EXAMPLE 7.9 Bootstrap Confidence Interval

Consider the eight time measurements (in minutes) spent using a smartphone in Example 7.1 (page 361):

We defended the use of the one-sided 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 . We use software to do this very quickly. One resample was

with . The middle 95% of our 1000 ’s runs from 93.125 to 128.003. We repeat the procedure and get the interval (93.872, 125.750).

The two bootstrap intervals are relatively close to each other and are more narrow than the one-sample confidence interval (88.3,130.7). This suggests that the standard interval is likely a little wider than it needs to be for these data.