Question

During the previous calendar year, a county's small claims court processed 870 cases. Describe how a simple random sample of size \(n=50\) might be selected from the case files to obtain information regarding the average award in such cases.

Short answer

To get a simple random sample of size \(n=50\) from the 870 cases, each case should be assigned a unique numerical identifier from 1 to 870. Then using a random number generator, select 50 different numbers between 1 and 870. The cases associated with these numbers form the sample. Analyze this sample to estimate the average award.

Step-by-step solution

Understand the concept of simple random sampling

In simple random sampling, every item or person of the population has an equal chance of being selected. It's like putting all the names into a hat and then drawing out several names at random.

Assign each case a numerical identifier

List all of the 870 cases, then assign a unique number to each case, from 1 to 870. This allows us to easily identify which cases are being selected.

Use a random number generator

To ensure all cases have an equal chance of selection, we will make use of a random number generator. This can be done through a software or website online that generates random numbers.

Select the cases

Set the random number generator to produce numbers between 1 and 870. Generate 50 different numbers and the cases that correspond to these numbers are selected for the sample. If a number is repeated, ignore it and generate a new one, as each case should only be included once.

Analyze the sample data

Now that we have a sample, it can be used to gather information about the average award in such cases. Analyze the data from these 50 cases to estimate the average award.