Point and interval estimates

In this section, we show how to use an interval estimate to indicate the accuracy of the sample mean, , as an estimate of a population mean, µ.

Silkworm survival

Interval estimate from error distribution

The error distribution is the key to interval estimation. For most common parameter estimates, we can find the error distribution (or an approximation to it).

The standard error of most commonly used estimators can be readily found by either a formula or statistical software, so this result is extremely useful in practice.

An approximate 95% confidence interval is

estimate  ±  2 × s.e.(estimate)

Refinements

The confidence level of a confidence interval that is found in this way is 95% only if we know the exact error distribution. Since we must often approximate the error distribution (e.g. by replacing σ by s when estimating a population mean), the confidence level may be only approximately 95%.

For some estimators, we will give a refinement to this type of confidence interval to make the confidence level closer to 95%. However the '± 2 s.e.' approximation is a useful guide in most circumstances.