8. (Exercise 6.3.10 from edition 8 of the textbook) Let X₁, X2,..., Xn be a random sample from a Bernoulli b(1, 0) distr

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8 Exercise 6 3 10 From Edition 8 Of The Textbook Let X X2 Xn Be A Random Sample From A Bernoulli B 1 0 Distr 1 (52.99 KiB) Viewed 43 times

8. (Exercise 6.3.10 from edition 8 of the textbook) Let X₁, X2,..., Xn be a random sample from a Bernoulli b(1, 0) distribution, 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 distribution of Y under Ho. (b). For n = 100 and 0o = 1/2, find c₁ so that the test rejects Ho when Y ≤ c₁ or Y ≥ c₂ = 100 – c₁ has the approximate significance level of a = 0.05. [Hint: Use the Central Limit Theorem.]