4. Suppose we are given a random sample X₁, X2,..., Xn from a normal distribution N(0,0²). (a) Find the Uniformly Most Powerful (UMP) critical region of significance level & for testing Ho: o² = 1 against H₁:0² < 1. (b) Show that the test statistic in this regard is T = ₁X² and it follows a chi-square x distribution under Ho. n i=1 (c) Find the power of the test if the value of o² under the alternative H₁ is of = 0.2, n = 10 and α = = 0.05.
4. Suppose we are given a random sample X₁, X2,..., Xn from a normal distribution N(0,0²). (a) Find the Uniformly Most Powerful (UMP) critical region of significance level & for testing Ho: o² = 1 against H₁:0² < 1. (b) Show that the test statistic in this regard is T = ₁X² and it follows a chi-square x distribution under Ho. n i=1 (c) Find the power of the test if the value of o² under the alternative H₁ is of = 0.2, n = 10 and α = = 0.05.
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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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!
Transcribed Image Text:4. Suppose we are given a random sample X₁, X2,..., Xn from a normal
distribution N(0,0²).
(a) Find the Uniformly Most Powerful (UMP) critical region of
significance level & for testing
Ho: 0²
=
1 against H₁ : 0² < 1.
(b) Show that the test statistic in this regard is T = ₁X² and it
follows a chi-square x² distribution under Ho.
(c) Find the power of the test if the value of o2 under the alternative
H₁ is o² = 0.2, n = 10 and α = 0.05.
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