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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