Notes,hws - Introduction to Inference Estimating with...

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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, . 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 . n Sample means, n subjects n Population, x individual subjects x x If the population is normally distributed N ( , ), so will the sampling distribution N ( , / n ), Red dot: mean value of individual sample 95% of all sample means will be within roughly 2 standard deviations (2* / n ) of the population parameter . Distances are symmetrical which implies that the population parameter must be within roughly 2 standard deviations from the sample average , in 95% of all samples. This reasoning is the essence of statistical inference. n x We know . ) ( * * C n z x n z P = + - This leads to the relationship . ) ( * * C n z x n z x P = + - . ) / ( * * C z n x z P = - - The weight of single eggs of the brown variety is normally distributed N (65 g,5 g)....
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Notes,hws - Introduction to Inference Estimating with...

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