Chapter 6

# Chapter 6 - CHAPTER 6: INFERENCES ABOUT TWO POPULATION...

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CHAPTER 6: INFERENCES ABOUT TWO POPULATION CENTRAL VALUES 6.1 DEPENDENT AND INDEPENDENT SAMPLES In chapter 5 , we studied methods for testing a claim about the value of a population parameter. In this chapter, we will learn how to test a claim comparing parameters from two populations. Again, the claims that we test regard the difference between two population means and the difference between two population proportions. To perform inference on the difference of two population means, we need two samples, one from each population. Two basic kinds of samples can be used: independent samples and dependent samples . The dependence or independence of two samples is determined by the sources of the data. A source can be a person, an object, or anything that yield a data value. If the same set of sources or related sets are used to obtain the data representing both populations, we have dependent samples . Putting it differently, a sampling method is dependent when the individuals selected to be in one sample are used to determine the individuals selected to be in the second sample. Dependent samples are often referred to as matched-pairs samples . If two unrelated sets of sources are used, one set from each population, we have independent samples . By independent samples we mean that the sample selected from one of the populations has no effect or bearing on the sample selected from the other population. In other words, two samples are said to be independent samples if the sample selected from one population is not related to the sample selected from the second population. The following examples should clarify these ideas. EXAMPLE 6.1 Problem : A test will be conducted to see whether the participants in a physical fitness class actually improve in their level of fitness. It is anticipated that approximately 600 people will sign up for this course. The instructor decides that she will give 60 of the participants at the end of the course (a posttest). Two sampling procedures are proposed: Plan A : Randomly select 60 participants from the list of those enrolled and give them the pretest. At the end of the course, make a second random selection of size 60 and give them the posttest. Plan B : Randomly select 60 participants and give them the pretest; give the same set of 60 the posttest when they complete the course. Identify which sampling procedure (dependent or independent) each plan ( Plan A or Plan B ) illustrates? Solution : Dr. LOHAKA – QBA 2302 Chapter 6: INFERENCES ABOUT 2 POPULATION VALUES Page 242

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Plan A illustrates independent sampling ; the sources (the class participants) used for each sample (pretest and posttest) were selected separately. Plan B illustrates dependent sampling ; the sources used for both samples (pretest and posttest) are the same. EXAMPLE 6.2
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## This note was uploaded on 04/15/2008 for the course QBA 2302 taught by Professor Dr.lohaka during the Spring '08 term at Baylor.

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Chapter 6 - CHAPTER 6: INFERENCES ABOUT TWO POPULATION...

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