The Practice of StatisticsThird 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?

p̂

Slide 7.6-17

p̂

p̂

Sampling Distribution Applet

http://onlinestatbook.com/stat_sim/sampling_dist/index.html

http://homepage.stat.uiowa.edu/~mbognar/applets/bin.html

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

p̂

p̂

Sample Means

Statistic Parameter

mean

Standard deviation s

proportion pp̂

x

Sample Population

• 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

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