2. Suppose that X1, X2, … , Xn are iid N (µ, 0²). To test the null hypothesis Ho:µ = Ho, the ... t-test is often used: X - Ho t Vn Under H, t follows at distribution with n-1 degrees of freedom. Show that the likelihood ratio test of this null hypothesis is equivalent to the t-test. [Hint: show that the rejection region for the likelihood ratio test is the same as the rejection region as for t-test above.]

2. Suppose that X1, X2, … , Xn are iid N (µ, 0²). To test the null hypothesis Ho:µ = Ho, the ... t-test is often used: X - Ho t Vn Under H, t follows at distribution with n-1 degrees of freedom. Show that the likelihood ratio test of this null hypothesis is equivalent to the t-test. [Hint: show that the rejection region for the likelihood ratio test is the same as the rejection region as for t-test above.]

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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Question

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2. Suppose that X1, X2, ., X, are iid N(u, o?). To test the null hypothesis Ho: µ = Ho, the
t-test is often used:
X - Ho
t :
Vn
Under Ho, t follows at distribution with n-1 degrees of freedom. Show that the
likelihood ratio test of this null hypothesis is equivalent to the t-test.
[Hint: show that the rejection region for the likelihood ratio test is the same as the
rejection region as for t-test above.]

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