### Chapter 7, Survey Sampling

#### Solution 55

#### (a)

Estimate of the population mean, , which as proved in the book is an unbiased estimate of population mean.

Thus .

#### (b)

Ignoring the finite population correction, We have . Thus standard error = .

#### (c)

If the standard error is less than the previous alllocation than the new allocation will be better. Thus, we first find standard error:

Ignoring the finite population correction, We have . Thus standard error = .

The standard error for the present allocation is higher than that of the previous allocation, thus this allocation is not better than the previous allocation.

#### (d)

We first find the standard error for the proportional allocation:

. Thus standard error is .

Here also standard error is more than the original allocation. Thus this allocation is also not better compared to the original allocation.

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