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Chapter 9: Sampling Distributions
9.1 Sampling Distribution of the Mean
•
Two methods to create a sampling distribution
o
Draw samples of the same size from a population, calculate the statistic of interest, and then use
descriptive techniques
to learn more about the sampling distribution
o
The second method relies on the rules of probability and the laws of expected value and variance to
derive the sampling distribution
•
Sampling Distribution of the Mean of Two Dice
o
Population Statistics
Population mean
Population Variance
Population standard deviation
Because the value of the sample mean varies randomly from sample to sample, we can
regard
as a new random variable created by sampling
o
Sampling Statistics
The most interesting aspect of the sampling distribution of
is how different it is from the
distribution of
Mean of the sampling distribution of
Variance of the sampling distribution of
Standard deviation of the sampling distribution of
It is important to recognize that the distribution of is different from the distribution of
However, the two random variables are related; their means are the same and their variances
are related
The variance of the sampling distribution of
is less than the variance of the population
we’re sampling from all sample sizes
•
Thus, a randomly selected value of is likely to be closer to the mean value than is a
randomly selected value of
•
As
gets larger, the sampling distribution of
becomes increasingly bell shaped
o
Central Limit Theorem
The sampling distribution of the mean of a random sample drawn from any population is
approximately normal for a sufficiently large sample size. The larger the sample size, the
more closely the sampling distribution of will resemble a normal distribution.
If the population is normal, then
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This note was uploaded on 11/09/2011 for the course ECO 220 taught by Professor Tanaka during the Fall '11 term at University of Toronto Toronto.
 Fall '11
 tanaka
 Economics

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