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2 13. Let X1,..., Xn ~ iid N(0, T) and consider the hypotheses Ho: T≥ TO VS H₁T

2 13. Let X1,..., Xn ~ iid N(0, T) and consider the hypotheses Ho: T≥ TO VS H₁T

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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13. Let X1,..., Xn ~iid N(0, 7) and consider the hypotheses Ho: T To vs H₁T < To- (a) Find the most powerful size-a test. You should provide to in terms of a x2 critical value. (b) If X1,..., Xn ~iid N(д, T) for known μ, find the UMP size-a test. (c) If X1,..., Xn ~iid N(μ, T) for unknown μ, propose a size-a test with similar from to (b). Comment on why you can't conclude that this test is UMP.
Transcribed Image Text:13. Let X1,..., Xn ~iid N(0, 7) and consider the hypotheses Ho: T To vs H₁T < To- (a) Find the most powerful size-a test. You should provide to in terms of a x2 critical value. (b) If X1,..., Xn ~iid N(д, T) for known μ, find the UMP size-a test. (c) If X1,..., Xn ~iid N(μ, T) for unknown μ, propose a size-a test with similar from to (b). Comment on why you can't conclude that this test is UMP.
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