# Mathematical Statistics and Data Analysis - Solutions

### Chapter 7, Survey Sampling

#### Solution 30

We can compare the variance of the two methods:

Note that in the first case, if $\, p = \frac 1 2 \,$, or even if p is close to $\, \frac 1 2 \,$, 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.

$$\tag*{\blacksquare}$$