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Chapter 6: Monte Carlo Methods for Inferential Statistics 229

average undergraduate grade point average (gpa) for the 1973 fresh-
man class at 82 law schools. Note that these data constitute the entire
population. The data contained in law comprise a random sample of
15 of these classes. Obtain the true population variances for the lsat
and the gpa. Use the sample in law to estimate the population vari-
ance using the sample central second moment. Get bootstrap esti-
mates of the standard error and the bias in your estimate of the
variance. Make some comparisons between the known population
variance and the estimated variance.
6.12. Using the lawpop data, devise a test statistic to test for the signifi-
cance of the correlation between the LSAT scores and the correspond-
ing grade point averages. Get a random sample from the population,
and use that sample to test your hypothesis. Do a Monte Carlo sim-
ulation of the Type I and Type II error of the test you devise.
6.13. In 1961, 16 states owned the retail liquor stores. In 26 others, the
stores were owned by private citizens. The data contained in whisky
reflect the price (in dollars) of a fifth of whisky from these 42 states.
Note that this represents the population, not a sample. Use the
whisky data to get an appropriate bootstrap confidence interval for
the median price of whisky at the state owned stores and the median
price of whisky at the privately owned stores. First get the random
sample from each of the populations, and then use the bootstrap with
that sample to get the confidence intervals. Do a Monte Carlo study
where you compare the confidence intervals for different sample
sizes. Compare the intervals with the known population medians
[Hand, et al., 1994].
6.14. The quakes data [Hand, et al., 1994] give the time in days between
successive earthquakes. Use the bootstrap to get an appropriate con-
fidence interval for the average time between earthquakes.

© 2002 by Chapman & Hall/CRC