Statement of a problem № m41006


Comparison of domain means. Suppose the population may be divided into two groups, with respective sizes N1 and N2 and population means 1U and 2U. The overall population mean is U = (N1 1U + N2 2U)/N, with N = N1 + N2. Let xi = 1 if observation unit i is in group 1, and xi = 0 if it is in group 2. The weight for observation unit i is wi. Show that B1 = 1U − 2U and B0 = 2U. Also show that and Ḃ0 = 2.

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