11_16ans - STAT 410 Examples for 11/16/2009 Fall 2009 1....

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Unformatted text preview: STAT 410 Examples for 11/16/2009 Fall 2009 1. Suppose n = 49 observations are taken from a normal distribution where σ = 8.0 for the purpose of testing H : μ = 60 versus H 1 : μ > 60. a) What is the significance level associated with the rejection region “Reject H if x > 62” ? significance level = α = P ( Reject H | H is true ) = P ( 62 X | μ = 60 ) = - + - < 49 8 60 62 Z P 49 8 60 58 Z P = P ( Z > 1.75 ) = 0.0401 . b) Find the “best” rejection region with the significance level α = 0.05. Rejection Region: Reject H if Z = σ μ X n- > α z ⇒ σ μ α X n z + ⇒ 49 8 645 . 1 60 X + ⇒ 61.88 X c) Find the power of the test if the true mean is μ 1 = 61 at the α = 0.05 level of significance. Power ( μ = 61 ) = P ( Reject H | H is false ) = P ( 88 . 61 X | μ = 61 ) = - 49 8 61 88 . 61 Z P = P ( Z > 0.77 ) = 0.2206 ....
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This note was uploaded on 04/15/2010 for the course STAT 410 taught by Professor Monrad during the Fall '08 term at University of Illinois, Urbana Champaign.

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11_16ans - STAT 410 Examples for 11/16/2009 Fall 2009 1....

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