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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online