let xxxbe iid observations from a nuo distribution with known variance formulate the likelihood

For exercise 120A, we have Z equals Y sub 1 bar minus Y sub 2 bar minus mu sub 2. This will be d

To test null hypothesis H0, mu greater than equals to 12 versus H1, mu less than 12 at alpha equ

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Let X_1, X_2, ..., X_n be iid observations from a N(u,Ïƒ^2) distribution with known variance. Formulate the likelihood ratio test for testing Ho: u = 2 vs. Ho: u â‰ 2 (10 points). Write down the equations needed to determine the sample size n and the critical value c such that the size of the test is 0.05 and the probability of type-II error when u = 2.5 is 0.1 (6 points) (note: only the equations are needed, no table checking is needed). If we took 16 samples and observed XÌ„ = 2.5, and the population standard deviation is 0.5, compute the p-value based on the data for the test in a). Will you reject Ho at level Î± = 0.05 based on the p-value calculated? (4 points) Hint: You can use L(Î¸) = exp[-(n/2)ln(2Ï€Ïƒ^2) - (1/2Ïƒ^2)âˆ‘(Xi - XÌ„)^2] exp[-(n/2)ln(2Ï€Ïƒ^2) - (1/2Ïƒ^2)âˆ‘(Xi - u)^2] in part a) directly. In case you have difficulty deriving the rejection region in part a), please consider the rejection region |XÌ„ - u| > ZÎ±/2(Ïƒ/âˆšn) for part b).

          Let X_1, X_2, ..., X_n be iid observations from a N(u,Ïƒ^2) distribution with known variance.
Formulate the likelihood ratio test for testing Ho: u = 2 vs. Ho: u â‰  2 (10 points).
Write down the equations needed to determine the sample size n and the critical value c such that the size of the test is 0.05 and the probability of type-II error when u = 2.5 is 0.1 (6 points) (note: only the equations are needed, no table checking is needed).
If we took 16 samples and observed XÌ„ = 2.5, and the population standard deviation is 0.5, compute the p-value based on the data for the test in a). Will you reject Ho at level Î± = 0.05 based on the p-value calculated? (4 points)
Hint: You can use
L(Î¸) = exp[-(n/2)ln(2Ï€Ïƒ^2) - (1/2Ïƒ^2)âˆ‘(Xi - XÌ„)^2] exp[-(n/2)ln(2Ï€Ïƒ^2) - (1/2Ïƒ^2)âˆ‘(Xi - u)^2] in part a) directly. In case you have difficulty deriving the rejection region in part a), please consider the rejection region |XÌ„ - u| > ZÎ±/2(Ïƒ/âˆšn) for part b).

let xxxbe iid observations from a nuo distribution with known variance formulate the likelihood ratio test for testing ho u 2 vs ho ll 2 10 points 6 write down the equations needed to deter 07888

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