Chapter6.pdf Q SCI 381
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This 2 page Class Notes was uploaded by Claira Notetaker on Sunday February 14, 2016. The Class Notes belongs to Q SCI 381 at University of Washington taught by Patrick C, Tobin in Winter 2016. Since its upload, it has received 16 views. For similar materials see Introduction to Probability and Statisitics in Environmental Science at University of Washington.
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Date Created: 02/14/16
Chapter 6: Confidence intervals • Section 6.1, 6.2, 6.4 • Start using inferential statistics Confidence intervals • A range of values centered on a point estimate o Such as mean, variance, or SD • Denoted as a percentage or as a error rate = a (greek letter) o EX: § Level of confidence = 95% § A= .05 error rate Critical values • Denote observations that significantly differs from the expected distribution • Based upon the level of confidence used o Higher the level of confidence (lower a) the greater the critical value o Need the 2 tailed area Margin of error (E) • There are many sources of error in experiments o Random error, observational errors, environmental error o Some are unavoidable • Increase precisions, finding a sample size! o The n’s justify the means § n = (Z(c) x SD/ E)^2 ú Z(c) = level of confidence obtained from z score • In decimal form ú E = margin of error • E= Zc*(SD/n^1/2) ú SD = standard deviation o Higher background variation => sample size increase o Higher level of confidence => sample size increase o The lower the desired margin of error => sample size increases • Confidence interval o Point estimate – E < parameter < point estimate + E o EX: § Estimated mean – E < u , estimated mean + E Or § U = point estimate of the mean + or – E o –E = lower confidence interval o +E = upper confidence interval T-distribution • E = Tc*(SD/n^1/2) • Tc gives you both the level of confidence and the sample size Degree of freedom • The bigger the sample size, you have more wiggle room o SD estimation = one loss of degree of freedom Chi-squared distribution (X^2) • Calculating the confidence interval for the variance and the standard deviation o The confidence interval is based on a given level of confidence, degree of freedom, and the chi-squared distribution • Asymmetrical graphs o Have a bit of a long tail § Allows for a different level of variation • ((n-1)SD^2/X^2R)^1/2 < SD < ((n-1)SD^2/X^2L) o X^2R = right tail (5% above wanted Level of confidence) o X^2L = left tail (5% bellow wanted level of confidence) o N-1 because we estimated the SD (one less DoF) • 77.929 = .26 • 124.342 = .17 • 3.5 <4.4< 5.6
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