HW3sol - 11 95-2 028 ± 11 80 √ 37 11 95 2 028 ± 11 80...

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SOLUTIONS TO HWK 5 6.4-2 (a) [77 . 272 , 92 . 728]; ( b )[79 . 12 , 90 . 88]; ( c )[80 . 065 , 89 . 935]; (d) [81 . 154 , 88 . 846]. 6.4-4 (a) ¯ x = 56 . 8; (b) [56 . 8 - 1 . 96( 2 10 ) , 56 . 8 + 1 . 96( 2 10 )] = [55 . 56 , 58 . 04]. 6.4-5 ¯ x = 60 . 37 , s = 39 . 62. α = 0 . 1 , z α 2 = 1 . 645; Δ 0 . 05 = 1 . 645 ± 39 . 61 30 = 11 . 9 . The approximate 90% CI is: μ E [48 . 47 , 72 . 27]. In fact, using our tables we can find the explicit 90% CI; indeed, t 0 . 05 (29) = 1 . 697, the explicit Δ 0 . 05 = 1 . 697 ± 39 . 61 30 = 12 . 27, and the explicit 90% CI is [48 . 1 , 72 . 64]. 6.4-6 The approximate CI for μ W is: 11 . 95 - 1 . 96 ± 11 . 80 37 , 11 . 95 + 1 . 96 ± 11 . 80 37 ¶‚ = [8 . 15 , 15 . 75]. If more extensive t -tables are available or if a computer program is used we have the explicit CI
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Unformatted text preview: 11 . 95-2 . 028 ± 11 . 80 √ 37 ¶ , 11 . 95 + 2 . 028 ± 11 . 80 √ 37 ¶‚ = [8 . 016 , 15 . 884] . Problem A 1) 57 is contained in the the CI with confidence coefficient ).95 so this value of μ agrees with the observed data. 2) 58.2 is not contained in the CI so it contradicts our data and we decide that it is not a possible value of μ . Problem B The CI [8 . 15 , 15 . 75] for μ W is located to the left of the CI [48 . 1 , 72 . 64] for μ E , therefore μ W < μ E . 1...
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This note was uploaded on 02/24/2009 for the course STAT 415 taught by Professor Senturk,damla during the Spring '06 term at Penn State.

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