Describing accuracy with an interval estimate

Reporting a single value as a parameter estimate (a point estimate) does not convey any information about the estimator's accuracy — i.e. the likely size of the estimation error.

A better way to present a parameter estimate is with an interval estimate. An interval estimate indicates the degree of uncertainty in our knowledge of the parameter value. For example, we prefer to make a statement

 µ is probably between 10.5 and 11.5.

rather than simply

our estimate of µ is 11.0.

Will our interval estimate include the actual parameter value?

Consider an interval estimate of a population mean, µ, centred on the mean of a random sample, . As we reduce the width of this interval estimate, we become less confident that the interval will include the unknown value of µ.

We will later describe how to quantify our confidence that any particular interval estimate will include a parameter such as µ.