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

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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
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This note was uploaded on 04/29/2010 for the course STAT stat 420 taught by Professor Stepanov during the Spring '07 term at University of Illinois at Urbana–Champaign.

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

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