#Tutorial 2


#Q1

x1=c(0.05, 0.15, 0.35, 0.25, 0.20, 0.05, 0.10, 0.05, 0.30, 0.05, 0.25 )
x2=c(0, 0.15, 0, 0.05, 0, 0, 0.05, 0.10)

#(i)  
t.test(x1,x2,alternative = "two.sided",  var.equal = T, onf.level = 0.95)


#(ii) 
y1=asin(sqrt(x1))
y2=asin(sqrt(x2))

t.test(y1,y2,alternative = "two.sided",  var.equal = T, onf.level = 0.95)

#(iii)

x=c(x1,x2)
id.x=1:length(x)
 
g1=rep(1, length(x1))
g2=rep(2, length(x2))
g=c(g1,g2)

od.x = order(x)

od.g = g[od.x]


cbind( g[od.x], x[od.x], id.x)

rk.x = id.x
rk.x[1:4]=2.5
rk.x[5:10]=7.5
rk.x[11:12]=11.5
rk.x[13:14]=13.5
rk.x[16:17]=16.5
cbind( od.g, x[od.x], id.x, rk.x)

R1 = mean(rk.x[od.g==1])

R2 = mean(rk.x[od.g==2])


c(R1,R2)


xx=(12*11*8* (12.73-6.25)^2)/( 19^2 * 20 ) 

1-pchisq(6.4114,1)

4*3*5 + 6*5*7 +3*2*3

19*18*20



Q3


s2 = (5*0.94^2 + 3*0.9^2 + 4 * 1.56^2 )/(6+4+5-3)

L1 = (8.9 - 8.25)/sqrt(s2)*sqrt(6*4/(4+6))
L2 = (10.88 - 8.25)/sqrt(s2)*sqrt(6*5/(5+6))