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uppose μ0 is known and the parameter of interest is 0 = o. he sample collected will be used to test Ho: 0= 2 vs. Ho: 0= 3. a) Show that the Neyman-Pearson form of the rejection region is {EX> D} for some constant D. b) Specify multiplying Ei=1 Xi| by what will make the product to have a chi-square distribu- tion. c) For sample size n = 45 and a = 0.05, find D and specify the rejection region. d) For the rejection region found in the previous part, find the P(Type II Error) to 5 decimal place accuracy.

uppose μ0 is known and the parameter of interest is 0 = o. he sample collected will be used to test Ho: 0= 2 vs. Ho: 0= 3. a) Show that the Neyman-Pearson form of the rejection region is {EX> D} for some constant D. b) Specify multiplying Ei=1 Xi| by what will make the product to have a chi-square distribu- tion. c) For sample size n = 45 and a = 0.05, find D and specify the rejection region. d) For the rejection region found in the previous part, find the P(Type II Error) to 5 decimal place accuracy.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Suppose that a random sample (i.i.d. observations) X₁,..., Xn of size n is to be taken from a Laplace distribution with the PDF f(x; μ,0): e 20 |x-μ| 0 -8<<∞ Suppose μ = 0 is known and the parameter of interest is 0 = 0. The sample collected will be used to test Ho: 0= 2 vs. Ho : 0 = 3. (a) Show that the Neyman-Pearson form of the rejection region is { constant D. |X₁|> D} for some (b) Specify multiplying 1Xi| by what will make the product to have a chi-square distribu- tion. (c) For sample size n = 45 and a = 0.05, find D and specify the rejection region. (d) For the rejection region found in the previous part, find the P(Type II Error) to 5 decimal place accuracy.
Transcribed Image Text:Suppose that a random sample (i.i.d. observations) X₁,..., Xn of size n is to be taken from a Laplace distribution with the PDF f(x; μ,0): e 20 |x-μ| 0 -8<<∞ Suppose μ = 0 is known and the parameter of interest is 0 = 0. The sample collected will be used to test Ho: 0= 2 vs. Ho : 0 = 3. (a) Show that the Neyman-Pearson form of the rejection region is { constant D. |X₁|> D} for some (b) Specify multiplying 1Xi| by what will make the product to have a chi-square distribu- tion. (c) For sample size n = 45 and a = 0.05, find D and specify the rejection region. (d) For the rejection region found in the previous part, find the P(Type II Error) to 5 decimal place accuracy.
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