a

Model Equation: y_ijk = mu + alpha_i + beta_j + e_ijk

#Question 13


library(GAD)
## Warning: package 'GAD' was built under R version 4.2.2
## Loading required package: matrixStats
## Loading required package: R.methodsS3
## R.methodsS3 v1.8.2 (2022-06-13 22:00:14 UTC) successfully loaded. See ?R.methodsS3 for help.
process <- c(rep(1,12),rep(2,12),rep(3,12))  
batch <-c(rep(1,3),rep(2,3),rep(3,3),rep(4,3))
batch <-rep(batch,3)
observation<- c(25,30,26,19,28,20,15,17,14,15,16,13,29,27,24,23,24,21,28,21,27,35,27,25,24,25,20,35,21,24,38,34,30,25,29,33)

batch<- as.random(batch)
process<- as.fixed(process)

model<- lm(observation~process+batch%in%process)
gad(model)
## Analysis of Variance Table
## 
## Response: observation
##               Df Sum Sq Mean Sq F value   Pr(>F)   
## process        2 446.06 223.028  3.5365 0.073563 . 
## process:batch  9 567.58  63.065  4.1965 0.002349 **
## Residual      24 360.67  15.028                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

b and c

The P-value of batch (Nested) = 0.002349 >0.05

Therefore it is not significant effect