hw3_solution_1

# hw3_solution_1 - Homework Solution 4 1a H 0 3 750 3 750 P(X...

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Homework Solution 4 1a) 018422 . 0 ) 50 / 03 . 0 75 . 3 74 . 3 ( 2 ) 74 . 3 ( 2 ) 76 . 3 ( ) 74 . 3 ( 750 . 3 : 750 . 3 : 1 0 = - < = < = + < = = Z P X P X P X P H H α μ μ b) 0.09896 ) 50 / 03 . 0 75 . 3 743 . 3 ( 2 ) 743 . 3 ( 2 ) 757 . 3 ( ) 743 . 3 ( = - < = < = + < = Z P X P X P X P α c) 742 . 3 50 03 . 0 96 . 1 750 . 3 758 . 3 50 03 . 0 96 . 1 750 . 3 2 / 0 = - = = + = ± = - + ± c c n z c σ μ α d) reject X X < = 742 . 3 741 . 3 2a) - - Φ - - Φ = σ δ σ δ β α α n z n z 2 / 2 / ( 29 ( 29 0.78146 0.000845 - 0.782305 14 . 3 78 . 0 03 . 0 50 005 . 0 96 . 1 03 . 0 50 005 . 0 96 . 1 03 . 0 50 005 . 0 03 . 0 50 005 . 0 025 . 0 025 . 0 = = - Φ - Φ = - - Φ - - Φ = - - Φ - - Φ = z z β b) ( 29 ( 29 0.34457 06 - 7.8072E - 0.3445783 32 . 4 40 . 0 03 . 0 50 01 . 0 96 . 1 03 . 0 50 01 . 0 96 . 1 03 . 0 50 01 . 0 03 . 0 50 01 . 0 025 . 0 025 . 0 = = - Φ - - Φ = - - Φ - - Φ = - - Φ - - Φ = z z β 3a) + = + n z c σ μ α 2 / 0

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0.007661 0.00383043 3 8 2 / 66667 . 2 3 8
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