Let Y₁, Y2, Y3,..., Yn ind 1. Find the asymptotic distribution of Z := the asymptotic distribution of μ? N(μ, o²), where ² μμ √o²/n = 25 is known. where is the MLE. Hint: what is 2. Suppose now we do not know o2 and instead plug in the MLE estimator 2 1/1(Y₂-μ)² to obtain Z := μμ Is the asymptotic distribution still N(0, 1)? If yes, why? (hint: what do we know about consistency of MLEs? Slutsky's theorem?). √ô²/n 3. Suppose we collect data of size n = 16 and the MLE turns out to be û = 2 and ² = 25. Using the result from the previous part, conduct an a = .05 level test of Hoμ = 0 in favor of Haµ ‡0. Find the critical value, rejection region, and p-value. Interpret the p-value. Do you reject or fail to reject the null?

Let Y₁, Y2, Y3,..., Yn ind 1. Find the asymptotic distribution of Z := the asymptotic distribution of μ? N(μ, o²), where ² μμ √o²/n = 25 is known. where is the MLE. Hint: what is 2. Suppose now we do not know o2 and instead plug in the MLE estimator 2 1/1(Y₂-μ)² to obtain Z := μμ Is the asymptotic distribution still N(0, 1)? If yes, why? (hint: what do we know about consistency of MLEs? Slutsky's theorem?). √ô²/n 3. Suppose we collect data of size n = 16 and the MLE turns out to be û = 2 and ² = 25. Using the result from the previous part, conduct an a = .05 level test of Hoμ = 0 in favor of Haµ ‡0. Find the critical value, rejection region, and p-value. Interpret the p-value. Do you reject or fail to reject the null?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.CR: Chapter 2 Review

Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

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