In Example A of Section 10.4.6, a 90% bootstrap confidence interval based on the trimmed...

In Example A of Section 10.4.6, a 90% bootstrap confidence interval based on the trimmed mean was found to be (133.65, 135.58). Compare these values to the list of data values given in Section 10.4.1 and observe that 133.65 is smaller than the smallest observation. Explain why the bootstrap confidence interval extends so far in this direction.

Reference

We illustrate this idea on the platinum data by using the bootstrap to approximate the sampling distribution of the 20% trimmed mean and its standard error. To this end, 1000 samples of size n = 26 were drawn randomly with replacement from the collection of 26 values.Ahistogram of the 1000 trimmed means is displayed in Figure 10.11. The standard deviation of the 1000 values was .64, which is the estimated standard error of the 20% trimmed mean. The histogram is interesting—note the skewed tail to the right. We see that some of the trimmed means were far from the bulk of the data. This happened because some of the samples drawn with replacement included several