(a) Show that the likelihood ratio test of Ho: 0 = 0o versus H₁ : 000 is based upon the statistic Y = 1 X₁. Obtain the null distribution of Y. (b) For n = 100 and 0o = 1/2, find c₁ so that the test rejects Ho when Y ≤ c₁ or Y Z C₂ = 100 - c₁ has the approximate significance level of a = Use the Central Limit Theorem. 0.05. Hint:
(a) Show that the likelihood ratio test of Ho: 0 = 0o versus H₁ : 000 is based upon the statistic Y = 1 X₁. Obtain the null distribution of Y. (b) For n = 100 and 0o = 1/2, find c₁ so that the test rejects Ho when Y ≤ c₁ or Y Z C₂ = 100 - c₁ has the approximate significance level of a = Use the Central Limit Theorem. 0.05. Hint:
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.CR: Chapter 13 Review
Problem 3CR
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Transcribed Image Text:6.3.10. Let X1, X2,..., Xn be a random sample from a Bernoulli b(1,0) distribu-
tion, where 0 <0 < 1.
(a) Show that the likelihood ratio test of Ho: 0 = 0o versus H₁ : 000 is based
upon the statistic Y = 1 X₁. Obtain the null distribution of Y.
(b) For n = 100 and 0o = 1/2, find c₁ so that the test rejects Ho when Y ≤ c₁ or
Y 2 C₂ = 100 - c₁ has the approximate significance level of a = 0.05. Hint:
Use the Central Limit Theorem.
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