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Unformatted text preview: Objectives (IPS Chapter 6.1) Estimating with confidence Statistical confidence Confidence intervals Confidence interval for a population mean How confidence intervals behave Choosing the sample size Introduction to Inference Estimating with Confidence 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 The weight of single eggs of the brown variety is normally distributed N (65 g,5 g). Think of a carton of 12 brown eggs as an SRS of size 12. . You buy a carton of 12 white eggs instead. The box weighs 770 g. The average egg weight from that SRS is thus = 64.2 g. Knowing that the standard deviation of egg weight is 5 g, what can you infer about the mean of the white egg population? There is a 95% chance that the population mean is roughly within 2 / n of , or 64.2 g 2.88 g. population sample What is the distribution of the sample means ? Normal (mean , standard deviation / n ) = N (65 g,1.44 g). Find the middle 95% of the sample means distribution. Roughly 2 standard deviations from the mean, or 65g 2.88g. x x x Confidence intervals The confidence interval is a range of values with an associated probability or confidence level C . The probability quantifies the chance that the interval contains the true population parameter....
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This note was uploaded on 04/25/2009 for the course ECON 41 taught by Professor Guggenberger during the Winter '07 term at UCLA.
 Winter '07
 Guggenberger

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