Chapter 7, Survey Sampling

Solution 47

From Corollary B we have:


We just need to plugin the values in the above expression. All the values are given in Example-D on page-226 in the book.

Skipping the computation part :)

I think the point of this problem is to compare the bias and variance as sample size increases. Looking at the formulae we can see that the bias should decrease as sample size increases as well as the is very small compared to the variance(because contains but variance contains ). Thus the take away point is that bias can be ignored if a sample size is large.

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