# ch7.docx

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26 Apr 2012
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STATS-CHAPTER 7
Sampling Error: the discrepancy, or amount of error between a sample statistic and its corresponding
population parameter
Problem with samples:
- Are variable
- Not 100% representative of the population
The Distribution of Sample Means: is the collection of sample means for all the possible random
samples of a particular size (n) that can be obtained from a population
Sampling Distribution: a distribution of statistics obtained by selecting all the possible samples of a
specific size from a population
To Construct a Distribution of Sample Means:
1) Select a sample of size (n), and calculate mean continue to do this until you have selected all
the possible samples from the population
Characteristics:
a) Sample means should pile up around the population mean (are suppose to be representative of
the population mean)
b) The pile of sample means should tend to form a normal shaped distribution most of the
sample means should come close to the population mean (µ)
c) The larger the sample size, the closer the sample means should be to the µ
Central Limit Theorem: for any population with a mean µ, and standard deviation σ, the distribution of
sample means for sample size (n) will have a mean of µ, and a standard deviation of σ/√n and will
approach a normal distribution as n approaches infinity
The distribution of sample means will be almost perfectly normal if either of the two conditions are
met:
1) The population from which the sample is selected is normal
2) The number of scores in each sample (n) is large, 30 or more
The average value of all the sample means is exactly equal to the value of the population mean
Expected Value of M: the mean of the distribution of sample means is equal to (µ) and is called the
expected value of M
The standard deviation of the distribution of sample means is called the standard error of M. the
standard error measures the standard amount of difference between M and µ that is reasonable to
expect simply by chance
Standard Error of M = ___= standard distance between M and µ
Magnitude of standard error is determined by two factors:
1) Size of sample
2) Standard deviation of the population from which the sample is selected
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