A population can be divided into K strata, with numbers N. NN. Let ..... denote the stratum population standard deviations, and define where N N N = N

(a) Show that N ( 2 (3)

(b) From the result in (a), deduce that unless the , are all the same (N)

(c) From the result in (b), deduce that unless the o, are all the same, more observations will be required in proportional allocation than under optimal allocation in order to obtain for the population mean a 95% confidence interval of specific width.

(d) Discuss the position when the or, are all the same.