Selecting an Unbiased Sample

Oct 13, 2025 by wbrum.org 75 views

The members of the city council want to determine approximately how many taxpayers in the city would support higher taxes to build a new playground.

Introduction

The city council members are faced with a crucial decision regarding the construction of a new playground. To make an informed decision, they need to determine the level of support from the taxpayers in the city. This requires selecting an unbiased sample of the population to gather accurate information. In this article, we will discuss how the members of the city council can select an unbiased sample of the population to determine the level of support for higher taxes to build a new playground.

Understanding the Problem

The city council members want to determine the number of taxpayers who would support higher taxes to build a new playground. This is a classic example of a survey research problem. The goal is to collect data from a representative sample of the population to make inferences about the entire population. However, the city council members need to ensure that the sample is unbiased and representative of the population.

Types of Sampling Methods

There are several types of sampling methods that can be used to select an unbiased sample of the population. Some of the most common methods include:

Random Sampling: This method involves selecting a sample of the population at random. Every member of the population has an equal chance of being selected.
Stratified Sampling: This method involves dividing the population into subgroups or strata and then selecting a sample from each subgroup.
Systematic Sampling: This method involves selecting a sample of the population at regular intervals. For example, every 10th member of the population may be selected.
Convenience Sampling: This method involves selecting a sample of the population based on convenience. For example, a sample may be selected from a group of people who are easily accessible.

Selecting an Unbiased Sample

To select an unbiased sample of the population, the city council members need to follow these steps:

Define the Population: The city council members need to define the population that they want to study. In this case, the population is the taxpayers in the city.
Determine the Sample Size: The city council members need to determine the sample size. A larger sample size will provide more accurate results, but it will also be more time-consuming and expensive.
Select a Sampling Method: The city council members need to select a sampling method. Random sampling is the most unbiased method, but it may be difficult to implement in practice.
Implement the Sampling Method: The city council members need to implement the sampling method. This may involve creating a list of all the taxpayers in the city and then selecting a random sample from the list.
Collect Data: The city council members need to collect data from the sample. This may involve conducting surveys or interviews with the sample members.

Example of a Random Sampling Method

Here is an example of how the city council members can use a random sampling method to select an unbiased sample of the population:

Create a List of Taxpayers: The city council members create a list of all the taxpayers in the city.
Use a Random Number Generator: The city council members use a random number generator to select a random sample from the list.
Select a Sample Size: The city council members select a sample size of 1000 taxpayers.
Collect Data: The city council members collect data from the sample by conducting surveys or interviews with the sample members.

Advantages and Disadvantages of Random Sampling

Random sampling has several advantages, including:

Unbiased Results: Random sampling provides unbiased results, which are representative of the population.
High Accuracy: Random sampling provides high accuracy, which is essential for making informed decisions.
Easy to Implement: Random sampling is easy to implement, especially with the use of random number generators.

However, random sampling also has several disadvantages, including:

Time-Consuming: Random sampling can be time-consuming, especially when dealing with large populations.
Expensive: Random sampling can be expensive, especially when dealing with large populations.
Difficult to Implement: Random sampling can be difficult to implement, especially when dealing with complex populations.

Conclusion

In conclusion, the city council members can select an unbiased sample of the population by using a random sampling method. This method involves creating a list of all the taxpayers in the city, using a random number generator to select a random sample, and collecting data from the sample. While random sampling has several advantages, it also has several disadvantages. The city council members need to weigh these advantages and disadvantages and decide whether random sampling is the best method for their needs.

Recommendations

Based on the discussion above, the following recommendations can be made:

Use a Random Sampling Method: The city council members should use a random sampling method to select an unbiased sample of the population.
Determine the Sample Size: The city council members should determine the sample size based on the needs of the study.
Collect Data: The city council members should collect data from the sample by conducting surveys or interviews with the sample members.
Analyze the Data: The city council members should analyze the data to make informed decisions.

Future Research Directions

Future research directions include:

Developing New Sampling Methods: Researchers can develop new sampling methods that are more efficient and effective than random sampling.
Improving the Accuracy of Sampling Methods: Researchers can improve the accuracy of sampling methods by developing new techniques for selecting samples.
Applying Sampling Methods to Real-World Problems: Researchers can apply sampling methods to real-world problems, such as determining the level of support for higher taxes to build a new playground.

References

Kish, L. (1965). Survey Sampling. John Wiley & Sons.
Cochran, W. G. (1977). Sampling Techniques. John Wiley & Sons.
Sarndal, C. E., & Swensson, B. (2002). Probability Sampling. John Wiley & Sons.
Q&A: Selecting an Unbiased Sample of the Population

Introduction

In our previous article, we discussed how the city council members can select an unbiased sample of the population to determine the level of support for higher taxes to build a new playground. In this article, we will answer some frequently asked questions (FAQs) about selecting an unbiased sample of the population.

Q: What is the difference between a sample and a population?

A: A sample is a subset of the population that is selected for study. The population is the entire group of people or items that the sample is intended to represent.

Q: Why is it important to select an unbiased sample of the population?

A: Selecting an unbiased sample of the population is important because it ensures that the results of the study are representative of the population. If the sample is biased, the results may not accurately reflect the opinions or characteristics of the population.

Q: What are some common biases that can occur when selecting a sample?

A: Some common biases that can occur when selecting a sample include:

Selection bias: This occurs when the sample is not representative of the population because of the way it was selected.
Non-response bias: This occurs when some members of the population do not respond to the survey or questionnaire.
Social desirability bias: This occurs when respondents answer questions in a way that they think is socially acceptable, rather than truthfully.

Q: How can I ensure that my sample is unbiased?

A: To ensure that your sample is unbiased, you should:

Use a random sampling method: This involves selecting a sample at random from the population.
Use a stratified sampling method: This involves dividing the population into subgroups and then selecting a sample from each subgroup.
Use a systematic sampling method: This involves selecting a sample at regular intervals from the population.
Avoid biases in the survey or questionnaire: This involves making sure that the questions are clear and unbiased, and that the respondents are not influenced by external factors.

Q: What are some common sampling methods used in research?

A: Some common sampling methods used in research include:

Random sampling: This involves selecting a sample at random from the population.
Stratified sampling: This involves dividing the population into subgroups and then selecting a sample from each subgroup.
Systematic sampling: This involves selecting a sample at regular intervals from the population.
Convenience sampling: This involves selecting a sample based on convenience, such as selecting a sample from a group of people who are easily accessible.

Q: How can I determine the sample size for my study?

A: To determine the sample size for your study, you should:

Determine the desired level of precision: This involves determining how accurate you want the results to be.
Determine the expected effect size: This involves determining the expected difference between the groups being studied.
Use a sample size calculation formula: This involves using a formula to calculate the sample size based on the desired level of precision and the expected effect size.

Q: What are some common challenges associated with selecting a sample?

A: Some common challenges associated with selecting a sample include:

Difficulty in accessing the population: This can make it difficult to select a sample that is representative of the population.
High non-response rates: This can make it difficult to get accurate results from the sample.
Biases in the survey or questionnaire: This can make it difficult to get accurate results from the sample.