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a) Suppose that Y₁, Y₂, ..., Yn is a random sample from a normal distribution with parameter mean 0 and variance 0, say N(0,0). If Mr Masela and Mr Sepuru desire to use 5% level of significance to test the null hypothesis Ho: 0 = 1 against alternative hypothesis H₁: 0 > 1. i) Show that the uniformly most powerful test of their hypothesis rejects Ho if Σ₁yc, where c is a constant that solves the probability equation 0.05 = P(₁Y² ≥ c|0 = 1). ii) What will be the value of c in part a) if n = 15.

a) Suppose that Y₁, Y₂, ..., Yn is a random sample from a normal distribution with parameter mean 0 and variance 0, say N(0,0). If Mr Masela and Mr Sepuru desire to use 5% level of significance to test the null hypothesis Ho: 0 = 1 against alternative hypothesis H₁: 0 > 1. i) Show that the uniformly most powerful test of their hypothesis rejects Ho if Σ₁yc, where c is a constant that solves the probability equation 0.05 = P(₁Y² ≥ c|0 = 1). ii) What will be the value of c in part a) if n = 15.

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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a) QUESTION 3 Suppose that Y₁, Y2, ..., Yn is a random sample from a normal distribution with parameter mean 0 and variance 0, say N(0,0). If Mr Masela and Mr Sepuru desire to use 5% level of significance to test the null hypothesis Ho: 0 = 1 against alternative hypothesis H₁:0 > 1. i) Show that the uniformly most powerful test of their hypothesis rejects Ho if Σ₁ yc, where c is a constant that solves the probability equation 0.05 = P₁Y≥ c|0 = 1). ii) What will be the value of c in part a) if n = 15.
Transcribed Image Text:a) QUESTION 3 Suppose that Y₁, Y2, ..., Yn is a random sample from a normal distribution with parameter mean 0 and variance 0, say N(0,0). If Mr Masela and Mr Sepuru desire to use 5% level of significance to test the null hypothesis Ho: 0 = 1 against alternative hypothesis H₁:0 > 1. i) Show that the uniformly most powerful test of their hypothesis rejects Ho if Σ₁ yc, where c is a constant that solves the probability equation 0.05 = P₁Y≥ c|0 = 1). ii) What will be the value of c in part a) if n = 15.
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