## Column 1 is the p-value, column 2 is the proportion of null test
## statistics exceeding the actual test statistic.
Q = array(0, c(1000,2))

## Null data for checking the accuracy of the p-values.
Z = array(rnorm(1000*20), c(1000,20))
M2 = apply(Z, 1, mean)

for (r in 1:1000)
{
  ## Generate an alternative data set.
  X = runif(1) + rnorm(20)

  ## Get the p-value, assuming that the variance is known to be 1.
  M1 = mean(X)
  p = 1-pnorm(sqrt(20)*M1)
    
  ## Store the p-value, and the proportion of null draws with a test
  ## statistic that is larger than the actual test statistic.
  Q[r,1] = p
  Q[r,2] = mean(M2 > M1)
}