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Chapter 4: Q. 14 (page 237)

Sampling gravestones The local genealogical society in Coles County, Illinois, has compiled records on all 55,194gravestones in cemeteries in the county for the years 1825to 1985. Historians plan to use these records to learn about African Americans in Coles County鈥檚 history. They first choose an SRS of 395records 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 3gravestones

Short Answer

Expert verified

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 95gravestones from part (a) above is chosen.

Step by step solution

01

Part (a) Step 1 : Given Information

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

02

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 395unique record samples.
Start at row 137and draw the first five samples for this problem 53645,66812,61421,47836,12609,15373are the first few random numbers from row 137.
As a result, we choose the 53, 645th record for random number = 53645. We skip the numbers 66812and 61421because they are both greater than55914. For 47836,12609, and 15373, we choose the 47836th, 12609th, and15373rd records, respectively.
We have four records thus far. One more is required. 98481,14592are the next two random numbers. We skip 98481and go straight to the 14592nd record. As a result, the five-person random sample is complete. This procedure should be repeated until we have95 distinct sample points.
03

Part (b) Step 1 : Given Information

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

04

Part (b) Step 2 : Simplification

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

Thus, from the above 95gravestones 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 95gravestones from part (a) above is chosen.

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

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