Let y 1 , y 2 , y 3 , ..... y n represent a random sample

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Let y1, y2, y3, ..... yn represent a random sample of size n selected from a normal probability distribution with unknown mean μ and variance σ2 = 1. Then the sample mean, y̅ , has a normal distribution with mean μ and variance σ2 = 1/n. Assume that the prior distribution for μ is a normal distribution with a mean of 5 and a variance of 1. Find a Bayesian decision rule for testing Ho: μ = μo versus Ha: μ < μo. Use the posterior distribution, g(μ Ι y̅).    

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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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