SP Statistics Chapter 9 Sample Dist. Powerpoint
Transcript SP Statistics Chapter 9 Sample Dist. Powerpoint
Daniel S. Yates
The Practice of Statistics
Copyright © 2008 by W. H. Freeman & Company
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
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
• How can we rely on a statistic to estimate a parameter?
Binomial Distribution APP
Sampling Distribution Applet
•Sampling distribution of the statistic p̂ has an approximately
Normal shape. Gets closer to Normal as the sample size n
• Its mean is equal to the population parameter p; p̂ is equal to p.
• Its standard deviation gets smaller as sample size gets larger
• 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.
• 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