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 tdistribution for small samples.
The 100(1α )% confidence interval
for the mean of a small sample (t
distribution) is:
See the ttest for
more information.
