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![Page 1: The Practice of Statistics Third Edition Chapter 9: Sampling Distributions Copyright © 2008 by W. H. Freeman & Company Daniel S. Yates.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697bfc71a28abf838ca7ac9/html5/thumbnails/1.jpg)
The Practice of StatisticsThird Edition
Chapter 9:Sampling Distributions
Copyright © 2008 by W. H. Freeman & Company
Daniel S. Yates
![Page 2: The Practice of Statistics Third Edition Chapter 9: Sampling Distributions Copyright © 2008 by W. H. Freeman & Company Daniel S. Yates.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697bfc71a28abf838ca7ac9/html5/thumbnails/2.jpg)
![Page 3: The Practice of Statistics Third Edition Chapter 9: Sampling Distributions Copyright © 2008 by W. H. Freeman & Company Daniel S. Yates.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697bfc71a28abf838ca7ac9/html5/thumbnails/3.jpg)
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?
p̂
Slide 7.6-17
p̂
p̂
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Sampling Distribution Applet
http://onlinestatbook.com/stat_sim/sampling_dist/index.html
http://homepage.stat.uiowa.edu/~mbognar/applets/bin.html
Binomial Distribution APP
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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
p̂
p̂
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Sample Means
Statistic Parameter
mean
Standard deviation s
proportion pp̂
x
Sample Population
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• 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.
x
x
nx
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Sampling Distributions; n=1 and n=10
Area
• getting an xbar that is 2.0 in. larger than is more likely for a sample size of 1 vs. 10