11_28_11_1ans - STAT 409 Fall 2011 Examples for 11/28/2011...

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Examples for 11/28/2011 Fall 2011 Let X 1 , X 2 , … , X n be a random sample from a continuous-type population. Let Y 1 < Y 2 < … < Y n denote the corresponding order statistics. P ( Y i < π p < Y j ) = P ( i [ number of observations to the left of π p ] j – 1 ) = P ( i Binomial ( n , p ) j – 1 ). 1. Consider a random sample form a certain population: 8 15 20 28 34 42 47 50 55 62 66 70 77 85 94 100 112 120 132 145 a) Find P ( 42 < m < 85 ) = P ( Y 6 < m < Y 14 ), where m is the population median. P ( 42 < m < 85 ) = P ( Y 6 < m < Y 14 ) = P ( 6 Binomial ( 20, 0.50 ) 13 ) = 0.942 – 0.021 = 0.921 . b) Find the endpoints for an approximate 95% confidence interval for the median m . P ( 6 Binomial ( 20, 0.50 ) 14 ) = 0.979 – 0.021 = 0.958 0.95. ( Y 6 , Y 15 ) = ( 42, 94 ) . c) Find P ( 20 < π 0.30 < 62 ) = P ( Y 3 < π 0.30 < Y 10 ). P
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This note was uploaded on 12/15/2011 for the course STAT 409 taught by Professor Stephanov during the Fall '11 term at University of Illinois at Urbana–Champaign.

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11_28_11_1ans - STAT 409 Fall 2011 Examples for 11/28/2011...

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