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Objectives After completing this chapter, you should be able to 1 Understand the defnitions used in hypothesis testing. 2 State the null and alternative hypotheses. 3 Find critical values ±or the z test. 4 State the fve steps used in hypothesis testing. 5 Test means ±or large samples, using the z test. 6 Test means ±or small samples, using the t test. 7 Test proportions, using the z test. 8 Test variances or standard deviations, using the chi-square test. 9 Test hypotheses, using confdence intervals. 10 Explain the relationship between type I and type II errors and the power o± a test. Outline 8–1 Introduction 8–2 Steps in Hypothesis Testing—Traditional Method 8–3 z Test for a Mean 8–4 t 8–5 Test for a Proportion 8–6 X 2 Test for a Variance or Standard Deviation 8–7 Additional Topics Regarding Hypothesis Testing 8–8 Summary 8–1 8 8 Hypothesis Testing CHAPTER
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392 Chapter 8 Hypothesis Testing 8–2 Statistics Today How Much Better Is Better? Suppose a school superintendent reads an article which states that the overall mean score for the SAT is 910. Furthermore, suppose that, for a sample of students, the average of the SAT scores in the superintendent’s school district is 960. Can the superintendent conclude that the students in his school district scored higher than average? At ±rst glance, you might be inclined to say yes, since 960 is higher than 910. But recall that the means of samples vary about the population mean when samples are selected from a speci±c pop- ulation. So the question arises, Is there a real difference in the means, or is the difference simply due to chance (i.e., sampling error)? In this chapter, you will learn how to answer that question by using statistics that explain hypothesis testing. See Statistics Today— Revisited for the answer. In this chapter, you will learn how to answer many questions of this type by using statistics that are explained in the theory of hypothesis testing. 8–1 Introduction Researchers are interested in answering many types of questions. For example, a scien- tist might want to know whether the earth is warming up. A physician might want to know whether a new medication will lower a person’s blood pressure. An educator might wish to see whether a new teaching technique is better than a traditional one. A retail merchant might want to know whether the public prefers a certain color in a new line of fashion. Automobile manufacturers are interested in determining whether seat belts will reduce the severity of injuries caused by accidents. These types of questions can be addressed through statistical hypothesis testing, which is a decision-making process for evaluating claims about a population. In hypothesis testing, the researcher must de±ne the population under study, state the particular hypotheses that will be investigated, give the signi±cance level, select a sample from the population, collect the data, perform the calculations required for the statistical test, and reach a conclusion.
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This note was uploaded on 11/25/2011 for the course MATH 063 taught by Professor Soshiani during the Spring '09 term at San Jose City College.

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ch08 - blu03683_ch08.qxd 09/19/2005 04:22 PM Page 391...

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