Question

Sampling gravestones The local genealogical society in Coles County, Illinois, has compiled records on all $55,194$gravestones in cemeteries in the county for the years $1825$to $1985$. Historians plan to use these records to learn about African Americans in Coles County’s history. They first choose an SRS of $395$records to check their accuracy by visiting the actual gravestones.

a. Explain how you would use a random number generator to choose the SRS. Your description should be clear enough for a classmate to carry out your plan.

b. Use your method from part (a) to choose the first $3$gravestones

Short answer

a. We'll use a simple structure to do an SRS once it's labelled this way. One number at a time will be drawn from the table supplied.

Formulation of a Research Design ,If the drawn random number is greater than $55914$, we draw another random number until it is less than $55914$.

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

Step-by-step solution

Part (a) Step 1 : Given Information

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

Part (a) Step 2 : Simplification

ToselectanSRS,

Let's call the first record $1$, the second record $2$, and so on until we reach $55914$. We'll use a simple structure to do an SRS once it's labelled this way. One number at a time will be drawn from the table supplied.

Formulation of a Research Design ,If the drawn random number is greater than $55914$, we draw another random number until it is less than $55914$.

Also, if the same random number appears twice, we skip the second draw and draw a new random number unless we obtain a different random number than the ones we've already seen, ensuring that no two records appear in the sample. We repeat this process until we get $395$unique record samples.

Start at row $137$and draw the first five samples for this problem $53645,66812,61421,47836,12609$,$15373$are the first few random numbers from row $137$.

As a result, we choose the $53$, $645$th record for random number = $53645$. We skip the numbers $66812$and $61421$because they are both greater than$55914$. For $47836,12609$, and $15373$, we choose the $47836$th, $12609$th, and$15373$rd records, respectively.

We have four records thus far. One more is required. $98481,14592$are the next two random numbers. We skip $98481$and go straight to the $14592$nd record. As a result, the five-person random sample is complete. This procedure should be repeated until we have$95$ distinct sample points.

Part (b) Step 1 : Given Information

We have to use your method from part (a) to choose the first three gravestones

Part (b) Step 2 : Simplification

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 gravestones in 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.