# Example Class7 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1302 PROBABILITY AND STATISTICS II (2010-11) EXAMPLE CLASS 7 1. Let X have the pdf f ( x | θ ) = θ x (1 - θ ) 1 - x , x = 0 , 1 , zero elsewhere for θ > 0. We test the simple hypothesis H 0 : θ = 1 4 against the alternative composite hypothesis H 1 : θ < 1 4 by taking a random sample of size 10 and rejecting H 0 if and only if the sum of the observed values 10 i =1 x i 1. The the power function of the test. 2. Let X have a pdf of the form f ( x ) = θx θ - 1 , 0 < x < 1 , where θ ∈ { θ : θ = 1 , 2 } . To test the simple hypothesis H 0 : θ = 1 against the alternative simple hypothesis H 1 : θ = 2, use a random sample X 1 , X 2 of size n=2 and deﬁne the critical region to be C = { ( x 1 ,x 2 ) : 3 / 4 x 1 x 2 } . Find the power function of the test. 3. A manufacturer has produced a large batch of fan-belts whose lengths have a normal distribution. From past experience he knows that his machine capability is

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## This note was uploaded on 11/17/2011 for the course MUSIC 1001 taught by Professor Dr.yun during the Spring '11 term at Princess Sumaya University for Technology.

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Example Class7 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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