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st422%20hw04%20solution

# st422%20hw04%20solution - Homework 4 Solutions 2 2 0.95...

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Unformatted text preview: Homework 4: Solutions 2 2 0.95 0.05 8.35: P( 2 / ) 0.9 P(0.71072 2 / 9.48733) 0.9 2Y 2 90% Confidence interval for is , 9.48733 0.710721 Y Y Y χ β χ β β ≤ ≤ = ≤ ≤ = ⇒ 2 2 2 2 0.975 0.025 2 2 2 2 2 2 2 2 0.95 2 2 2 2 8.37 : ) P( / ) 0.95 P(0.009821 / 5.02389) 0.95 95% Confidence interval for is , 5.02389 0.009821 ) P( / ) 0.95 P(0.0039321 / ) 0.95 P( / 0.0039321) 0.95 95% U a Y Y Y Y b Y Y Y χ σ χ σ σ χ σ σ σ ≤ ≤ = ≤ ≤ = ⇒ ≤ = ≤ = ≤ = 2 2 2 2 2 0.05 2 2 2 2 2 2 pper Confidence bound for is / 0.0039321 ) P( / ) 0.95 P( / 3.84146) 0.95 P( /3.84146) 0.95 95% Lower confidence bound for is /3.84146 Y c Y Y Y Y σ σ χ σ σ σ ≤ = ≤ = ≥ = ( ) ( ) ( ) u ( ) ( ) ( ) 8.39 : ) F ( ) ( ) ( / ) ( ) ( ) ( ) [ ( )] ( / ) ( ) ( ) 1 = 0 u<0 =1 u>1 b) ( / n n n n n Y n n Y Y n U Y n a u P U u P Y u P Y u F u F y F y y F u F u u u P Y θ θ θ θ θ θ = ≤ = ≤ = ≤ = = = ⇒ = = ≤ ≤ ( ) n 1/ (n) 1/ ) 0.95 ( ) = 0.95 a 0.95 0.95 Y 95% Lower bound for is 0.95 n Y n n a F a a θ θ < = ⇒ ⇒ = ⇒ = 2 Y 2 2 Y 2 Y 2 2 Y 8.40 : ) ( ) 2( ) / 0<y< 2( / 2) F ( ) 2( ) / F ( ) 0 y =(2y/ )-(y /...
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st422%20hw04%20solution - Homework 4 Solutions 2 2 0.95...

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