Question

The supervisors of a rural county are interested in the proportion of property owners who support the construction of a sewer system. Because it is too costly to contact all 7,000 property owners, a survey of 500 owners (selected at random) is undertaken. Describe the population and sample for this problem.

Short answer

The population for this problem includes all of the 7,000 property owners in the rural county. The sample is the 500 property owners out of this population that were selected at random and surveyed.

Step-by-step solution

Identify the Population

In this scenario, the population is the entire group of property owners in the rural county. This is because the supervisors are interested in the opinion of all property owners, thus making all of them the population. Therefore, the population in this case includes a total of 7,000 property owners.

Identify the Sample

Now, the sample is the group of people or items selected from the population for data collection. For the above problem, the sample is the 500 property owners who were selected at random to participate in the survey.

Illustrate the Relationship

Lastly, it is critical to place the sample in the context of the population. In this problem, the 500 property owners who were surveyed represent the sample within the larger population of 7,000 property owners in the rural county. It is from this sample that conclusions or estimates about the population as a whole will be drawn.