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

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Unformatted text preview: Preparation for Test 2 (solutions) Problem#1 a) 1. 3 1 : 3 2 1 = = = 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 4. Rejection region: = + ) ; ( 2 ) ; 21 . 9 ( + (for 01 . = and df = k-1=2 21 . 9 01 , 2 = ) 5. Inference : Since 87.735>9.21 o pinions are not evenly divided. b) p =234/434=0.5391, n p p p p p ) 1 ( 96 . 1 96 . 1 - = = = 0.5391 0469 . 5391 . 434 ) 5391 . 1 ( 5391 . 96 . 1 =- = (0.492;0.586) Problem #2 a) 1. H : 1 p =0.32, 2 p =0.50, 3 p =0.18 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- = ( 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 ( 29 + ; 99 . 5 (for 05 . = , df = n-1=3-1=2, ) 99 . 5 2 05 . = 5. Inference: Since observed 2 statistics does not fall into rejection region, we cannot reject Ho with 05 . = . b) ( 29 529 . ; 317 . 106 . 423 ....
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This note was uploaded on 03/11/2012 for the course FIN FIN 3230 taught by Professor Petrivanov during the Spring '12 term at Kazakhstan Institute of Management, Economics and Strategic Research.

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

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