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Chapter 14: Problem 4
Use Table 5 in Appendix I to bound the \(p\) -value for a chi-square test: a. \(X^{2}=4.29, d f=5\) b. \(X^{2}=20.62, d f=6\)
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Medical statistics show that deaths due to four major diseases \(-\) call them \(\mathrm{A}\), \(\mathrm{B}, \mathrm{C},\) and \(\mathrm{D}-\) account for \(15 \%, 21 \%, 18 \%,\) and \(14 \%,\) respectively, of all nonaccidental deaths. A study of the causes of 308 nonaccidental deaths at a hospital gave the following counts: Do these data provide sufficient evidence to indicate that the proportions of people dying of diseases \(A, B\), \(\mathrm{C},\) and \(\mathrm{D}\) at this hospital differ from the proportions accumulated for the population at large?
Random samples of 200 observations were selected from each of three populations, and each observation was classified according to whether it fell into one of three mutually exclusive categories: You want to know whether the data provide sufficient evidence to indicate that the proportions of observations in the three categories depend on the population from which they were drawn. a. Give the value of \(X^{2}\) for the test. b. Give the rejection region for the test for \(\alpha=.01\). c. State your conclusions. d. Find the approximate \(p\) -value for the test and interpret its value.
Give the rejection region for a chi-square test of specified probabilities if the experiment involves \(k\) categories in these cases: a. \(k=7, \alpha=.05\) b. \(k=10, \alpha=.01\)
Suppose that a response can fall into one of \(k=3\) categories with probabilities \(p_{1}=.4, p_{2}=.3,\) and \(p_{3}=.3,\) and \(n=300\) responses produce these category counts:
A particular poultry disease is thought to be noncommunicable. To test this theory, 30,000 chickens were randomly partitioned into three groups of 10,000 . One group had no contact with diseased chickens, one had moderate contact, and the third had heavy contact. After a 6 -month period, data were collected on the number of diseased chickens in each group of 10,000 . Do the data provide sufficient evidence to indicate a dependence between the amount of contact between diseased and nondiseased fowl and the incidence of the disease? Use \(\alpha=.05\)
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