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# 409Hw05 - 29 α<<-≈ 1 1 X P 2 2 z p p n p n z Show...

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STAT 409 Homework #5 Fall 2009 (due Thursday, October 1, by 4:00 p.m.) From the textbook: 6.6-2 6.6-4 6.6-8 6.6-10 6.7-2 6.7-4 6.7-12 6.7-18 6.8-12 a) … if we believe the seed distributor’s claim; b) … if we ignore the seed distributor’s claim. 10. Let X have a Binomial distribution with parameters n and p . Recall that ( 29 1 X p p n p n - - has an approximate Standard Normal N ( 0, 1 ) distribution, provided that n is large enough, and
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Unformatted text preview: ( 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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