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Chapter 9 - Sampling distributions - Coggle Diagram
Chapter 9 - Sampling distributions
Sampling distributions
A sampling distribution is a distribution of all of the possible values of a statistic for a given size sample selected from a population
If the population is normal
If a population is normal with mean
___
and standard deviation
, the sampling distribution of
__
is also normally distributed with
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and
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If the population is not normal
The central limit theorem = as the sample size becomes large enough the sampling distribution becomes almost normal regardless of shape of population
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Sampling distribution properties:
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We can apply the central limit theorem
Calculating the Z value for proportions
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Developing a sampling distribution
Assume there is a population
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Standard error of the mean
A measure of the variability in the mean from sample to sample is given by the standard error of the mean:
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Note that the standard error of the mean decreases as the sample size increases
Different samples of the same size from the same population will yield different sample means
Z value for sampling distributions of the mean
Z value of the sampling distribution of
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Properties of the sampling distribution
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How large is large enough?
For most distributions, n>=30 will give a sampling distribution that is nearly normal
For normal population distributions, the sampling distribution of the mean is always normally distributed
Population proportions
Sample proportion
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provides an estimate of p.
0 < =
___<=1
X has a binomial distribution
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p = the proportion of the population having some characteristic
Calculating the Z value for the difference between two means
Sampling distributions of the difference between two sample means
The sampling distribution of
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is normal with mean
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And standard error
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Assumptions:
Samples are randomly and independently drawn
Population distributions are normal or both sample sizes are large (n>=30)
Population standard deviations are known
Sampling distribution
Approximated by a normal distribution if:
and
where