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a) Suppose that Y₁, Y₂,...,Y, is a random sample from a normal distribution with parameter mean O and variance 8, say N(0,8). If Mr Masela and Mr Sepuru desire to use 5% level of significance to test the null hypothesis H,: 0 = 1 against alternative hypothesis H₁:8 > 1. i) Show that the uniformly most powerful test of their hypothesis rejects H, if Σ₁² ≥c, where c is a constant that solves the probability equation 0.05 = P(Z₁Y² ≥c|8 = 1).

a) Suppose that Y₁, Y₂,...,Y, is a random sample from a normal distribution with parameter mean O and variance 8, say N(0,8). If Mr Masela and Mr Sepuru desire to use 5% level of significance to test the null hypothesis H,: 0 = 1 against alternative hypothesis H₁:8 > 1. i) Show that the uniformly most powerful test of their hypothesis rejects H, if Σ₁² ≥c, where c is a constant that solves the probability equation 0.05 = P(Z₁Y² ≥c|8 = 1).

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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6.STATISTICAL INFERENCE
Question 3 a i)

a) Suppose that Y₁, Y₂,...,Y, is a random sample from a normal distribution with parameter mean o and variance 8, say N(0,8). If Mr Masela and Mr Sepuru desire to use 5% level of significance to test the null hypothesis H₁: 0 = 1 against alternative hypothesis H₁:0 > 1. i) Show that the uniformly most powerful test of their hypothesis rejects H, if Σ₁y? ≥c, where is a constant that solves the probability equation 0.05 = P(Z₁Y²2c|08 = 1).
Transcribed Image Text:a) Suppose that Y₁, Y₂,...,Y, is a random sample from a normal distribution with parameter mean o and variance 8, say N(0,8). If Mr Masela and Mr Sepuru desire to use 5% level of significance to test the null hypothesis H₁: 0 = 1 against alternative hypothesis H₁:0 > 1. i) Show that the uniformly most powerful test of their hypothesis rejects H, if Σ₁y? ≥c, where is a constant that solves the probability equation 0.05 = P(Z₁Y²2c|08 = 1).
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