Question

State whether the data are best described as a population or a sample. A questionnaire to understand athletic participation on a college campus is emailed to 50 college students, and all of them respond.

Short answer

The data provided in the exercise best describes a sample.

Step-by-step solution

Identifying the Population and Sample

Firstly, identify the population and sample of the study. Here, the population would be all the students on the campus.

Analyzing the Information Provided

Next, analyze the data that is provided in the exercise. The exercise mentions that the questionnaire was emailed to 50 students on the campus, and all of them responded.

Determining Whether Data represents Population or Sample

Now based on the information, determine whether the data represents a sample or population. It was mentioned that an email was sent to only a small group of students out of all the students on the campus. So, even though all the students to whom the questionnaire was sent responded, this group only represents a part of all the students on the campus, thus, this information is a sample.

Key concepts

Statistical Population

The term statistical population is a cornerstone of statistical analysis, referring to the entire group of individuals or observations about which researchers are interested. In the context of a college campus athletic participation survey, the statistical population would be all students enrolled at the college. When researchers focus on this entire population, they aim to gather insights into every student's behavior or characteristics regarding athletic participation.

However, studying an entire population can often be impractical, expensive, or time-consuming. This is where the distinction between population and sample becomes crucial. A population encompasses every member within the defined group, providing a full picture of the subject matter. When you have the data for an entire population, you can make definitive statements about it without needing to account for uncertainty due to sampling.

Sample Data

In contrast to a statistical population, sample data represent a subset of the population, selected to make inferences about the population as a whole. If you consider the same scenario of the athletic participation survey, sample data was collected by sending questionnaires to just 50 students. The essence of sampling lies in the hope that this small group can effectively represent the broader student body's athletic participation trends.

It's critical to select a sample carefully, ensuring it's representative of the population. This way, the findings from the sample can be generalized to the population with a certain level of confidence. Sample data makes research feasible when it is not possible to study the entire population. The use of sampling, however, introduces the element of uncertainty, as the sample may or may not perfectly reflect the entire population's characteristics.

Athletic Participation Survey

An athletic participation survey is a practical tool for gathering data on students' involvement in sports and physical activities on campus. This type of survey typically includes questions about frequency of participation, types of sports engaged in, and possibly the motivations or barriers to participation. When it's deployed correctly, it can yield valuable insights for campus athletics departments to understand current participation levels and to inform future programming.

In the given problem, the survey was distributed to a select group of 50 students. The survey's design and the questions it asks are essential, as they need to be relevant, clear, and unbiased to obtain reliable and valid data. Despite the survey's potential insights, one must remember the responses only reflect a sample of the entire student population's athletic habits, not the entire demographic.

Questionnaire Response Analysis

The process of questionnaire response analysis involves interpreting the answers received from the survey participants to draw meaningful conclusions. This analysis should consider the survey's methodological strengths and limitations to accurately reflect the sentiments and behaviors of the sample. For the athletic participation survey of 50 college students, each response provided data points detailing individual student involvement in athletics.

To analyze these responses, researchers employ techniques ranging from basic data tabulation to more complex statistical methods, depending on the survey's goals. They look for patterns, correlations, and trends among the responses that can indicate broader participation issues. Important to note is that the results from this sample will be used to estimate the behavior of the population as a whole, keeping in mind the possible margin of error or bias introduced by the sample's limited scope.