Let each observation in a set of k independent random samples be normally distributed with means μ1,..., μk and common variance σ2. If H0 = μ1 = μ2 = ... = μk is true, show that SST /(k - 1) MST F = SSE/(n - k) = MSE has an F -distribution with k - 1 numerator and n - k denominator degrees of freedom.