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Chapter 2: Problem 12

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

Expert verified
A simple random sample can be obtained by assigning unique numbers to each of the 870 cases and then randomly selecting 50 unique numbers. The cases corresponding to these numbers will form the required sample. The average award can then be calculated by summing the award values from these 50 cases, and dividing that by 50.

Step by step solution

01

Understanding the Problem

The problem is asking for a description of the procedure to select a simple random sample from the court cases of the last year, which are 870 cases. The size of the sample that we need to select is 50 cases. A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. Each selection is independent of the others.
02

Procedure of Random Sampling

The process of selecting a simple random sample is straightforward. One common method is the lottery method, where each of the 870 cases can be associated with a unique number from 1 to 870. Then, these numbers can be written on slips of paper, and 50 numbers can be randomly drawn. The cases associated with these drawn numbers represent a simple random sample.
03

Alternative Procedure Using Technology

In real-life situations, the lottery method may be impractical due to time and resources, especially with larger populations. Hence, a more efficient method is to use statistical software or a random number generator. Each case can be associated with a number from 1 to 870. Using a random number generator, generate 50 unique random numbers between 1 and 870. The cases that correspond to these numbers will constitute a simple random sample.
04

Using the Sample to Calculate Average Award

Once the random sample is selected, one can calculate the average award from this sample. Add up all the award values from the 50 case files and then divide by 50. This will yield a good estimate of the average award value in the wider population of 870 cases.

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