Test%20Four%20Notes%20-%20Part%201

Test%20Four%20Notes%20-%20Part%201 - Chapter 9 Statistical...

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Page 1 of 86 Chapter 9 Statistical Inference: Significance Tests about Hypotheses (Hypothesis Testing) 9.1: What are the steps for performing a Significance Test? In this section we will introduce the language and steps of significance testing. The procedures will be addressed in later sections of Chapter 9. Basics of Significance Testing 1. A statement is made about a population parameter. 2. A claim is made that this statement is incorrect. 3. Evidence (sample data) is collected in order to test the claim. 4. The data are analyzed in order to support or refute the claim. Example: A car manufacturer advertises a mean gas mileage of 26 mpg. A consumer group claims that the mean gas mileage is less than 26 mpg. A sample of 33 cars is taken and the sample mean for these 33 cars is 25.2 mpg. Significance testing is a procedure, based on sample evidence and probability, used to test claims regarding a characteristic of one or more populations. We use sample data to test hypotheses. Page 2 of 86 The Five Steps of a Significance Test: 1. Assumptions 2. Hypotheses 3. Test Statistic 4. P-value 5. Conclusion Page 3 of 86 1. Assumptions – each type of test will have certain assumptions that we need to check (ex. is the sample size large enough?) 2. Hypotheses Each significance test has two hypotheses about a population parameter: the null and alternative hypotheses. The null hypothesis , denoted H 0 (read “H-naught”) is a statement to be tested. The null hypothesis is assumed true until evidence indicates otherwise. In this chapter, it will be a statement regarding the value of a population parameter. In our car example, the null hypothesis is H 0 : μ = 26 mpg This is the statement made by the car manufacturer that we have to accept as true before we test the claim. The alternative hypothesis , denoted H A , is a claim to be tested. Generally, this is a statement that says the population parameter has a value different, in some way, from the value given in the null hypothesis. In experiments, we are usually trying to find evidence for the alternative hypothesis. In our car example, the alternative hypothesis is H A : μ < 26 mpg This is the claim made by the consumer group, that the mileage is less than what the car manufacturer stated. Page 4 of 86 There are three ways to set up the null and alternative hypotheses. 1. Less than test (left-tailed test) H 0 : parameter = some value H A : parameter < some value Example: A car manufacturer advertises a mean gas mileage of 26 mpg. A consumer group claims that the mean gas mileage is less than 26 mpg. 2. Greater than test (right-tailed test) H 0 : parameter = some value H A : parameter > some value Example: A newspaper states that a candidate will receive 46% of the votes in an upcoming election. An analyst believes the percentage will be higher than 46%.
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This note was uploaded on 09/10/2011 for the course STAT 2000 taught by Professor Smith during the Spring '08 term at University of Georgia Athens.

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Test%20Four%20Notes%20-%20Part%201 - Chapter 9 Statistical...

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