/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 25 The supervisors of a rural count... [FREE SOLUTION] | 91Ó°ÊÓ

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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

Expert verified
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

01

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.
02

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.
03

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.

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Key Concepts

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

Statistical Survey
Conducting a statistical survey is a method for gathering information from a group of individuals or entities. The purpose is often to infer or make decisions about a larger group, known as the population. In our scenario, the supervisors aim to understand the sentiment towards the sewer system among property owners in a rural county. Rather than asking all 7,000 property owners, they choose to survey just 500. Surveys can be powerful tools because they allow for data collection that can reflect broader opinions or behaviors. They are cost-effective and time-saving, especially when dealing with large populations.
Surveys require careful planning and design. They must include relevant questions that are easy to understand and answer. The responses must be honest and accurate to provide valuable data. This data then needs to be analyzed meticulously to draw meaningful conclusions. By doing this, surveys help in making informed decisions that can influence policy and planning.
Random Sampling
Random sampling is a key component in conducting a reliable statistical survey. It involves selecting a sample from a larger population in such a way that each member of the population has an equal chance of being chosen. This method helps to ensure that the sample represents the population adequately. In our case, 500 property owners were chosen out of the 7,000. This random selection helps to mitigate any bias that could skew the results.
  • Random sampling enhances the validity of the survey outcomes.
  • It ensures that diverse opinions within the population are reflected in the sample.
  • Properly conducted, it allows for more generalizable and accurate results.
To implement random sampling, researchers can use various techniques such as simple random sampling, stratified sampling, or cluster sampling depending on the study requirements and the structure of the population.
Data Collection
Data collection in a survey involves gathering information to address specific research questions. It's a critical step that determines the quality of the data and, consequently, the reliability of the conclusions drawn from it. For our rural county example, data collection occurs when responses are recorded from the 500 selected property owners.
Depending on the nature of the survey, data can be collected through various methods:
  • Questionnaires: These can be distributed physically or electronically and are often used due to their wide reach and ease of analysis.
  • Interviews: Like phone or face-to-face conversations, which can provide deeper insights but are more resource-intensive.
  • Observation: Sometimes observing behaviors can provide data that is difficult to gather through direct questioning.
Whatever the method, data needs to be handled with care to ensure privacy and accuracy. It's vital that respondents feel their information is treated confidentially and respectfully. Proper training of personnel involved in data collection can help maintain data integrity.

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