A rocket propellant manufacturer is studying the burning rate of propellant from three production processes. Four batches of propellant are randomly selected from the output of each process, and three determinations of burning rate are made on each batch. The results follow. State the model equation and hypotheses to be tested. Perform the analysis and draw conclusions, using alpha=0.05 where applicable.

library(GAD)
results <- c(25,    19, 15, 15, 19, 23, 18, 35, 14, 35, 38, 25, 30, 28, 17, 16, 17, 24, 21, 27, 15, 21, 54, 29, 26, 20, 14, 13, 14, 21, 17, 25, 20, 24, 50, 33)
batch <- as.random(rep(seq(1,4),9))
obs <- as.fixed(c(rep(1,12),rep(2,12),rep(3,12)))
process <- as.fixed(rep(c(rep(1,4),rep(2,4),rep(3,4)),3))
dafr <- data.frame(process,batch,obs,results)
model <- lm(results~process+batch%in%process)
gad(model)
## Analysis of Variance Table
## 
## Response: results
##               Df  Sum Sq Mean Sq F value    Pr(>F)    
## process        2  676.06  338.03  1.4643    0.2815    
## process:batch  9 2077.58  230.84 12.2031 5.477e-07 ***
## Residual      24  454.00   18.92                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

It seems that which process is used is not significant, but the batches within the process did have a significant difference on our mean burning rate.

plot(model)

Additionally, there do not appear to be any violations of our normality and variance assumptions, therefore, this model is adequate.

All Code Used

library(GAD)
results <- c(25,    19, 15, 15, 19, 23, 18, 35, 14, 35, 38, 25, 30, 28, 17, 16, 17, 24, 21, 27, 15, 21, 54, 29, 26, 20, 14, 13, 14, 21, 17, 25, 20, 24, 50, 33)
batch <- as.random(rep(seq(1,4),9))
obs <- as.fixed(c(rep(1,12),rep(2,12),rep(3,12)))
process <- as.fixed(rep(c(rep(1,4),rep(2,4),rep(3,4)),3))
dafr <- data.frame(process,batch,obs,results)
model <- lm(results~process+batch%in%process)
gad(model)

plot(model)