231hw9solutionsF11

# 231hw9solutionsF11 - Will Landau October 3, 2011 STAT 231...

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Will Landau October 3, 2011 STAT 231 Problem Set 9 Solutions Exercise 9.1 (Devore 8.82) . H 0 : σ = σ 0 H a : σ > σ 0 α = . 01 X 2 = ( n - 1) S 2 2 0 χ 2 n - 1 Reject H 0 when X 2 χ 2 α,n - 1 σ 0 = . 5 , S = . 58 , n = 10, so X 2 = (10 - 1)( . 58 2 ) / ( . 5 2 ) = 12 . 1104 χ 2 α,n - 1 = χ 2 . 01 , 9 = 21 . 665 (from table A.7) Hence, X 2 < χ 2 . 01 , 9 . We fail to reject H 0 . The data do not strongly contradict the uniformity speciﬁcation. Now, for the problems from Chapter 9: 1

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Here, we assume the data points were drawn from independent observations. Also, within each sample, we assume the data are identically distributed with some normal distribution. The conﬁdence interval for μ 1 - μ 2 is ( x 1 - x 2 ) ± t α = . 025 =14 · q S 2 1 n 1 + S 2 2 n 2 = (19 . 2 - 23 . 13) ± 2 . 145 · q 1 . 58 2 12 + 4 . 01 2 12 = - 3 . 93 ± 2 . 669 = (-6.599,-1.261) 3

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49. H 0 : p 1 - p 2 = 0 H a : p 2 - p 2 < 0 α = . 01 Under H 0 , X = b p 1 - b p 2 b p (1 - b p )( 1 m + 1 n ) N (0 , 1) Let x be the realized value of X from the data and Z N (0 , 1). Reject H 0 if p-value = P ( Z x ) = Φ( x ) < α = . 01. From the data, we have: b p 1 = 30 200 = . 15 b p 2 = 180 600 = . 3 b p = 30+180 200+600 = . 2625 x = b p 1 - b p 2 b p (1 - b p )( 1 m + 1 n ) = . 15 - . 3 . 2625(1 - . 2625)(

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## This note was uploaded on 02/11/2012 for the course STAT 231 taught by Professor Staff during the Fall '08 term at Iowa State.

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231hw9solutionsF11 - Will Landau October 3, 2011 STAT 231...

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