10_10_11_1ans

10_10_11_1ans - STAT 409 Examples for 10/10/2011 (1) Fall...

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STAT 409 Examples for 10/10/2011 (1) Fall 2011 2. Let X have a Binomial distribution with the number of trials n = 15. To test H 0 : p = 0.30 vs. H 1 : p > 0.30, we will use the rejection ( critical ) region rejection ( critical ) region “Reject H 0 if X 9”. a) Find the significance level of this test. α = P ( Type I error ) = P ( Reject H 0 | H 0 true ) = P ( X 9 | p = 0.30 ) = 1 – CDF ( 8 | p = 0.30 ) = 1 – 0.985 = 0.015 . b) Suppose we observe X = 10. Find the p-value of this test. p-value = P ( value of X as extreme or more extreme than X = 10 | H 0 true ) = P ( X 10 | p = 0.30 ) = 1 – CDF ( 9 | p = 0.30 ) = 1 – 0.996 = 0.004 . c) Find the “best” rejection region with the significance level α closest to 0.05. Rejection Region for a Right – tailed test: Find b such that P ( X b – 1 ) 1 – α . Then the Rejection Region is “Reject H 0 if X b .” Want P ( Type I error ) = 0.05. P
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10_10_11_1ans - STAT 409 Examples for 10/10/2011 (1) Fall...

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