Chapter 7, Survey Sampling

Solution 4

The key here is - a statistic/estimate is better if its variance is small because the smaller the variance better the accuracy of the estimate.

Denoting the variance of the estimate as and for Population 1 and Population 2 and ignoring the finite population correction:

Thus variance of the sample mean of second sample is twice the variance of the sample mean of first sample. Or the first sample has small variance - thus first sample is better for estimating the Population mean.

$$\tag*{$\blacksquare$} $$