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3.3 Toward Statistical Inference
Statistical inference
is using a fact about a sample to estimate the truth about the whole
population.
A simple random sample (SRS)
of size
n
consists of
n
individuals from the population
chosen in such a way that every set of
n
individuals has an equal chance to be the sample
actually selected.
A parameter
is a number that describes the population.
A parameter is a fixed number,
but in practice we do not know its value.
A statistic
is a number that describes a sample.
The value of a statistic is known when we
have taken a sample, but it can change from sample to sample.
We often use a statistic to
estimate an unknown parameter.
Example) A researcher takes a nationwide SRS of 2500 adults that asks if they agree with
the statement “I support President Obama.”
Suppose 1650 agreed.
p
ˆ
= (1650/2500) = 0.66 = 66%
p
ˆ
= 0.66 is a statistic (proportion of sample that agrees)
p
= ? is a parameter (proportion of population (all US adults) that would agree if asked)
If the researcher sampled another 2500 adults, he would almost certainly get a different
value for
p
ˆ
.
Sampling variability
means that the value of a statistic varies in repeated
random sampling.
if the variation when we take repeat samples from the same population is too great, we
can’t trust the results of any one sample
Advantages of random samples
•choosing at random eliminates bias
•if we take lots of random samples of the same size from the same population, the
variation from sample to sample will follow a predictable pattern
What would happen if we took many samples?
•take a large number of samples from the same population.
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 '08
 ABDUS,S.

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