Chapter 14 - Bootstrap Methods and Permutation Tests - WH Freeman

14-44 CHAPTER 14 Bootstrap Methods and Permutation Tests
14.33 The distribution of the 72 guinea pig lifetimes in Table 1.8 (page 38) is strongly
skewed. In Exercise 14.9 (page 14-23) you found a bootstrap t confidence interval
for the population mean µ, even though some skewness remains in the
bootstrap distribution. Bootstrap the mean lifetime and give all four bootstrap
95% confidence intervals: t, percentile, BCa, and tilting. Make a graphical
comparison by drawing a vertical line at the original sample mean x and
displaying the four intervals horizontally, one above the other. Discuss what
you see: Do bootstrap t and percentile agree? Do the more accurate intervals
agree with the two simpler methods?
14.34 We would like a 95% confidence interval for the standard deviation σ of
Seattle real estate prices. Your work in Exercise 14.11 probably suggests
that it is risky to bootstrap the sample standard deviation s from the sample
in Table 14.1 and use the bootstrap t interval. Now we have more accurate
methods. Bootstrap s and report all four bootstrap 95% confidence intervals:
t, percentile, BCa, and tilting. Make a graphical comparison by drawing a vertical
line at the original s and displaying the four intervals horizontally, one
above the other. Discuss what you see: Do bootstrap t and percentile agree?
Do the more accurate intervals agree with the two simpler methods? What
interval would you use in a report on real estate prices?
CHALLENGE
CHALLENGE
14.35 Exercise 14.7 (page 14-13) gives an SRS of 20 of the 72 guinea pig survival
times in Table 1.8. The bootstrap distribution of x from this sample is clearly
right-skewed. Give a 95% confidence interval for the population mean µ based
on these data and a method of your choice. Describe carefully how your result
differs from the intervals in Exercise 14.33, which use the full sample of 72
lifetimes.
14.36 The CLEC data for Example 14.6 are strongly skewed to the right. The 23
CLEC repair times appear in Exercise 14.22 (page 14-26).
(a) Bootstrap the mean of the data. Based on the bootstrap distribution,
which bootstrap confidence intervals would you consider for use? Explain
your answer.
(b) Find all four bootstrap confidence intervals. How do the intervals compare?
Briefly explain the reasons for any differences. In particular, what
kind of errors would you make in estimating the mean repair time for all
CLEC customers by using a t interval or percentile interval instead of a
tilting or BCa interval?
14.37 Example 14.6 (page 14-19) considers the mean difference between repair
times for Verizon (ILEC) customers and customers of competing carriers
(CLECs). The bootstrap distribution is nonnormal with strong left skewness,
so that any t confidence interval is inappropriate. Give the BCa 95% confidence
interval for the mean difference in service times for all customers. In
practical terms, what kind of error would you make by using a t interval or
percentile interval instead of a BCa interval?
14.38 Figure 2.3 (page 108) is a scatterplot of field versus laboratory measurements
of the depths of 100 defects in the Trans-Alaska Oil Pipeline. The correlation
is r = 0.944. Bootstrap the correlation for these data. (The data are in the file
ex14 038.dat.)