Chapter 4.1, Problem 14E

(a)

To determine

To explain how would you use a random numbers generator to choose the SRS.

Explanation of Solution

To choose an SRS,

Let us number the first record as $00001,\text{ second record as }00002\text{ and so on till }55914$ .

Once it is labelled in this way, we will follow a simple structure to perform an SRS.

We will draw from the table provided one random number after another.

If the random number drawn is $>55914$ then we re-draw another random number until it is $\le 55914$ .

Also if the same random number comes twice then also we skip the second draw and draw another random number unless we get a different random number from the ones already observed, so that no two records come in the sample.

We continue this procedure until we get $395$ distinct record samples.

For this problem we are to start at row $137$ and draw the first five samples.

The first few random numbers from row $137$ are $53645,66812,61421,47836,12609,15373$

So for random no. $=53645$ we select the $53,645$ th record.

We skip the random numbers $66812\text{ and }61421\text{ because they are}>55914$ .

Again for $47836,12609,15373\text{ we select the }47836th,12609th\text{ and }15373th\text{ record}$ . So far we have got four records.

We need one more. The next few random numbers are $98481,14592$ .

We skip $98481\text{ and select }14592$ th record.

So the random sample of five is complete. We should continue this method till we have got $95$ distinct sample points.

(b)

To determine

To use your method from part (a) to choose the first three gravestones.

Explanation of Solution

From the above part (a) the SRS of $95$ gravestones are selected using random numbers generator.

Thus, from the above $95$ gravestones we will select the first three five-digits numbers to find out the first three gravestonesin the country. Thus, any first three five-digit numbers selected from the sample of $95$ gravestones from part (a) above is chosen.

For example we consider that, $53645,47836,12609$ are chosen from the sample of $95$ gravestones, if these were the first three five-digit numbers chosen from the sample.