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Preparation%20for%20Test%202-%20solutions

# Preparation%20for%20Test%202-%20solutions - Preparation for...

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Preparation for Test 2 (solutions) Problem#1 a) 1. 3 1 : 3 2 1 0 = = = p p p H 2. : a H At least one p i differs from its hypothesized value 434 = N , 67 . 144 434 3 1 ) ( 1 1 = = = n p n E , 67 . 144 434 3 1 ) ( 2 2 = = = n p n E 67 . 144 434 3 1 ) ( 3 3 = = = n p n E 3. Test Statistic 735 . 87 67 . 144 ) 67 . 144 81 ( 67 . 144 ) 67 . 144 119 ( 67 . 144 ) 67 . 144 234 ( ) ( )) ( ( 2 2 2 2 2 = - + - + - = - = i i i n E n E n χ 4. Rejection region: = + ∞ ) ; ( 2 α χ ) ; 21 . 9 ( + ∞ (for 01 . 0 = α and df = k -1=2 21 . 9 01 , 0 2 = χ ) 5. Inference : Since 87.735>9.21 o pinions are not evenly divided. b) p ˆ =234/434=0.5391, n p p p p p ) ˆ 1 ( ˆ 96 . 1 ˆ 96 . 1 ˆ ˆ - ± = ± σ = = 0.5391 0469 . 0 5391 . 0 434 ) 5391 . 0 1 ( 5391 . 0 96 . 1 ± = - ± = (0.492;0.586) Problem #2 a) 1. H 0 : 1 p =0.32, 2 p =0.50, 3 p =0.18 α H . 2 : At least one of probabilities differs from their hypothesized values. 85 = N , E ( 1 n )=(85)0.32=27.2 , E ( 2 n )=(85)0.50=42.5, E ( 3 n )=(85)0.18=15.3 3 . Test Statistic [ ] ) ( ) ( 2 2 i i i n E n E n - = χ ( 29 ( 29 ( 29 3 . 15 3 . 15 17 5 . 42 5 . 42 32 2 . 27 5 . 27 36 2 2 2 - + - + - = =5.630 4. Rejection region = + ∞ ) ; ( 2 α χ ( 29 + ∞ ; 99 . 5 (for 05 . 0 = α , df = n-1=3-1=2, ) 99 . 5 2 05 . 0 = χ 5. Inference: Since observed 2 χ statistics does not fall into rejection region, we cannot reject Ho with 05 . 0 = α . b) ( 29 529 . 0 ; 317 . 0 106 . 0 423 . 0 85 ) 577 . 0 ( ) 423 . 0 ( 96 . 1 85 36 ˆ ˆ 2 = ± = ± = ± p z p δ α Problem #3 2 1 σ - Population variance of errors made by Novice Inspector 2 2 σ - Population variance of errors made by Experienced Inspectors a) 1. 2 2 2 1 0 : σ σ = H 2. 2 2 2 1 : σ σ a H 3. Test statistic variance sample smaller variance sample larger = F

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1 x 2 1 x 2 x 2 2 x 35 1225 19 361 26 676 17 289 36 1296 19 361 40 1600 10 100 45 2025 20 400 33 1089 Total 85 Total 1511 29 841 Total 244
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Preparation%20for%20Test%202-%20solutions - Preparation for...

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