m = 200000;  n = 5;  x = rnorm(m*n, 100, 15)
DTA = matrix(x, nrow=m);  a = rowMeans(DTA);  s = apply(DTA, 1, sd)
plot(a, s, pch=".", xlab="Sample Mean", ylab="Sample SD")
t = (a-100)*sqrt(n)/s;  t.crit = qt(.975, n-1);  cond = (abs(t) > t.crit)
points(a[cond],s[cond], pch=".", col="red")
pm = c(-1,1); abline(v=100+pm*1.96*15/sqrt(n), col="darkgreen", lwd=2)