4.7 Show algebraically that when ei nui and k 2, we have Q X2...
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4.7 Show algebraically that when ei ¼ nui and k ¼ 2, we have Q ¼
X2 i¼1
(Fi ei)2 ei ¼
(F1 nu1)2 nu1(1 u1)
so that when k ¼ 2, ffiffiffiffi pQ is the statistic commonly used for testing a hypothesis concerning the parameter of the binomial distribution for large samples. By the central-limit theorem, the distribution of ffiffiffiffi pQ approaches the standard normal distribution as n!1and the square of any standard normal variable is chi-square-distributed with 1 degree of freedom. Thus we have an entirely different argument for the distribution of Q when k ¼ 2.
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Related Book For
Nonparametric Statistical Inference
ISBN: 9781420077612
5th Edition
Authors: Jean Dickinson Gibbons, Subhabrata Chakraborti
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