Tutorial 3
Q1

ss=c(6.66,8.45,11.39, 9.72)
n=c(15,14,13,15)
s2 = sum((n-1)*ss^2)/(sum(n)-4)
s = sqrt(s2)


x =c(12.2, 19.3,20.6, 38.5)

l1 = (x[2]-x[1])/s*sqrt(n[1]*n[2]/(n[1]+n[2]) )

l2 = (x[3]-x[1])/s*sqrt(n[1]*n[3]/(n[1]+n[3]) )

l3 = (x[4]-x[3]-x[2]+x[1])/s/sqrt(1/n[1]+1/n[2]+1/n[3]+1/n[4])

c(s2, s, l1,l2,l3)

0.05/6

qt(1-0.05/6, 53)
qt(1-0.05/2, 53)


Q4  

x1=c(8,13,0,3,13,19,0,2,18,5)
x2=c(7,11,0,6,13,23,0,0,20,3)
x3=c(11,15,2,9,17,27,1,4,22,8)
x4=c(7,13,1,6,10,18,0,5,16,3)
X =cbind(x1,x2,x3,x4)

Xi. = apply(X,1,mean)
X.j = apply(X,2,mean)

X.. = sum(apply(X,1,sum))/40

E1 = Xi.%*% t(rep(1,4))
E2 = rep(1,10)%*%t(X.j)

E3 = rep(1,10)%*%t(rep(1,4))
E3 = E3*X..

Xij = X-E1-E2+E3
Xij=Xij^2

s2 = sum(apply(Xij,1,sum))

s = sqrt(s2/27)
nn = 1/10 + 1/9*(3/10)


l1 = (X.j[1] - (sum(X.j) -X.j[1])/3 )/sqrt(nn)/s
l2 = (X.j[2] - (sum(X.j) -X.j[2])/3 ) /sqrt(nn)/s
l3 = (X.j[3] - (sum(X.j) -X.j[3])/3 ) /sqrt(nn)/s
l4 = (X.j[4] - (sum(X.j) -X.j[4])/3 ) /sqrt(nn)/s
c(l1,l2,l3,l4)

qt(1-0.05/8, 27)

sqrt(3*qf(0.95,3,27))