409Hw09 - STAT 409 Fall 2009 Homework#9(due Friday October...

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STAT 409 Homework #9 Fall 2009 (due Friday, October 30, by 4:00 p.m.) From the textbook: 8.2-16 9.1-4 9.1-6 9.1-7 9.1-10 9.1-12 7. Let X 1 , X 2 , … , X 25 be a random sample from a N ( μ , 100 ) population, and suppose the null hypothesis H 0 : μ = 100 is to be tested. a) If the alternative hypothesis is H 1 : μ > 100, compute the power of the appropriate test at μ = 101 and at μ = 102. Use α = 0.05. b) If the alternative hypothesis is H 1 : μ 100, compute the power of the appropriate test at μ = 101 and at μ = 102. Use α = 0.05. c) For the test in (a) compute the p-value associated with X = 103.5. d) For the test in (b) compute the p-value associated with X = 103.5. 8. Let X 1 , X 2 , … , X 12 be a random sample of size n =12 from a Poisson distribution with mean λ . That is, P ( X 1 = k ) = ! λ λ k e k - , k = 0, 1, 2, 3, … . Consider the test H 0 : λ = 1 / 2 vs. H 1 : λ < 1 / 2 . The rejection region is given by
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409Hw09 - STAT 409 Fall 2009 Homework#9(due Friday October...

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