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Daniel S. Yates The Practice of Statistics Third Edition Chapter 9: Sampling Distributions Copyright © 2008 by W. H. Freeman & Company Sampling Variability Ex. A Presidential poll finds that 45% of Americans are going to vote for Obama. The poll found that 1125 people out of the 2500 in the sample said they would vote for Obama. p̂ = sample proportion = 1125/2500 = 0.45 •We will use the statistic p̂ to estimate the parameter p • If we did another poll, assuming attitudes did not change, with a different SRS we would get a different p̂ . • Sampling variability - the value of a statistic varies in repeated sampling. • How can we rely on a statistic to estimate a parameter? Slide 7.6-17 Sampling Distribution Applet http://onlinestatbook.com/stat_sim/sampling_dist/index.html Sample Proportions •Sampling distribution of the statistic p̂ has an approximately Normal shape. Gets closer to Normal as the sample size n increases. • Its mean is equal to the population parameter p; p̂ is equal to p. • Its standard deviation gets smaller as sample size gets larger Sample Means Sample Population Statistic Parameter mean x m Standard deviation s s proportion p̂ p • The sample mean x is an unbiased estimator of m. • The standard deviation of the sampling distribution of x decreases as sample size n increases. s • Can only use sx n for standard deviation when; population > 10 * sample size •These facts about the sample mean and Std. are true regardless of the shape of the population distribution. Sampling Distributions; n=1 and n=10 • getting an xbar that is 2.0 in. larger than m is more likely for a sample size of 1 vs. 10 Area