Bootstrap Confidence Interval for a Population Parameter

Previously, a bootstrap confidence interval for a population mean was constructed by using percentiles from a bootstrap distribution formed by calculating the value of the sample mean for a large number of bootstrap samples. But, what if we wanted to get a confidence interval for a different population parameter?

For example, maybe a population distribution is quite skewed, so the median might be a better choice for describing the center of the distribution. Could we use sample data to calculate a confidence interval for the population median? There is no [latex]t[/latex] confidence interval or [latex]z[/latex] confidence interval for a population median.

In the previous in-class activity, we were able to use sample data to construct a bootstrap confidence interval for a population mean by carrying out the following steps:

1. Create a bootstrap sample by selecting a sample with replacement from the original sample.
2. Calculate the sample mean for the bootstrap sample.
3. Repeat Steps [latex]1[/latex] and [latex]2[/latex] a large number of times.
4. Create a bootstrap distribution of the bootstrap sample means and then determine the end points of the confidence interval by using appropriate percentiles of the bootstrap distribution.