Question

Suppose that a study was carried out in which each student in a random sample of students at a particular college was asked if he or she was registered to vote. Would these data be used to estimate a population mean or to estimate a population proportion? How did you decide?

Short answer

These data would be used to estimate a population proportion. This is because the data generated from the responses to the question asked (whether a student is registered to vote or not) is categorical, allowing for a proportion (ratio) to be calculated. A population mean would require quantitative or measurement data.

Step-by-step solution

Understanding the question type

First, analyse the type of question asked. In this case, every student in the sample is asked if they are registered to vote. This is a categorical question where the answer can be either 'Yes' (they are registered) or 'No' (they are not registered).

Type of data generated

Categorical questions like these generate binary or nominal data. The responses to these questions can’t be measured on a scale, but they can be counted up to provide proportions. The proportion here would represent the ratio of students who are registered to vote in the total student population.

Type of population parameter estimated

Since the responses can be used to estimate the proportion of the total student population that are registered to vote, you are estimating a population proportion.