A general proof of the fact that 2 possesses approximately a chi-square sampling distribution when n

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A general proof of the fact that χ 2 possesses approximately a chi-square sampling distribution when n is large is beyond the scope of this text. However, it can be justified for the binomial case (k = 2). In Optional Exercise 6.118 (p. 259), we stated that if Z is a standard normal random variable, then Z2 is a chi-square random variable with 1 degree of freedom. Denote the two cell counts for a binomial experiment as n1 = Y and (n - Y). Then, for large n,

has approximately a standard normal distribution and Z2 will be approximately distributed as a chi-square random variable with 1 degree of freedom. Show algebraically that for k = 2, x2 = Z2.

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Statistics For Engineering And The Sciences

ISBN: 9781498728850

6th Edition

Authors: William M. Mendenhall, Terry L. Sincich

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