Page 241 - Computational Statistics Handbook with MATLAB

228 Computational Statistics Handbook with MATLAB

Exercises

6.1. Repeat Example 6.1 where the population standard deviation for the
travel times to work is σ X = 5 minutes. Is x = 47.2 minutes still
consistent with the null hypothesis?
6.2. Using the information in Example 6.3, plot the probability of Type II
µ
error as a function of . How does this compare with Figure 6.2?
6.3. Would you reject the null hypothesis in Example 6.4 if α = 0.10 ?
6.4. Using the same value for the sample mean, repeat Example 6.3 for
,
,
different sample sizes of n = 50 100 200 . What happens to the curve
showing the power as a function of the true mean as the sample size
changes?
6.5. Repeat Example 6.6 using a two-tail test. In other words, test for the
alternative hypothesis that the mean is not equal to 454.
6.6. Repeat Example 6.8 for larger M. Does the estimated Type I error get
closer to the true value?
6.7. Write MATLAB code that implements the parametric bootstrap. Test
it using the forearm data. Assume that the normal distribution is a
reasonable model for the data. Use your code to get a bootstrap
estimate of the standard error and the bias of the coefficient of skew-
ness and the coefficient of kurtosis. Get a bootstrap percentile interval
for the sample central second moment using your parametric boot-
strap approach.
6.8. Write MATLAB code that will get the bootstrap standard confidence
interval. Use it with the forearm data to get a confidence interval
for the sample central second moment. Compare this interval with
the ones obtained in the examples and in the previous problem.
6.9. Use your program from problem 6.8 and the forearm data to get a
bootstrap confidence interval for the mean. Compare this to the the-
oretical one.
6.10. The remiss data set contains the remission times for 42 leukemia
patients. Some of the patients were treated with the drug called 6-
mercaptopurine (mp), and the rest were part of the control group
(control). Use the techniques from Chapter 5 to help determine a
suitable model (e.g., Weibull, exponential, etc.) for each group. Devise
a Monte Carlo hypothesis test to test for the equality of means between
the two groups [Hand, et al., 1994; Gehan, 1965]. Use the p-value
approach.
6.11. Load the lawpop data set [Efron and Tibshirani, 1993]. These data
contain the average scores on the LSAT (lsat) and the corresponding

© 2002 by Chapman & Hall/CRC