Dr. Hackney STA Solutions pg 181

Dr. Hackney STA Solutions pg 181 - 1 r r X j =1 + i + b j +...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Second Edition 11-9 = k X i =1 n i X j =1 ( y ij - ¯ y i · ) 2 + k X i =1 n i X j =1 y i · - ¯ ¯ y ) 2 + k X i =1 n i X j =1 ( y ij - ¯ y i · ) (¯ y i · - ¯ ¯ y ) , where the cross term (the sum over j ) is zero, so the sum of squares is partitioned as k X i =1 n i X j =1 ( y ij - ¯ y i · ) 2 + k X i =1 n i y i - ¯ ¯ y ) 2 c. From a), the F statistic for the ANOVA is 110.42. The individual two-sample t ’s, using s 2 p = 1 15 - 3 (66 . 74) = 5 . 5617, are t 2 12 = (3 . 508 - 9 . 274) 2 (5 . 5617)(2 / 5) = 33 . 247 2 . 2247 = 14 . 945 , t 2 13 = (3 . 508 - 24 . 926) 2 2 . 2247 = 206 . 201 , t 2 23 = (9 . 274 - 24 . 926) 2 2 . 2247 = 110 . 122 , and 2(14 . 945) + 2(206 . 201) + (110 . 122) 6 = 110 . 42 = F. 11.23 a. E Y ij = E( μ + τ i + b j + ± ij ) = μ + τ i + E b j + E ± ij = μ + τ i Var Y ij = Var b j + Var ± ij = σ 2 B + σ 2 , by independence of b j and ± ij . b. Var ± n X i =1 a i ¯ Y i · ! = n X i =1 a 2 i Var ¯ Y i · + 2 X i>i 0 Cov( a i Y i · ,a i 0 Y i 0 · ) . The first term is n X i =1 a 2 i Var ¯ Y i · = n X i =1 a 2 i Var
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 r r X j =1 + i + b j + ij = 1 r 2 n X i =1 a 2 i ( r 2 B + r 2 ) from part (a). For the covariance E Y i = + i , and E( Y i Y i ) = E + i + 1 r X j ( b j + ij ) + i + 1 r X j ( b j + i j ) = ( + i )( + i ) + 1 r 2 E X j ( b j + ij ) X j ( b j + i j )...
View Full Document

This note was uploaded on 02/03/2012 for the course STA 1014 taught by Professor Dr.hackney during the Spring '12 term at UNF.

Ask a homework question - tutors are online