Suppose that a random sample of size n is taken from the normal distribution with mean μ and variance σ2. Before the sample is observed, the random variables are divided into p groups of sizes n1, . . . , np, where ni ≥ 2 for i = 1, . . . , p and For i = 1, . . . , p, let Qi denote the sum of the squares of the deviations of the ni observations in the ith group from the sample mean of those ni observations. Find the distribution of the sum Q1 + . . . + Qp and the distribution of the ratio Q1/Qp.