This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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)....
View
Full Document
 Spring '08
 Staff
 Normal Distribution, Standard Deviation, Confidence Level

Click to edit the document details