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Unformatted text preview: _________________________________________________________________________ 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 ( 29 1 X p p n p nhas an approximate Standard Normal N ( 0, 1 ) distribution, provided that n is large enough, and ( 29 α <<≈ 1 1 X P 2 2 z p p n p n z . Show that an approximate 100 ( 1 – ) % confidence interval for p is ( 29 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 ( 29 n p p z p 2 ˆ ˆ ˆ 1± ....
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 Spring '08
 STEPANOV
 Statistics, Normal Distribution, maximum likelihood estimator

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