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Confidence Interval

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: