Suppose that a sample of n observations is formed from k

Chapter 11, Problem 9

(choose chapter or problem)

Suppose that a sample of n observations is formed from k subsamples containing n1,...,nk observations (n1 + ... + nk = n). Let xij (j = 1,...,ni) denote the observations in the ith subsample, and let xi+ and v2 i denote the sample mean and the sample variance of that subsample: xi+ = 1 ni ni j=1 xij , v2 i = 1 ni ni j=1 (xij xi+) 2. Finally, let x++ and v2 denote the sample mean and the sample variance of the entire sample of n observations: x++ = 1 n k i=1 ni j=1 xij , v2 = 1 n n i=1 ni j=1 (xij x++) 2. Determine an expression for v2 in terms of x++, xi+, and v2 i (i = 1, . . . , k).