### Chapter 7, Survey Sampling

#### Solution 7

Ignoring the finite population correction: .

Since it is a dichotomous case i.e. value of each member can either be 1 or 0 based on if this member/family is below the poverty level or not respectively, we have where p denotes the fraction of population below the poverty line.

This give us:

.

We know and .

This gives us

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