> # population
> x <- scan("http://www.ms.unimelb.edu.au/~s620374/sampling/lab1data.txt")
Read 100 items
> N <- length(x)
> # population mean
> mean(x)
[1] 1.96
> # population variance
> var(x)*(N-1)/N
[1] 1.3784
> 
> # sample
> set.seed(620374)
> n <- 20
> f <- n/N
> xs <- sample(x, n)
> # sample mean
> mean(xs)
[1] 1.65
> # estimated variance of sample mean
> mean.xs.var <- var(xs)/n*(1 - f)
> # 95% CI for population mean
> CI <- c(mean(xs)-qt(0.975, 19)*sqrt(mean.xs.var),
+         mean(xs)+qt(0.975, 19)*sqrt(mean.xs.var))
> CI
[1] 1.214655 2.085345
> # estimate of population variance
> var(xs)*(N-1)/N
[1] 1.070763