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hw10_sol

# hw10_sol - Homework 10 Problem 1 a)a 1 α level con dence...

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Unformatted text preview: Homework 10 November 30, 2007 Problem 1. a)a 1- α level con dence interval is ( ¯ X- z α 2 σ √ n , ¯ X + z α 2 σ √ n ) . Thus z α 2 = 2 . 81 ⇒ 1- 2 α = 0 . 9854 ⇒ 1- α = 0 . 9702 b) z α 2 = 1 . 44 ⇒ 1- 2 α = 0 . 9265 ⇒ 1- α = 0 . 8530 c) 1- α = . 997 ⇒ 1- α 2 = 0 . 9985 ⇒ z α 2 = 2 . 97 d)The length l of a con dence interval is 2 z α 2 σ √ n . z α 2 = 1 . 96 ⇒ n = ( 3 . 92 σ l ) 2 l = 1 ⇒ n = (3 . 92 σ ) 2 ,l = 1 / 2 ⇒ n = (7 . 84 σ ) 2 ,l = 1 ⇒ n = (1 . 96 σ ) 2 e) n = (2 z α 2 σ ) 2 . 1- α = . 9 ⇒ n = (3 . 3 σ ) 2 , 1- α = . 99 ⇒ n = (5 . 16 σ ) 2 , 1- α = . 999 ⇒ n = (6 . 54 σ ) 2 Problem 2. a) EY=950 b)Y is binomial with P = 0 . 95 ,n = 1000 c) P (940 ≤ Y ≤ 960) = P ( Y ≤ 960)- P ( Y ≤ 939) = . 9402- . 0671 = 0 . 8731 Problem 3. (a) Note that √ n ( ¯ X n- μ ) /σ ∼ N (0 , 1) , so LHS = Φ( z α 2 )- Φ(- z α 1 ) = 1- α 2- α 1 = 1- α , where Φ is the distribution function of a standard normal....
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hw10_sol - Homework 10 Problem 1 a)a 1 α level con dence...

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