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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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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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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Calculus For The Life Sciences
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ISBN:
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