Gosset - The God

> n <- 10 * 10000
> x <- matrix(rnorm(n, 1, 2), ncol = 10000)
> mu <- apply(x, 2, mean)
> sample.sd <- apply(x, 2, sd)/sqrt(10)
> t.stat <- (mu - 1)/sample.sd
> plot.new()
> plot(density(t.stat), col = "blue", xlim = c(-4, 4), xlab = "Quantile",
+     main = "", ylim = c(0, 0.4))
> par(new = T)
> plot(density(rnorm(1e+05, 0, 1)), col = "red", xlim = c(-4, 4),
+     xlab = "", main = "", ylim = c(0, 0.4))
> legend("topleft", legend = c("Normal", "T Dist"), fill = c("red",
+     "blue"))