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a) Suppose that Y₁, Y2, Y 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. 1) Show that the uniformly most powerful test of their hypothesis rejects Ho if Ey ≥c where is a constant that solves the probability equation 0.05 = POZY ≥c|0 = 1). ii) What will be the value of c in part a) if n = 15.

a) Suppose that Y₁, Y2, Y 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. 1) Show that the uniformly most powerful test of their hypothesis rejects Ho if Ey ≥c where is a constant that solves the probability equation 0.05 = POZY ≥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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xAA ht a) 5x Paragraph 1 Correct decision. AaBbCc AaBbCc AaBbC AaBbCcE AaB ABBI 1 Normal 1 No Spac... Heading 1 Heading 2 Title Sub Styles Suppose that Y₁, Y2Yn 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. 1) Show that the uniformly most powerful test of their hypothesis rejects Ho if Ey ≥c where is a constant that solves the probability equation 0.05= POZY ≥ c0 = 1). ii) What will be the value of c in part a) if n = 15. An academic Professor conducted a research aimed at exploring the experience and challenges faced by people who are diagnosed with dementia and their families. If the professor perform a hypothesis test to decide whether the mean age of all people diagnosis with initial occurrence of dementia is less than 55 years old. Based on the statement, explain, what each of the following would mean. i) Type I error. iii) Type Il error. that the results of carrying out the hypothesis test lead to non-rejection of the null
Transcribed Image Text:xAA ht a) 5x Paragraph 1 Correct decision. AaBbCc AaBbCc AaBbC AaBbCcE AaB ABBI 1 Normal 1 No Spac... Heading 1 Heading 2 Title Sub Styles Suppose that Y₁, Y2Yn 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. 1) Show that the uniformly most powerful test of their hypothesis rejects Ho if Ey ≥c where is a constant that solves the probability equation 0.05= POZY ≥ c0 = 1). ii) What will be the value of c in part a) if n = 15. An academic Professor conducted a research aimed at exploring the experience and challenges faced by people who are diagnosed with dementia and their families. If the professor perform a hypothesis test to decide whether the mean age of all people diagnosis with initial occurrence of dementia is less than 55 years old. Based on the statement, explain, what each of the following would mean. i) Type I error. iii) Type Il error. that the results of carrying out the hypothesis test lead to non-rejection of the null
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