Bootstrap Distribution and Confidence Interval for a Population Mean – Learn It 4

  • Create a bootstrap distribution for a sample mean
  • Find and describe a bootstrap percentile confidence interval for a population mean

To create a bootstrap distribution, we want to take a large number of bootstrap samples. So, we turn to technology. A statistics software package was used to create the following histogram of the bootstrap distribution based on [latex]1,000[/latex] bootstrap samples:

Example bootstrap distribution of 1000 samples, with a mean of 34.

The bootstrap distribution is used to obtain a confidence interval for the population mean. Notice that the bootstrap distribution is centered at [latex]34[/latex], which was the sample mean of the original sample.

For a [latex]95\%[/latex] confidence level, using the boundaries that capture the middle [latex]95\%[/latex] of the bootstrap distribution to determine the endpoints of the confidence interval is equivalent to adding a number to the original sample mean and subtracting a number from the original sample mean. For a bootstrap confidence interval, the number that is added and the number that is subtracted are not the same because the bootstrap distribution is not symmetric.