| Suppose that
sample of items is taken at random from
a process and the mean
of the sample is used as an estimator
of the process mean. This sample mean is
a point estimate, and is unlikely to exactly
equal the true population mean.
The confidence interval defines a band
around the sample mean within which the
true population will lie, to some degree
of confidence:
For example, there is a 95% probability
that the true population mean will lie within
the 95% confidence interval of the sample
mean. The method used to calculate the confidence
interval will vary, but usually involves
the normal distribution for large samples,
or the t-distribution for small samples.
The 100(1-α )% confidence interval
for the mean of a small sample (t
distribution) is:
See the t-test for
more information.
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