Final-Fall-2005-06 - n be chosen so that when testing H :...

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STAT 230 Final Exam Feb 1, 2006 Time = 1 hour 1. Let X = ( x 1 , ··· ,x m ) 0 be a random sample from the pdf f ( x ; σ ) = 1 σ 2 π exp[ - 1 2 σ 2 ( x - 10) 2 ] If 20 i =1 X i = 180 and 20 i =1 X 2 i = 2000, find a 90% confidence interval for σ . 2. Let X be a Bernoulli random variable with a pdf f ( x ; θ ) = θ x (1 - θ ) 1 - x if x = 0 or 1 and 0 < θ < 1 We would like to test the hypothesis H 0 : θ = 1 2 vs H a : θ = 2 3 It is agreed to perform two observations X 1 and X 2 . If both X 1 = 1 and X 2 = 1 then we reject H 0 ; otherwise we don’t reject H 0 . Find α = P (Type I error) and β = P (Type II error). 3. If X has the pdf f ( x ; μ ) = 1 10 2 π exp[ - 1 2 ( x - μ 10 ) 2 ], How large should
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Unformatted text preview: n be chosen so that when testing H : μ = 100 vs H a : μ = 110 the values of α = 0 . 05 and β = 0 . 10? 4. A box is known to contain either 3 red and 5 black balls or 5 red and 3 black balls. Three balls are drawn randomly and without replacement. If three red balls are obtained, the decision will be 5 red and 3 black; otherwise, the decision will be 3 red and 5 black balls. Calculate the values of α and β . 1...
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This note was uploaded on 03/01/2010 for the course STAT 230 taught by Professor Variousteachers during the Spring '10 term at American University of Beirut.

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