HW4_sol - 1 843 a)95%upperCIanddf=24 b)99%lowerCIanddf=9...

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1. 8 43 a) 95% upper CI and df = 24 = 2 , 1 df α χ = 2 24 , 95 . 0 χ 13.8484 b) 99% lower CI and df = 9 = 2 , df α χ = 2 9 , 01 . 0 χ 21.6660 c) 90% CI and df = 19 14 . 30 2 19 , 05 . 0 2 , 2 / = = χ χ α df and 12 . 10 2 19 , 95 . 0 2 , 2 / 1 = = χ χ α df 2. 8 52 a) 99% two sided confidence interval on σ 2 913 . 1 10 = = s n 59 . 23 2 9 , 005 . 0 = χ and 73 . 1 2 9 , 995 . 0 = χ 038 . 19 396 . 1 73 . 1 ) 913 . 1 ( 9 59 . 23 ) 913 . 1 ( 9 2 2 2 2 σ σ b) 99% lower confidence bound for σ 2 For α = 0.01 and n = 10, = 2 1 , n α χ = 2 9 , 01 . 0 χ 21.67 2 2 2 5199 . 1 67 . 21 ) 913 . 1 ( 9 σ σ c) 90% lower confidence bound for σ 2 For α = 0.1 and n = 10, = 2 1 , n α χ = 2 9 , 1 . 0 χ 14.68 σ σ σ 498 . 1 2436 . 2 68 . 14 ) 913 . 1 ( 9 2 2 2
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