# Hw12ans - STAT 410 Homework#12(due Thursday April 17 by...

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STAT 410 Homework #12 Spring 2008 (due Thursday, April 17, by 5:00 p.m.) 1. 5.7.4 H 0 : p 1 = 16 9 , p 2 = 16 3 , p 3 = 16 3 , p 4 = 16 1 . O 86 35 26 13 160 E 90 30 30 10 160 ( ) E E O 2 - ( ) 90 90 86 2 - ( ) 30 30 35 2 - ( ) 30 30 26 2 - ( ) 10 10 13 2 - 0.17778 0.83333 0.53333 0.90 2.44444 k – 1 = 4 – 1 = 3 d.f. ( ) 3 2 01 . 0 ° = 11.34 . Rejection Region: “Reject H 0 if Q 2 α χ 2.4444 = Q < 2 α χ = 11.34 . Do NOT Reject H 0 at α = 0.01. P-value 0.4854 . Note that E ( Q ) = 3 when H 0 is true. 2. 5.7.5 Grade Group A B C D F Total O I 15 25 32 17 11 100 12 21.5 30.5 22.5 13.5 0.75 0.569767 0.07377 1.344444 0.462963 II 9 18 29 28 16 100 E ( ) E E O 2 - 12 21.5 30.5 22.5 13.5 0.75 0.569767 0.07377 1.344444 0.462963 24 43 61 45 27 200

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Q = 6.401891 . ( r – 1 ) × ( c – 1 ) = 4 d.f. ( ) 4 2 05 . 0 ° = 9.488 . Rejection Region: “Reject H 0 if Q 2 α χ 6.401891 = Q < 2 α χ = 9.488 . Do NOT Reject H 0 at α = 0.05. P-value 0.171 . 3. 5.7.6 B1 B2 B3 B4 10 21 15 6 52 A1 7.02 17.42 16.38 11.18 1.265014 0.735729 0.116264 2.400036 O 11 27 21 13 72 A2 9.72 24.12 22.68 15.48 0.16856 0.343881 0.124444 0.397313 6 19 27 24 76 E ( ) E E O 2 - A3 10.26 25.46 23.94 16.34 1.768772 1.639104 0.391128 3.590918 27 67 63 43 200 Q = 12.94116 . ( r – 1 ) × ( c – 1 ) = 6 d.f. ( ) 6 2 05 . 0 ° = 12.59 . Rejection Region: “Reject H 0 if Q 2 α χ 12.94116 = Q > 2 α χ = 12.59 . Reject H 0 at α = 0.05. P-value 0.04398 .
4. Let X 1 , X 2 , … , X n be a random sample of size n from a N ( 0 , σ 2 ) distribution. a) Find the sufficient statistic Y for σ 2 . ( See 7.2.1 .

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• Spring '08
• AlexeiStepanov
• Maximum likelihood, Estimation theory, Likelihood function, 1 L, Sufficient statistic, 2 10 0.90 2.44444 k

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