4) Let X have the p.m.f. f(r; 8) = 0" (1 – 0)*-z, x = 0,1. We test Ho : 0 = 0.5 vs. Ha : 0 < 0.5 by taking a random sample X1, X2, ..., X, of size n = 5 and rejecting Ho if Y = EX; is observed to be less than or equal to a constant c. a) Show that this is a uniformly most powerful test. b) Find the significance level when c= 1. c) Find the significance level when c= = 0.
4) Let X have the p.m.f. f(r; 8) = 0" (1 – 0)*-z, x = 0,1. We test Ho : 0 = 0.5 vs. Ha : 0 < 0.5 by taking a random sample X1, X2, ..., X, of size n = 5 and rejecting Ho if Y = EX; is observed to be less than or equal to a constant c. a) Show that this is a uniformly most powerful test. b) Find the significance level when c= 1. c) Find the significance level when c= = 0.
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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![4) Let X have the p.m.f.
f(x; 8) = 6" (1 – 0)'-², x = 0, 1.
We test Ho : 0 = 0.5 vs. H. : 0 < 0.5 by taking a random sample
X1, X2, ..., X, of size n = 5 and rejecting Ho if Y = EX; is observed
to be less than or equal to a constant c.
a) Show that this is a uniformly most powerful test.
b) Find the significance level when c = 1.
c) Find the significance level when c= 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7eebb740-a373-4c85-98d2-7b97f64873d1%2Fa7aa6368-3c65-4193-8d02-7d2fdc8d51d3%2Fnilt7s_processed.png&w=3840&q=75)
Transcribed Image Text:4) Let X have the p.m.f.
f(x; 8) = 6" (1 – 0)'-², x = 0, 1.
We test Ho : 0 = 0.5 vs. H. : 0 < 0.5 by taking a random sample
X1, X2, ..., X, of size n = 5 and rejecting Ho if Y = EX; is observed
to be less than or equal to a constant c.
a) Show that this is a uniformly most powerful test.
b) Find the significance level when c = 1.
c) Find the significance level when c= 0.
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