### Chapter 7, Survey Sampling

#### Solution 48

Note: Initially I planned to solve problem-49 instead of 48 as both are similar. In my copy of the book, it seems that the answer mentioned in the book for problem-49 are actually for problem-48 or perhaps while computing the answers data of problem 48 is used.

#### (a)

The estimate for the ratio is:

. Thus we only need to plugin the given values to get .

#### (b)

To compute confidence interval, first we need to find the standard error, of our esitmate . Now we just need to plugin the values in the expression derived in the book for .

To compute , we use which simplifies to .

Similarly,

and,

Pluging the values we get , which gives .

Thus the confidence interval is .

#### (c)

We can estimate the total using .

Thus

To compute confidence interval,

.

To compute variance of the sample mean , we use , where , variance of the sample, is already computed in part-b. This gives (ignoring the finite population correction).

Thus we get . Thus . Thus the condidence interval is .

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