With the advent of high-speed computing, new procedures have been developed that permit statistical inferences to be performed under less restrictive conditions than those of classical procedures. Bootstrap confidence intervals constitute one such collection of new procedures. To obtain a bootstrap confidence interval for one population mean, proceed as follows.

1. Take a random sample of size n (the sample size) with a replacement from the original sample.

2. Compute the mean of the new sample.

3. Repeat steps 1 and 2 a large number (hundreds or thousands) of times.

4. The distribution of the resulting sample means provides an estimate of the sampling distribution of the sample mean. This estimate is called a bootstrap distribution.

5. The (estimated) endpoints of a 95% confidence interval for the population mean are the 2.5th and 97.5th percentiles of the bootstrap distribution.