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Section 7.4
Sampling Distributions
7.4 / 1
Review of Statistical Terms
Population is the set of all measurements or counts
(either existing or conceptual) under consideration
Sample
is a subset of measurements from a population
Parameter is a numerical descriptive measure of a
population
Statistic
is a numerical descriptive measure of a sample
We use a statistic to make
inferences about a population parameter.
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Some Common Statistics
and Corresponding Parameters
It is important to notice that for a given population, a
specified parameter is a fixed quantity. On the other
hand, the value of a statistic might vary depending on
which sample has been selected.
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Principal Types of Inferences
Estimation: estimate the value of a population
parameter
Testing: formulate a decision about the value of
a population parameter
Regression: Make predictions or forecasts about
the value of a statistical variable
To evaluate the reliability of our inferences, we will need to know
the probability distribution for the statistics we are using,
Such a probability distribution is called a sampling
distribution.
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Sampling Distribution
• Is a probability distribution for the sample
statistic
• based on all possible random samples of the
same size from the same population
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Example of a Sampling Distribution
• Select samples with two elements each (in
sequence with replacement) from the set
• {1, 2, 3, 4, 5, 6}.
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Constructing a Sampling Distribution of the
Mean for Samples of Size n = 2
List all samples (with 2 items in each) and compute the
mean of each sample.
sample:
mean:
sample:
mean
{1,1}
{1,2}
{1,3}
{1,4}
{1,5}
1.0
1.5
2.0
2.5
3.0
{1,6}
{2,1}
{2,2}
…
…
3.5
1.5
2
...
…
How many different samples are there?
36
7
Sampling Distribution of the Mean
x
p
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
1/36
2/36
3/36
4/36
5/36
6/36
5/36
4/36
3/36
2/36
1/36
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GUIDED EXERCISE 9 PAGE,284
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