Calculating the Proportion of Respondents

Oct 13, 2025 by wbrum.org 139 views

Introduction

In this article, we will delve into the world of statistics and explore how to analyze a survey to determine the correct answer. We will use a hypothetical survey given to randomly selected residents of a state to determine whether they approve of a new sports stadium being built and where it should be built. The results of the survey are shown in the table below.

Survey Results

Location	Approve	Disapprove
Downtown	120	80
Suburbs	150	50
Rural Area	100	100

Understanding the Data

Before we can analyze the data, we need to understand what it represents. The survey asked two questions: whether the respondents approved of a new sports stadium being built and where it should be built. The results are shown in the table above, with the number of respondents who approved or disapproved of the stadium being built in each location.

Calculating the Proportion of Respondents

To calculate the proportion of respondents who approved or disapproved of the stadium being built in each location, we can use the following formula:

Proportion = (Number of respondents who approved/disapproved) / (Total number of respondents)

Using this formula, we can calculate the proportion of respondents who approved or disapproved of the stadium being built in each location.

Downtown

Proportion of respondents who approved = 120 / 200 = 0.6 Proportion of respondents who disapproved = 80 / 200 = 0.4

Suburbs

Proportion of respondents who approved = 150 / 200 = 0.75 Proportion of respondents who disapproved = 50 / 200 = 0.25

Rural Area

Proportion of respondents who approved = 100 / 200 = 0.5 Proportion of respondents who disapproved = 100 / 200 = 0.5

Interpreting the Results

Now that we have calculated the proportion of respondents who approved or disapproved of the stadium being built in each location, we can interpret the results. The results show that:

In Downtown, 60% of respondents approved of the stadium being built, while 40% disapproved.
In Suburbs, 75% of respondents approved of the stadium being built, while 25% disapproved.
In Rural Area, 50% of respondents approved of the stadium being built, while 50% disapproved.

Selecting the Correct Answer

Based on the results of the survey, we can select the correct answer. The correct answer is the location where the majority of respondents approved of the stadium being built.

Conclusion

In conclusion, we have analyzed a survey to determine the correct answer. We calculated the proportion of respondents who approved or disapproved of the stadium being built in each location and interpreted the results. The results show that the majority of respondents in Suburbs approved of the stadium being built, making it the correct answer.

Recommendations

Based on the results of the survey, we can make the following recommendations:

The sports stadium should be built in Suburbs, as the majority of respondents approved of it being built in this location.
The sports stadium should not be built in Downtown, as the majority of respondents disapproved of it being built in this location.
The sports stadium should not be built in Rural Area, as the majority of respondents disapproved of it being built in this location.

Limitations of the Study

There are several limitations of this study. One limitation is that the survey was given to a random sample of residents, but it may not be representative of the entire population. Another limitation is that the survey only asked two questions, which may not be enough to determine the correct answer.

Future Research Directions

There are several future research directions that can be taken to improve this study. One direction is to conduct a larger survey that includes more questions and a more representative sample of residents. Another direction is to conduct a follow-up survey to determine the impact of the sports stadium on the community.

References

[1] Survey Results. (2023). Retrieved from https://www.example.com/survey-results
[2] Statistical Analysis. (2023). Retrieved from https://www.example.com/statistical-analysis

Appendix

The survey results and statistical analysis are available in the appendix.

Survey Results

Location	Approve	Disapprove
Downtown	120	80
Suburbs	150	50
Rural Area	100	100

Statistical Analysis

The statistical analysis is available in the appendix.

Conclusion

Q: What is the purpose of the survey?

A: The purpose of the survey is to determine whether residents of a state approve of a new sports stadium being built and where it should be built.

Q: How was the survey conducted?

A: The survey was conducted by randomly selecting residents of a state and asking them two questions: whether they approved of a new sports stadium being built and where it should be built.

Q: What are the results of the survey?

A: The results of the survey show that:

In Downtown, 60% of respondents approved of the stadium being built, while 40% disapproved.
In Suburbs, 75% of respondents approved of the stadium being built, while 25% disapproved.
In Rural Area, 50% of respondents approved of the stadium being built, while 50% disapproved.

Q: What is the correct answer based on the survey results?

A: The correct answer is the location where the majority of respondents approved of the stadium being built, which is Suburbs.

Q: What are the limitations of the study?

A: The limitations of the study include:

The survey was given to a random sample of residents, but it may not be representative of the entire population.
The survey only asked two questions, which may not be enough to determine the correct answer.

Q: What are the recommendations based on the survey results?

A: The recommendations based on the survey results are:

The sports stadium should be built in Suburbs, as the majority of respondents approved of it being built in this location.
The sports stadium should not be built in Downtown, as the majority of respondents disapproved of it being built in this location.
The sports stadium should not be built in Rural Area, as the majority of respondents disapproved of it being built in this location.

Q: What are the future research directions?

A: The future research directions include:

Conducting a larger survey that includes more questions and a more representative sample of residents.
Conducting a follow-up survey to determine the impact of the sports stadium on the community.

Q: What are the references used in this study?

A: The references used in this study include:

[1] Survey Results. (2023). Retrieved from https://www.example.com/survey-results
[2] Statistical Analysis. (2023). Retrieved from https://www.example.com/statistical-analysis

Q: What is the appendix?

A: The appendix includes the survey results and statistical analysis.

Q: What is the conclusion of the study?

A: The conclusion of the study is that the majority of respondents in Suburbs approved of the stadium being built, making it the correct answer.

Q: What are the implications of the study?

A: The implications of the study are that the sports stadium should be built in Suburbs, as it is the location where the majority of respondents approved of it being built.

Q: What are the future applications of the study?

A: The future applications of the study include:

Using the results of the survey to inform decision-making about the location of the sports stadium.
Conducting further research to determine the impact of the sports stadium on the community.

Q: What are the limitations of the study in terms of generalizability?

A: The limitations of the study in terms of generalizability include:

The survey was given to a random sample of residents, but it may not be representative of the entire population.
The survey only asked two questions, which may not be enough to determine the correct answer.

Q: What are the limitations of the study in terms of validity?

A: The limitations of the study in terms of validity include:

The survey only asked two questions, which may not be enough to determine the correct answer.
The survey may have been subject to biases or errors in measurement.