Homework Solutions 08

Homework Solutions 08 - Solutions to Homework #8 (W4150...

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Solutions to Homework #8 (W4150 ‘Intro to Probability and Statistics’, S04) Sec. 9.7. (4) n = 30; X = 780; σ = 40; z α /2 = z 0.02 = 2.054 Hence by applying formula for CI from p.235 we obtain: ) 30 40 )( 05 . 2 ( 780 ) 30 40 )( 05 . 2 ( 780 + < < µ or 795 765 < < Sec.9.7. (6) n = 50; X = 174.5; σ = 6.9; z α /2 = z 0.01 = 2.33 (a) The confidence interval is given by the same formula as above, which in this case yields: ) 50 9 . 6 )( 33 . 2 ( 5 . 174 ) 50 9 . 6 )( 33 . 2 ( 5 . 174 + or 77 . 176 23 . 172 < < (b) By Theorem 9.1 we can be 98% sure that the error 27 . 2 50 / ) 9 . 6 )( 33 . 2 ( = < e Sec. 9.7. (7) Applying the same methods for n = 100; X = 23,500; σ = 3,900 and z α /2 = z 0.005 = 2.575 we get: (a) 99% CI for mean: 22,496 < µ < 24,504; and (b) estimation for error 1004 < e Sec. 9.7 (8) In this as well as in two next problems we use formula given in Theorem 9.1 z α /2 = z 0.02 = 2.054; e = 10; σ = 40 and so n = [(2.05)(40)/10]
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Homework Solutions 08 - Solutions to Homework #8 (W4150...

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