Chapter15

The Basic Practice of Statistics (Paper) & Student CD

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Tests of significance: The basics BPS chapter 15 © 2006 W.H. Freeman and Company
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Objectives (BPS chapter 15) Tests of significance: the basics The reasoning of tests of significance Stating hypotheses Test statistics P -values Statistical significance Tests for a population mean Using tables of critical values Tests from confidence intervals
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We have seen that the properties of the sampling distribution of x bar help us estimate a range of likely values for population mean μ . We can also rely on the properties of the sample distribution to test hypotheses. Example: You are in charge of quality control in your food company. You sample randomly four packs of cherry tomatoes, each labeled 1/2 lb. (227 g). The average weight from your four boxes is 222 g. Obviously, we cannot expect boxes filled with whole tomatoes to all weigh exactly half a pound. Thus: Is the somewhat smaller weight simply due to chance variation? Is it evidence that the calibrating machine that sorts cherry tomatoes into packs needs revision?
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Hypotheses tests A test of statistical significance tests a specific hypothesis using sample data to decide on the validity of the hypothesis. In statistics, a hypothesis is an assumption, or a theory about the characteristics of one or more variables in one or more populations. What you want to know: Does the calibrating machine that sorts cherry tomatoes into packs need revision? The same question reframed statistically: Is the population mean µ for the distribution of weights of cherry tomato packages equal to 227 g (i.e., half a pound)?
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Apply your knowledge Go to pages 364-365 and work on the following problems: 15.1 Anemia 15.2 Student attitudes
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The null hypothesis is the statement being tested. It is a statement of “no effect” or “no difference,” and it is labeled H 0 . The alternative hypothesis is the claim we are trying to find evidence for , and it is labeled H a . Weight of cherry tomato packs: H 0 : µ = 227 g ( µ is the average weight of the population of packs) H a : µ 227 g ( µ is either larger or smaller)
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One-sided and two-sided tests A two-tail or two-sided test of the population mean has these null and alternative hypotheses: H 0 : µ = [a specific number] H a : µ
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Chapter15 - Tests of significance: The basics BPS chapter...

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