420Hw02 - STAT 420 Homework#2(due Friday February 1 by 4:00...

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STAT 420 Homework #2 Spring 2008 (due Friday, February 1, by 4:00 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, n = 25. Let 1 X = ° = n i i n 1 1 X 1 , 2 X = ° = n i i n 1 2 X 1 , D = 1 X 2 X . a) Find P ( 0 < D < 2 ) . b) Empirical distribution of D: Generate S = 1000 datasets for each of group 1 and group 2. For each of the s = 1 : 1000 datasets, compute d s = s x 1 s x 2 . Plot the histogram for the 1000 values of d . What is the proportion of values of d ( among the 1000 values of d generated ) that are between 0 and 2? 2. The upper management at Initech wants to examine the relationship between the number of years on the job ( x ) and the number of TPS reports produced ( y ) for the middle-management employees. The data are as follows: x 1 2 3 3 4 5 Y 7 4 13 10 10 16 Consider the model Y i = β 0 + β 1 x i + ε i , where ε i ’s are i.i.d.
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