Question

Sampling gravestones The local genealogical society in Coles County, Illinois, has compiled records on all $55,914$ gravestones in cemeteries in the county from 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.$13$

(a) Explain how you would use technology or Table D to choose the SRS. Your description should be clear enough for a classmate to obtain your results.

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

Short answer

Part (a) You have $395$ unique numbers between $00001$ and $55914$

Part (b) The first three gravestones are$439092533040085$

Step-by-step solution

Part (a) Step 1: Given information

From $1825$ until $1985$ the local genealogy organization in Coles Country, Illinois, maintained records on all $55,914$ gravestones in the country's cemeteries. They chose an SRS of $395$ records to double-check their accuracy by visiting the gravestones themselves.

Part (a) Step 2: Concept

Divide the population into smaller groups before taking a cluster sample. These groups should ideally reflect the population's features. Then pick one of the clusters' SRS. The sample includes all individuals in the designated clusters.

Part (a) Step 3: Explanation

From $00001$ to $55914$ write a number on each gravestone. Pick a starting point from the random number table. Count up to $395$ $5$-digit numbers between $00001$ and $55914$ skipping those that aren't within $00001$ and $55914$ or are repetitions.

Part (b) Step 1: Calculation

A random number table will be used to select an SRS in a two-step process.

1) Write $00001$ to $55914$ on each gravestone.

2) To use a random number table, begin reading five-digit groupings from the left-hand side of line $127$ Because our gravestones are labeled from $00001$ to $55914$ select the first three unique numbers spanning from $00001$ to $55914$ which will be selected gravestones. The same gravestone cannot be selected more than once if the number is repeated and used only once.

Here is the beginning of line $127$: $4390999477253306435940085169258511736071$

The above digits are already grouped in $5$ digit numbers.$4390999477253306435940085$

✔ Skip ✔ Skip ✔

Too big Too big

As a result, the first three gravestones chosen are:$439092533040085$