### Chapter 7, Survey Sampling

#### Solution 32

#### (a)

We have:

Total Population,

Sample size,

Sample proportion,

To compute estimated standard error, , we use . Thus we get . Thus .

The confidence interval can be computed using where . Thus the confidence interval becomes , or .

#### (b)

We are given two samples from two populations - one from the example quoted and another given in the problem itself.

**Sample 1:**(from example)

**Sample 2:**(from problem)

and and .

Since and are independent random variables, it follows that .

Now putting and , we get:

.

Using the standard error computed in example, we have . Similarly from part-a, we have . Thus . Thus .

#### (c)

The confidence interval is given by .

We have .

For confidence interval, . Thus . Thus the confidence interval is

Similarly, for , we have . Thus

And for , we get . Thus

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