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Let X1, ..., Xn be i.i.d. N (u, O^2) samples, where u and o^2 are both unknown. You want to test the null hypothesis: HO : µ = 0; against the two sided alternative H1: p# 0. We can use the the likelihood ratio statistics. (a) Express the rejection region in terms of a statistic whose distribution you know under the null hypothesis. (b) Suppose that you have a sample of size n = 10 and observations 0.1635, 2.4237, -1.8584, 2.6294, 0.7376, 1.4001, -1.2642, -0.1900, 0.1219, 0.8227. Compute the p-value. With explanations please

Let X1, ..., Xn be i.i.d. N (u, O^2) samples, where u and o^2 are both unknown. You want to test the null hypothesis: HO : µ = 0; against the two sided alternative H1: p# 0. We can use the the likelihood ratio statistics. (a) Express the rejection region in terms of a statistic whose distribution you know under the null hypothesis. (b) Suppose that you have a sample of size n = 10 and observations 0.1635, 2.4237, -1.8584, 2.6294, 0.7376, 1.4001, -1.2642, -0.1900, 0.1219, 0.8227. Compute the p-value. With explanations please

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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Let X1, ..., Xn be i.i.d. N (u, o^2) samples, where u and o^2 are both unknown. You want to test the null hypothesis: HO : µ = 0; against the two sided alternative H1: µ # 0. We can use the the likelihood ratio statistics. (a) Express the rejection region in terms of a statistic whose distribution you know under the null hypothesis. (b) Suppose that you have a sample of size n = 10 and observations 0.1635, 2.4237, -1.8584, 2.6294, 0.7376, 1.4001, -1.2642, -0.1900, 0.1219, 0.8227. Compute the p-value. With explanations please
Transcribed Image Text:Let X1, ..., Xn be i.i.d. N (u, o^2) samples, where u and o^2 are both unknown. You want to test the null hypothesis: HO : µ = 0; against the two sided alternative H1: µ # 0. We can use the the likelihood ratio statistics. (a) Express the rejection region in terms of a statistic whose distribution you know under the null hypothesis. (b) Suppose that you have a sample of size n = 10 and observations 0.1635, 2.4237, -1.8584, 2.6294, 0.7376, 1.4001, -1.2642, -0.1900, 0.1219, 0.8227. Compute the p-value. With explanations please
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