Download Properties of Sampling Distributions of Sampling Means:

5.4SamDistCLT.notebook
February 24, 2016
Properties of Sampling Distributions of Sampling Means:
The Histogram represents
the distribution of many sample means
taken from the population
The Density curve represents
the distribution of
the actual population
The bigger the n, the closer the mean of the population is to the
mean of the sampling distribution.
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5.4SamDistCLT.notebook
February 24, 2016
"The Central Limit Theorem"
n=100
n=500
n=1500
The blue curve is the density curve of some sampling distribution of means.
The red curve is the normal curve with mean and standard deviation that represents
the population.
As you increase n, the density curve looks more and more normal.
Or put another way: it's shaped more like a classicBELL CURVE!
And, is more like the actual population!
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5.4SamDistCLT.notebook
February 24, 2016
5.4 Sampling Distributions and the Central Limit Theorem
The Central Limit Theorem
Is the foundation on which the
Inferential Branch of Statistics is built
≥ 30, are drawn from any population with mean =µ
and standard deviation =σ , If samples of size n
then the sampling distribution of the sample means approximates
a normal distribution.
The greater the sample size, the better the approximation, and the more sample
means in the sampling distribution, the better as well.
The Distribution of Sample Means will always be
normal regardless of whether or not the population
is normally distributed!
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5.4SamDistCLT.notebook
February 24, 2016
Properties of Sampling Distributions of Sampling Means:
1. 2. The mean of the sampling distribution will be the same value as the population mean
The standard deviation of the sampling distribution will be equal to the population standard deviation divided by the square root of n
Note: Another name for the standard deviation of the sampling distribution of the sample means is called the
STANDARD ERROR OF THE MEAN
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5.4SamDistCLT.notebook
February 24, 2016
The mean of the sampling distribution will be the same value as the
population mean
The standard deviation of the sampling distribution will be
equal to the population standard deviation divided by the
square root of n
standard deviation
"standard error of the mean"
30
Normal
Sample Size(n)
approximation
equal
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5.4SamDistCLT.notebook
February 24, 2016
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