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Unformatted text preview: Introduction to Inference Estimating with Confidence © 2009 W.H. Freeman and Company Objectives Estimating with confidence Statistical confidence Confidence intervals Confidence interval for a population mean How confidence intervals behave Choosing the sample size Overview of Inference Methods for drawing conclusions about a population from sample data are called statistical inference Methods Confidence Intervals estimating a value of a population parameter Tests of significance assess evidence for a claim about a population Inference is appropriate when data are produced by either a random sample or a randomized experiment Statistical confidence Although the sample mean, , is a unique number for any particular sample, if you pick a different sample you will probably get a different sample mean. In fact, you could get many different values for the sample mean, and virtually none of them would actually equal the true population mean, μ . x But the sample distribution is narrower than the population distribution, by a factor of √ n . Thus, the estimates gained from our samples are always relatively close to the population parameter µ . n Sample means, n subjects μ n σ σ Population, x individual subjects x x If the population is normally distributed N ( µ , σ ), so will the sampling distribution N ( µ , σ /√ n ), Red dot: mean value of individual sample 95% of all sample means will be within roughly 2 standard deviations (2* σ /√ n ) of the population parameter μ. Distances are symmetrical which implies that the population parameter μ must be within roughly 2 standard deviations from the sample average , in 95% of all samples. This reasoning is the essence of statistical inference. σ n € x We know . ) ( * * C n z x n z P = + ≤ ≤ σ μ σ μ This leads to the relationship . ) ( * * C n z x n z x P = + ≤ ≤ σ μ σ . ) / ( * * C z n x z P = ≤ ≤ σ μ The weight of single eggs of the brown variety is normally distributed N (65 g,5 g)....
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 Spring '08
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 Normal Distribution, Standard Deviation, Confidence Level

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