> # load data: x is a dataframe; x.vec is vectorised form
> x <- read.csv('http://www.ms.unimelb.edu.au/~s620374/sampling/lab3data.csv',
+     header=F)
> x.vec <- unlist(x)
> 
> # population mean
> cat('population mean =', mean(x.vec), '\n')
population mean = 0.4913768 
> 
> # variance under srs
> cat('variance of muhat_srs =', var(x.vec)/30*(1 - 30/100), '\n')
variance of muhat_srs = 0.02645129 
> 
> # variance under proportional samping
> vars <- sd(x)^2 # S2_i for each strata
> cat('variance of muhat_st with proportional sampling =', sum(vars)/10^2/3*(1 - 3/10), '\n')
variance of muhat_st with proportional sampling = 0.02316186 
> 
> # variance under cluster sampling
> mus <- mean(x) # mu_i for each cluster
> cat('variance of muhat_cl =', var(mus)/3*(1 - 3/10), '\n\n')
variance of muhat_cl = 0.0593456 

> 
> # simple ramdom sample
> y <- sample(x.vec, 30)
> cat('muhat_srs =', mean(y), '\n')
muhat_srs = 0.4311255 
> cat('varhat =', var(y)/30*(1 - 30/100), '\n\n')
varhat = 0.0298737 

> 
> # proportional stratified sample
> y <- data.frame(lapply(x, sample, size=3))
> cat('muhat_st =', sum(mean(y))/10, '\n')
muhat_st = 0.4460459 
> vars <- sd(y)^2 # S2_i for each strata
> cat('varhat =', sum(vars)/10^2/3*(1 - 3/10), '\n\n')
varhat = 0.02254223 

> 
> # cluster sample
> y <- sample(x, 3)
> cat('muhat_cl =', mean(mean(y)), '\n')
muhat_cl = 0.7235606 
> mus <- mean(y) # mu_i for each cluster
> cat('variance of muhat_cl =', var(mus)/3*(1 - 3/10), '\n\n')
variance of muhat_cl = 0.06858882 

>