The 2 goodness-of-fit test (see Chapter 10) is based on an asymptotic approximation to the distribution of
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a. Simulate v =10,000 samples of size n = 23 from the normal distribution with mean 3.912 and variance 0.25. For each sample, compute the χ2 goodness of-fit statistic Q using the same four intervals that were used in Example 10.1.6. Use the simulations to estimate the probability that Q is greater than or equal to the 0.9, 0.95, and 0.99 quantiles of the χ2 distribution with three degrees of freedom.
b. Suppose that we are interested in the power function of a χ2 goodness-of-fit test when the actual distribution of the data is the normal distribution with mean 4.2 and variance 0.8. Use simulation to estimate the power function of the level 0.1, 0.05, and 0.01 tests at the alternative specified.
Distribution
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Probability And Statistics
ISBN: 9780321500465
4th Edition
Authors: Morris H. DeGroot, Mark J. Schervish
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