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Chapter 4: Problem 1

A high school's student newspaper plans to survey local businesses about the importance of students as customers. From an alphabetical list of all local businesses, the newspaper staff chooses 150 businesses at random. Of these, 73 return the questionnaire mailed by the staff. Identify the population and the sample.

Short Answer

Expert verified
Population: all local businesses; Sample: 150 selected businesses.

Step by step solution

01

Understand the Population

The population is the entire group that you are interested in studying or collecting data from. In this case, the population consists of all local businesses the high school student newspaper is targeting for their survey.
02

Define the Sample

The sample is a subset of the population that is selected for the actual study or survey. Here, the sample includes the 150 businesses chosen at random from the alphabetical list to participate in the survey.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Population
In statistics, the term "population" refers to the entire group about which you want to draw conclusions. It's the full set of individuals or items that you're interested in studying. In the context of our high school's student newspaper survey exercise, the population comprises all local businesses. These businesses are the main subjects the students want to learn about to understand their importance as customers.

A population can be large, and in many cases, it's impractical to collect data from each member. Hence, it鈥檚 crucial to clearly define the population to ensure that studies like surveys achieve their intended purpose. The characteristics of the population should be well understood to precisely tailor survey questions and conduct flawless inferences.
Sample
A sample is a smaller, manageable version of a population. It is a selection of individuals, events, or objects taken from the population of interest. Sampling makes it feasible to collect and analyze data without the need to survey every single member of the population. This is especially helpful when populations are large, like in our example of local businesses.

In the provided scenario, a sample of 150 businesses was randomly chosen from an alphabetical list of all local businesses. Random sampling is a common method employed to ensure every member of the population has an equal opportunity to be selected. Randomization helps in achieving a representative sample that mirrors the characteristics of the population, thereby enhancing the validity of findings.
Survey
A survey is a research tool used to gather information from a set of individuals, which can represent a larger group or population. It involves collecting data through questionnaires or interviews. Surveys are valuable as they can provide information about opinions, behaviors, or characteristics of a group.

In the student newspaper鈥檚 exercise, a mailed questionnaire was used as the survey method. Out of the 150 businesses that received the survey, 73 returned it. This response rate is critical to ensuring the survey results are reflective of the targeted population. Surveys should be designed with clarity to ensure that the questions gather the structured information needed to make confident conclusions about the population of interest.

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Most popular questions from this chapter

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