## Sample sizes.
N = c(5,10,30,50,70,90,110,130)

## Coverage probabilities.
CP = NULL

for (k in 1:length(N))
{
    n = N[k]

    X = array(rnorm(n*1e4), c(1e4,n))
 
    ## Estimate sigma from the data.
    SD = apply(X, 1, sd)

    ## Construct the CI, correctly adjusting for the
    ## uncertainty in SD.
    M = apply(X, 1, mean)
    C = qt(0.975,n-1)*SD/sqrt(n)

    ## Determine which intervals cover.
    ci = ((M-C < 0) & (M+C > 0))

    ## Calculate the proportion of intervals that cover.
    CP[k] = mean(ci)
}