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PSLS.PPT.Ch15 - Inferenceinpractice PSLS chapter 15 2009...

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    Inference in practice PSLS chapter 15 © 2009 W.H. Freeman and Company
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Objectives (PSLS chapter 15) Inference in practice Confidence intervals in practice Significance tests in practice Beware of multiple analyses Caution about z procedures for a population mean
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The margin of error does not cover all errors: The margin of error in a confidence interval covers only random sampling error. Undercoverage, nonresponse, or other forms of bias are often more serious than random sampling error (e.g., our elections polls). The margin of error does not take these into account at all. Remember: Surveys typically have > 50% non-response! Only government survey have a lower rate. Confidence intervals in practice
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Sample size and experimental design You may need a certain margin of error (e.g., drug trial, manufacturing specs). In many cases, the population variability ( σ 29 is fixed, but we can choose the number of measurements ( n ). So plan ahead what sample size to use to achieve that margin of error. m = z * σ n n = z * σ m 2 Sample size is not always stretchable at will. There are costs and constraints associated with large samples.
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What sample size for a given margin of error? Density of bacteria in solution: Measurement equipment has standard deviation σ = 1 million bacteria/ml fluid. How many measurements should you make to obtain a margin of error of at most 0.5 million bacteria/ml with a confidence level of 90%? For a 90% confidence interval, z *= 1.645. 8241 . 10 29 . 3 5 . 0 1 * 645 . 1 * 2 2 2 = = = = n m z n σ Using only 10 measurements will not be enough to ensure that m is no more than 0.5 million/ml. Therefore, we need at least 11 measurements.
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Statistical significance only says whether the effect observed is likely to be due to chance alone because of random sampling.
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