The Practice of Statistics Third Edition Chapter 9: Sampling Distributions Copyright © 2008 by W. H. Freeman & Company Daniel S. Yates

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. = sample proportion = 1125/2500 = 0.45 We will use the statistic to estimate the parameter p If we did another poll, assuming attitudes did not change, with a different SRS we would get a different. Sampling variability - the value of a statistic varies in repeated sampling. How can we rely on a statistic to estimate a parameter? Slide

Sampling Distribution Applet Binomial Distribution APP

Sample Proportions Sampling distribution of the statistic has an approximately Normal shape. Gets closer to Normal as the sample size n increases. Its mean is equal to the population parameter p; is equal to p. Its standard deviation gets smaller as sample size gets larger

Sample Means StatisticParameter mean  Standard deviations  proportion p SamplePopulation

The sample mean is an unbiased estimator of  The standard deviation of the sampling distribution of decreases as sample size n increases. Can only use 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 Area getting an x bar that is 2.0 in. larger than  is more likely for a sample size of 1 vs. 10