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.
