a) Suppose that Y₁, Y₂, ..., Y₁ 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 H, if Σ=1 y² ≥ c, where c is a constant that solves the probability equation 0.05 = P₁Y² ≥c|0 = 1). ii) What will be the value of c in part a) if n = 15.
a) Suppose that Y₁, Y₂, ..., Y₁ 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 H, if Σ=1 y² ≥ c, where c is a constant that solves the probability equation 0.05 = P₁Y² ≥c|0 = 1). ii) What will be the value of c in part a) if n = 15.
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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![a)
Suppose that Y₁, Y₂, ..., Y₁ 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 H, if
Σ=1 y² ≥ c, where c is a constant that solves the probability equation
0.05 = P₁Y² ≥c|0 = 1).
ii) What will be the value of c in part a) if n = 15.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e062e9b-adec-4860-8e7c-6104f4664ec5%2Ff842e521-5dc6-423c-a708-9af63dd8982e%2Fc23tunh_processed.png&w=3840&q=75)
Transcribed Image Text:a)
Suppose that Y₁, Y₂, ..., Y₁ 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 H, if
Σ=1 y² ≥ c, where c is a constant that solves the probability equation
0.05 = P₁Y² ≥c|0 = 1).
ii) What will be the value of c in part a) if n = 15.
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