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Unformatted text preview: ≥ 3”. a) Find the significance level of this test. b) Find the power of this test. c) Suppose the observed value of X is x = 2. Find the pvalue. 9. 8.2.2 Hint: Consider three cases: 0 < θ < ½ , ½ < θ < 1, and θ > 1. _________________________________________________________________________ If you are registered for 4 credit hours: ( to be handed in separately ) 10. Let X have a Binomial distribution with parameters n and p . Recall that ( ) 1 X p p n p nhas an approximate Standard Normal N ( 0, 1 ) distribution, provided that n is large enough, and ( ) α& & ± ² ³ ³ ´ µ <<≈ 1 1 X P 2 2 z p p n p n z . Show that an approximate 100 ( 1 – ) % confidence interval for p is ( ) n z n z n p p z n z p 2 2 2 2 2 2 2 2 1 4 1 2 ˆ ˆ ˆ + +± + , where n p X ˆ = . This interval is called the Wilson interval. Note that for large n , this interval is approximately equal to ( ) n p p z p 2 ˆ ˆ ˆ 1± ....
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This note was uploaded on 02/11/2011 for the course STAT 410 taught by Professor Monrad during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Monrad

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