Consider a random sample of size one (n = 1) from the distribution with probability function [@y(0-1), if 0 0 otherwise. f(y; 0) = 0, (a) To test Ho: 0 = 0, versus H₂ : 0 = 0₁ > 80, find a most powerful test. Let the positive constant to define the rejection region of the test be k. (b) Find the value of k so that at 0 = 2 the size of the test is 5%. (e) Obtain the power function of the test in part (a).
Consider a random sample of size one (n = 1) from the distribution with probability function [@y(0-1), if 0 0 otherwise. f(y; 0) = 0, (a) To test Ho: 0 = 0, versus H₂ : 0 = 0₁ > 80, find a most powerful test. Let the positive constant to define the rejection region of the test be k. (b) Find the value of k so that at 0 = 2 the size of the test is 5%. (e) Obtain the power function of the test in part (a).
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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![Consider a random sample of size one (n 1) from the distribution with probability
function
f(y; 0) =
[0y(0-1), if 0 <y<1 for € > 0
[o,
otherwise.
(a) To test Ho: 0 = 0, versus H₁ : 0 = 0 > 00, find a most powerful test. Let the
positive constant to define the rejection region of the test be k.
(b) Find the value of k so that at 0 = 2 the size of the test is 5%.
(c) Obtain the power function of the test in part (a).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17176ae9-b253-442d-89f9-517b049b4c59%2F7a9250d9-8492-4a77-80e4-4d39322708c1%2Fgow8w_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a random sample of size one (n 1) from the distribution with probability
function
f(y; 0) =
[0y(0-1), if 0 <y<1 for € > 0
[o,
otherwise.
(a) To test Ho: 0 = 0, versus H₁ : 0 = 0 > 00, find a most powerful test. Let the
positive constant to define the rejection region of the test be k.
(b) Find the value of k so that at 0 = 2 the size of the test is 5%.
(c) Obtain the power function of the test in part (a).
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