Chap 7 - Exercise 3

> library(mnormt)
> set.seed(1977)
> sample.mean <- c(1, 2)
> sample.cov <- matrix(c(1, 0.5, 0.5, 1), nrow = 2)
> n <- 1000
> x <- rmnorm(n, mean = sample.mean, varcov = sample.cov)
> A <- matrix(c(2, -1), nrow = 1)
> sim.cov <- var(x)
> sim.mean <- colMeans(x)
> teststat.known.sig <- n * (A %*% sim.mean - 0.2) * solve(A %*%
+     sample.cov %*% t(A)) * t((A %*% sim.mean - 0.2))
> teststat.unknown.sig <- (n - 1) * (A %*% sim.mean - 0.2) * solve(A %*%
+     sim.cov %*% t(A)) * t((A %*% sim.mean - 0.2))

> teststat.known.sig
         [,1]
[1,] 18.56751
> qchisq(0.95, 1)
[1] 3.841459

> teststat.unknown.sig
         [,1]
[1,] 18.05155
> qf(0.95, 1, (n - 1))
[1] 3.850784