# 420Hw01 - 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) i) Find P ( 3 < X 1 1 < 9 ). ii) Find ε so that P ( | X 1 1 – 6 | < ε ) = 0.95. b) Let 1 X = = n i i n 1 1 X 1 . i) Suppose n = 25. Find P ( 5 < 1 X < 7 ). ii) Suppose n = 25. Find ε so that P ( | 1 X – 6 | < ε ) = 0.95. iii) Find the smallest value of n so that P ( | 1 X – 6 | < 0.1 ) > 0.95. 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 ). 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 an average salary of \$16,400, what is the 95% confidence interval for μ

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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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420Hw01 - STAT 420 Homework #1 (due Friday, August 31, by...

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