STAT 2 – SOME COMMENTS AND WARNINGS CONCERNING INFERENCE
The confidence intervals and significance tests we have discussed concern the
population mean
μ
and are based on the sample mean
X
.
These meanbased
inference procedures assume an SRS from a large population.
Since the sample mean is not resistant to outliers, any outliers in the data have the
potential to wreak havoc on these meanbased procedures.
For example, they can
affect the
p
values of tests and the true confidence levels of confidence intervals.
Our meanbased procedures assume that
X
is either normal or approximately normal.
If the sample size
n
is large, this will be true by the central limit theorem.
If
n
is small,
then the population distribution must be normal or approximately normal for
X
to be
normal or approximately normal.
Even if one estimates the population mean
μ
accurately or finds a highly statistically
significant result concerning the mean, keep in mind that the mean is only a summary of
all the individuals in the population and doesn’t say anything about specific individuals
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 Spring '08
 sugahara
 Statistics, Normal Distribution, Statistical hypothesis testing, Statistical significance

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