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Part 2
Sampling
1.
Statistical Inference
2.
Sampling Plans
3.
Simple Random Sampling
4.
Distributions of Sample Means
Section 2.1
Statistical Inference
Statistical inference
: using data obtained
from a sample to make decisions or
predictions about the population from which
the sample is drawn
Parameter
: a numerical characteristic of a
population (for example, population mean
and population variance).
The sample results provide estimates
of the
values of the population parameters. With
proper sampling methods, the sample results
will provide good estimates of the population
parameters.
Suppose we want to know the mean income
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of all families in a city. The population is
therefore the incomes of all families in the
city. We then select randomly a family from a
city and know its income. In this experiment,
the sample space is the city and the sample
points are families in the city. The income
corresponds to the
outcome (a family
randomly selected) of the experiment.
Therefore we say that the income of a family
randomly selected is a random variable. For
convenience, we define the distribution of the
population
as the distribution of this random
variable.
Section 2.2
Sampling Plans
We introduce three different sampling plans.
Simple random sampling
: all the samples
with the same size are equally likely to be
chosen.
A
simple random sample
is a sample
selected using a simple random sampling
plan.
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To conduct random sampling,
•
assign a number to each element of the
chosen population (or use already given
numbers),
•
randomly select the sample numbers using
a random number table or a software
package.
Stratified random sampling
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 Spring '07
 Wood
 Standard Deviation, Variance

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