EXAMPLE 7.9

A bootstrap confidence interval. Consider the eight time measurements (in hours per week) spent watching traditional television in Example 7.1:

3.0 16.5 10.5 40.5 5.5 33.5 0.0 6.5

We defended the use of the one-sided t confidence interval for an earlier analysis. Let’s now compare those results with the confidence interval constructed using the bootstrap.

We decide to collect the ’s from 1000 resamples of size n = 8. We use software to do this very quickly. One resample was

5.5 6.5 5.5 40.5 16.5 33.5 10.5 6.5

with . The middle 95% of our 1000 ’s runs from 7.0 to 25.0. We repeat the procedure and get the interval (6.6, 25.1).

The two bootstrap intervals are relatively close to each other and are more narrow than the one-sample t confidence interval (2.1, 26.9). This suggests that the standard t interval is likely a little wider than it needs to be for this data set.