Robert_V._Hogg,_Joseph_W._McKean,_Allen_T._Craig
4.7. Chi-Square Tests 285 to rejectH 0 ifQk− 1 ≥c. To determine a test with level of significanceα,we can use tables of theχ^2 - ...
286 Some Elementary Statistical Inferences ofQ 3 = ∑ 4 1 (Xi−npi^0 ) (^2) /(np i 0 )is (6−5)^2 5 (18−15)^2 15 (20−25)^2 25 ( ...
4.7. Chi-Square Tests 287 is somewhat greater than it would be if minimum chi-square estimates are used. Hence, when comparing i ...
288 Some Elementary Statistical Inferences experiment is repeatednindependent times andXijdenotes the frequency of the eventAi∩B ...
4.7. Chi-Square Tests 289 Fair Red Medium Dark Black Margin Blue 1368 170 1041 398 1 2978 Light 2577 474 2703 932 11 6697 Medium ...
290 Some Elementary Statistical Inferences hypothesis (concerning the multinomial pdf withk=4)istobetestedatthe5% level of signi ...
4.7. Chi-Square Tests 291 Table 4.7.1:Contingency Table for Type of Crime and Alcoholic Status Data Crime Alcoholic Non-Alcoholi ...
292 Some Elementary Statistical Inferences x 01233 <x Frequency 20 40 16 18 6 (a)Compute the corresponding chi-square goodnes ...
4.8. The Method of Monte Carlo 293 ui 0.4743 0.7891 0.5550 0.9693 0.0299 xi 00001 ui 0.8425 0.6012 0.1009 0.0545 0.4677 xi 00110 ...
294 Some Elementary Statistical Inferences n 100 500 1000 10,000 100,000 4 x 3.24 3.072 3.132 3.138 3.13828 1. 96 · 4 √ x(1−x)/n ...
4.8. The Method of Monte Carlo 295 Then the corresponding stream of exponential observations is 0 .641, 1.95, 0.696, 1.13, 0. 27 ...
296 Some Elementary Statistical Inferences ThenY is a unbiased estimator ofπ.NotethatY is estimating a mean, so the large sample ...
4.8. The Method of Monte Carlo 297 Since the joint pdf ofY 1 andY 2 is 1 on 0<y 1 < 1 , 0 <y 2 <1, and zero elsewher ...
298 Some Elementary Statistical Inferences Thenα̂is our simulated estimate ofαand the half-width of a confidence interval forαse ...
4.8. The Method of Monte Carlo 299 Hence, by differentiating both sides, we find that the pdf ofXisf(x). There are two facts wor ...
300 Some Elementary Statistical Inferences Assume then thatXhas a Γ(α,1) distribution, whereαis not an integer. As- sume first t ...
4.8. The Method of Monte Carlo 301 4.8.2.Recall that log 2 = ∫ 1 0 1 x+1dx. Hence, by using a uniform(0,1) generator, approximat ...
302 Some Elementary Statistical Inferences 4.8.11.Consider the situation in Example 4.8.6 with the hypotheses (4.8.3). Write an ...
4.9. Bootstrap Procedures 303 (a)Use Theorem 4.8.1 to generate an observation from this pdf. (b)Use the accept–reject algorithm ...
304 Some Elementary Statistical Inferences Informative discussions of such procedures can be found in Efron and Tibshirani (1993 ...
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