglyceride levels of the same patients are taken, the samples are related. The samples can be paired with respect to each patient. 2. These samples are independent. It is not possible to form a pairing between the members of samples, the sample sizes are different, and the data represent scores for different individuals. TRY IT YOURSELF 1 Classify each pair of samples as independent or dependent. 1. Sample 1: Systolic blood pressures of 30 adult females Sample 2: Systolic blood pressures of 30 adult males 2. Sample 1: Midterm exam scores of 14 chemistry students Sample 2: Final exam scores of the same 14 chemistry students Answer: Page A41 EXAMPLE 1 Study Tip Dependent samples often involve before and after results for the same person or object (such as a person’s weight before starting a weight-loss program and after 6 weeks), or results of individuals matched for specific characteristics (such as identical twins).
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