chapter 1

Chapter 11: Multifactor Analysis of Variance23. Summary quantities include x 1 •• = 9410 , x 2 •• = 8835 , x3 ••= 9234 , x • 1 • = 5432 ,x • 2 • = 5684 , x• 3 •= 5619 , x • 4 • = 5567 , x• 3 •= 5177 , x ••• = 27, 479 ,22CF = 16,779,898.69 , Σ x i• •= 251,872, 081, Σ x • j•= 151,180, 459 , resulting in theaccompanying ANOVA table.Source Df SS MS fMSAA 2 11,573.38 5786.69 = 26. 70MSABMSBB 4 17,930.09 4482.52 = 20. 68MSABMSABMSEAB 8 1734.17 216.77 =1. 38Error 30 4716.67 157.22Total 44 35,954.31Since .38 3. 171. 01,8, 30=. 01,2,=< F , H oG cannot be rejected, and we continue:26.70≥ F88.65 , and 20.68≥ F. 01,4, 8= 7. 01, so both H oA and H oB are rejected.Both capping material and the different batches affect compressive strength of concretecylinders.24.11a. E( X − X ) = Σ Σ E( X ) − ΣΣΣE( X )i.....ijkJKj kIJKi j k11= Σ Σ( µ + αi+ βj+ γij) − ΣΣΣ( µ + αi+ βj+ γij) = µ + αi− µ = αiJKj kIJKi j kijk1111b. E( ˆγ ) = Σ E( X ) − ΣΣ E( X ) − ΣΣ E( X ) + Σ ΣΣE( X )ijijkKkJKj kIKi k= µ + α + β + γ − µ + α − µ + β + µ = γijijijk(i) (j)ijijkIJKijkijk326