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8-2.6. Show that the likelihood ratio principle leads to the same test whentesting a simple hypothesis Ho against an alternative simple hypothesis Hi as that given by the Neyman-Pearson Theorem. Note that there are only two points in 2.

8-2.6. Show that the likelihood ratio principle leads to the same test whentesting a simple hypothesis Ho against an alternative simple hypothesis Hi as that given by the Neyman

VIDEO ANSWER: Hello. The likelihood ratio principle states to test between two simple hypotheses, the null hypothesis and the alternative hypothesis. You shoul…

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Consider a simple hypothesis testing problem, where P(X=i): X ... | Filo

Consider a simple hypothesis testing problem, where P(X=i): X ... | Filo

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VIDEO solution:Let X have a Poisson distribution with mean θ. Consider the simple hypothesis H0: θ=(1)/(2) and the alternative composite hypothesis H1: θ<(1)/(2) . Thus Ω={θ: 0<θ≤(1)/(2)}. Let X1, …, X12 denote a random sample of size 12 from this distribution. We reject H0 if and only if the observed value of Y=X1 ⋯ X12 ≤2. Show that the following R code graphs the power function of this test: theta=seq (.1, .5, .05) ; gam=ppois (2, theta*12 ) plot (gam "theta, pch=" ", xlab=expression(theta),

VIDEO solution:Let X have a Poisson distribution with mean θ. Consider the simple hypothesis H0: θ=(1)/(2) and the alternative composite hypothesis H1: θ<(1)/(2) . Thus Ω={θ: 0<θ≤(1)/(2)}. Let X1, …, X12 denote a random sample of size 12 from this distribution. We reject H0 if and only if the observed value of Y=X1 ⋯ X12 ≤2. Show that the following R code graphs the power function of this test: theta=seq (.1, .5, .05) ; gam=ppois (2, theta*12 ) plot (gam "theta, pch=" ", xlab=expression(theta),

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