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# Section6.1posted - STOR 155, Section 2 Tuesday, April 6,...

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STOR 155, Section 2 Tuesday, April 6, 2010 Section 6.1

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Chapter 6: Introduction to Inference Basic question: What can we say about a population, given the information in a sample? Specific question addressed in this chapter for illustration: Suppose we know the population is Normal we know the population standard deviation σ we don’t know the population mean μ we take a sample and we know the sample mean x. What can we say about μ ? _
Two types of inference: Confidence interval (Section 6.1): An interval around x that we believe contains μ, with a level of confidence that we can specify. Test of significance (Section 6.2): A decision about whether μ equals some hypothesized value, or whether the observed x would be too improbable if that were the case. (Will also cover Section 6.3 on use and abuse of tests. Will omit Section 6.4.) Chapter 6: Introduction to Inference _ _

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Population is Normal; mean is μ and standard deviation is σ . Sample of size n has mean x. Then (from 5.2) x is a Normal random variable, with mean μ and standard deviation σ / n. So (68-95-99.7) the probability is 95% that x is within 2 σ / n of μ. More accurately, within 1.96
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## Section6.1posted - STOR 155, Section 2 Tuesday, April 6,...

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