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Random Sampling
In general, when we take a sample from a population
we do it to estimate some characteristic (i.e.
parameter) of a population with an appropriate
statistic calculated from the sample. Of course, we
want our sample to be representative of the
population from which it was taken. In other words,
we want our sample to be
unbiased
. If we want our
sample to be unbiased and to be able to use our
sample data to draw valid conclusions about our
population, we need to employ
random sampling
.
Simple random sampling
is a method of sampling
designed so that every item in the population has an
equally likely chance of being selected.
114
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View Full Document Sample Statistics and Sampling Distributions
Very important concepts in statistics because they
form the foundation for
statistical inference
.
That is,
they enable us to make valid statements about
populations based on random samples drawn from
those populations.
Recall that a
parameter
is a characteristic of a
population.
For example, a population mean, µ, or a
population standard deviation, σ.
Usually, we do not
know the true value of a parameter, but instead must
estimate it by taking a random sample from the
population and calculating a
sample statistic
from
the sample data.
The sample statistic serves as a
point estimate
for the population parameter.
For
example,
x is a point estimate for µ and s is a point
estimate for
σ .
Also, a point estimate for the binomial parameter,
p, can be obtained by taking a random sample of size
n from a population, calculating the number of items
(or objects or people) that have the characteristic of
interest.
A point estimate of p can then be calculated
as
p
= x/n.
So, the sample statistic
p
is a point
estimate of p.
Sampling Distributions
:
Sample statistics are
summary measures obtained from random samples.
Sample statistics are themselves random variables.
So,
x, s, and
p
are random variables, just like x is a
random variable.
As such,
x, s, and
p
have
115
probability distributions.
A sampling distribution is
simply a probability distribution for a statistic.
They are important because they allow us to say how
reliable the point estimate (sample statistic) is.
For
example, suppose that I find that the mean selling
price for a sample of 50 homes in South Carolina was
x=$154,500 last month.
I know that this value almost
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This note was uploaded on 06/06/2011 for the course MGSC 291 taught by Professor Rollins during the Fall '09 term at South Carolina.
 Fall '09
 Rollins

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