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# 420Hw01ans - STAT 420 Homework#1(due Friday August 31 by...

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STAT 420 Fall 2007 Homework #1 (due Friday, August 31, by 3:00 p.m.) 1. We would like to test the effect of drugs 1 and 2 on a physiological measure X. Consider the model: X 1 1 , X 1 2 , … , X 1 n are i.i.d. N ( μ 1 , σ 2 ) X 2 1 , X 2 2 , … , X 2 n are i.i.d. N ( μ 2 , σ 2 ) Assume that μ 1 = 6, μ 2 = 5, σ 2 = 4. a) X 1 1 ~ N ( μ 1 , σ 2 ) = N ( 6 , 4 ) 2 6 X 11 - = Z ~ N ( 0 , 1 ) i) Find P ( 3 < X 1 1 < 9 ) . P ( 3 < X 1 1 < 9 ) = P ( 1.50 < Z < 1.50 ) = 0.8664 . ii) Find ε so that P ( | X 1 1 – 6 | < ε ) = 0.95. 2 ° = 1.96. ε = 3.92 . b) Let 1 X = ° = n i i n 1 1 X 1 . i) Suppose n = 25. Find P ( 5 < 1 X < 7 ) . 1 X ~ N ( μ 1 , n 2 ± ) = N ( 6 , 25 4 ) 25 2 6 X 1 - = Z ~ N ( 0 , 1 ) P ( 5 < 1 X < 7 ) = P ( 2.50 < Z < 2.50 ) = 0.9876 . ii) Suppose n = 25. Find ε so that P ( | 1 X – 6 | < ε ) = 0.95. 25 2 ° = 1.96. ε = 0.784 .

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iii) Find the smallest value of n so that P ( | 1 X – 6 | < 0.1 ) > 0.95. n 2 0.1 > 1.96. n > 39.2. n > 1536.64. n 1537 . c) Let 2 X = ° = n i i n 1 2 X 1 , D = 1 X 2 X . Suppose n = 25. Find P ( 0 < D < 2 ) . D = 1 X 2 X ~ N ( μ 1 μ 2 , n n 2 2 ± ± + ) = N ( 6 – 5 , 25 4 25 4 + ) D ~ N ( 1 , 0.32 ) 32 . 0 1 D - = Z ~ N ( 0 , 1 ) P ( 0 < D < 2 ) P ( 1.77 < Z < 1.77 ) = 0.9232 . 2. The salary of junior executives in a large retailing firm is normally distributed with standard deviation σ = \$1,500. If a random sample of 25 junior executives yields
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420Hw01ans - STAT 420 Homework#1(due Friday August 31 by...

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