Tutorial 4
Q1

(9.3-11.025)/0.6559*sqrt(4)
(9.713-11.025)/0.6559*sqrt(4)
(9.938-11.025)/0.6559*sqrt(4)


sqrt(3*qf(0.95,3,21))

qt(1-0.05/6, 21)

3.958/sqrt(2)


Q2

x = c(3,2,2.5,3,3,3.5,
      5.5,4,5,4.5,4,4.5,
      5,4.5,4,4.5,2.5,4.5,
      6,5.5,5,6,5.5,5.5)
p = factor(c(rep(1,12), rep(2,12)))
d = factor(rep( c(rep(1,6), rep(2,6)), 2))
b = factor( rep(1:6,4) )
options(contrasts=c("contr.treatment","contr.poly"))
lm.o = lm(x~p+b+d+p*d)
anova(lm.o)


xb=mean(x)

x1 = c(3,2,2.5,3,3,3.5)
x2=c(5.5,4,5,4.5,4,4.5)
x3=c(5,4.5,4,4.5,2.5,4.5)
x4=c(6,5.5,5,6,5.5,5.5)

x1. = c(x1,x3)
x2. = c(x2,x4)
x1b=mean(x1.)
x2b=mean(x2.)

12*((x1b-xb)^2 + (x2b-xb)^2 )

qf(0.95,1,15)