Chapter 7, Survey Sampling

Solution 30

We can compare the variance of the two methods:

Note that in the first case, if , or even if p is close to , then variance is undefined or becomes very large. While in the second case this problem does not arise. Thus the second method is better.

I am not sure how to understand this conceptually that second method is better without looking at the variances.

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