1 Question 14.3

1.1 Loading Libraries

library(GAD)

We want to test the hypotheses that either machine or spindle (which is nested in machine) significantly affects the response of the collected data:

\[ H_0:\alpha=0\\ H_a:\alpha \neq0\\ H_0:\beta=0\\H_a:\beta\neq0\]

machine <- c(rep(1,8),rep(2,8),rep(3,8))
spindle <- rep(c(rep(1,4),rep(2,4)),3)
obs <- c(12,9,11,12,8,9,10,8,14,15,13,14,12,10,11,13,14,10,12,11,16,15,15,14)

machine <- as.fixed(machine)
spindle <- as.random(spindle)
model <- aov(obs~machine+spindle%in%machine)
gad(model)
## Analysis of Variance Table
## 
## Response: obs
##                 Df Sum Sq Mean Sq F value    Pr(>F)    
## machine          2  55.75 27.8750  1.9114 0.2915630    
## machine:spindle  3  43.75 14.5833  9.9057 0.0004428 ***
## Residual        18  26.50  1.4722                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

From the statistical testing, we can see that the machine are not significant but the spindles are significant.