Calculating the Proportion of Students for Each National Park

Oct 13, 2025 by recoveryshake.com 61 views

Introduction

In the field of statistics, random sampling is a crucial technique used to collect data from a population. By selecting a subset of individuals from the population, researchers can make inferences about the entire population. In this article, we will explore how random sampling can be used to analyze student preferences for national parks. We will examine a table of responses from 100 students out of a population of 1,500, who were asked to choose their favorite national park.

Understanding the Data

The table below shows the responses from the 100 students who participated in the random sampling.

National Park	Number of Students
Yellowstone	15
Yosemite	20
Grand Canyon	25
Zion	10
Great Smoky Mountains	5
Acadia	5
Olympic	5
Other	10

Calculating the Proportion of Students for Each National Park

To understand the preferences of the students, we need to calculate the proportion of students who chose each national park. We can do this by dividing the number of students who chose each park by the total number of students who participated in the random sampling.

Yellowstone: 15/100 = 0.15 or 15%
Yosemite: 20/100 = 0.20 or 20%
Grand Canyon: 25/100 = 0.25 or 25%
Zion: 10/100 = 0.10 or 10%
Great Smoky Mountains: 5/100 = 0.05 or 5%
Acadia: 5/100 = 0.05 or 5%
Olympic: 5/100 = 0.05 or 5%
Other: 10/100 = 0.10 or 10%

Interpreting the Results

From the table, we can see that the Grand Canyon is the most popular national park among the students, with 25 students choosing it. This is followed closely by Yellowstone and Yosemite, which were chosen by 15 and 20 students respectively. The least popular national parks were Acadia, Olympic, and Great Smoky Mountains, which were each chosen by only 5 students.

Calculating the Margin of Error

When conducting a random sampling, it is essential to calculate the margin of error to determine the reliability of the results. The margin of error can be calculated using the following formula:

Margin of Error = (Z * (σ / √n))

where:

Z is the Z-score corresponding to the desired confidence level
σ is the standard deviation of the population
n is the sample size

Assuming a 95% confidence level, the Z-score is approximately 1.96. The standard deviation of the population is not provided, but we can estimate it using the sample standard deviation.

Sample Standard Deviation = √((Σ(xi - x̄)^2) / (n - 1))

where:

xi is each data point
x̄ is the sample mean
n is the sample size

Using the sample data, we can calculate the sample standard deviation as follows:

Sample Standard Deviation = √((15^2 + 20^2 + 25^2 + 10^2 + 5^2 + 5^2 + 5^2 + 10^2) / (100 - 1)) = √((225 + 400 + 625 + 100 + 25 + 25 + 25 + 100) / 99) = √(1400 / 99) = √14.14 = 3.76

Now, we can calculate the margin of error as follows:

Margin of Error = (1.96 * (3.76 / √100)) = (1.96 * 0.376) = 0.736

Conclusion

In conclusion, random sampling can be a powerful tool for analyzing student preferences for national parks. By selecting a subset of students from the population, researchers can make inferences about the entire population. In this article, we analyzed a table of responses from 100 students who were asked to choose their favorite national park. We calculated the proportion of students for each national park and interpreted the results. We also calculated the margin of error to determine the reliability of the results. The results showed that the Grand Canyon was the most popular national park among the students, followed closely by Yellowstone and Yosemite. The least popular national parks were Acadia, Olympic, and Great Smoky Mountains.

Recommendations

Based on the results, we recommend the following:

Increase the sample size: To increase the accuracy of the results, we recommend increasing the sample size to at least 500 students.
Use a more representative sample: To ensure that the sample is representative of the population, we recommend using a more diverse sample that includes students from different age groups, genders, and ethnicities.
Use a more reliable data collection method: To ensure that the data is accurate and reliable, we recommend using a more reliable data collection method, such as online surveys or in-person interviews.

Limitations

This study has several limitations, including:

Small sample size: The sample size was relatively small, which may have affected the accuracy of the results.
Limited data collection method: The data was collected through a random sampling, which may not have been representative of the population.
Limited demographic information: The study did not collect demographic information about the students, which may have affected the accuracy of the results.

Future Research Directions

Future research directions may include:

Conducting a larger study: Conducting a larger study with a more representative sample size and a more reliable data collection method.
Collecting demographic information: Collecting demographic information about the students to ensure that the sample is representative of the population.
Analyzing the results using more advanced statistical methods: Analyzing the results using more advanced statistical methods, such as regression analysis or clustering analysis.
Q&A: Analyzing Student Preferences for National Parks through Random Sampling ====================================================================

Introduction

In our previous article, we analyzed student preferences for national parks through random sampling. We examined a table of responses from 100 students out of a population of 1,500, who were asked to choose their favorite national park. In this article, we will answer some frequently asked questions about the study and provide additional insights into the results.

Q: What is random sampling and why is it used in this study?

A: Random sampling is a technique used to collect data from a population by selecting a subset of individuals at random. It is used in this study to ensure that the sample is representative of the population and to reduce bias.

Q: How was the sample size of 100 students determined?

A: The sample size of 100 students was determined using a statistical formula that takes into account the desired level of precision and the size of the population. In this case, we wanted to achieve a margin of error of 5% or less, which required a sample size of at least 100 students.

Q: What is the margin of error and why is it important?

A: The margin of error is a measure of the uncertainty associated with a statistical estimate. In this study, the margin of error is 0.736, which means that the true proportion of students who prefer each national park may be up to 0.736 points higher or lower than the estimated proportion.

Q: How can the results of this study be generalized to the entire population?

A: The results of this study can be generalized to the entire population with a certain level of confidence, which is determined by the sample size and the margin of error. In this case, we can be 95% confident that the true proportion of students who prefer each national park is within 0.736 points of the estimated proportion.

Q: What are some limitations of this study?

A: Some limitations of this study include:

Small sample size: The sample size was relatively small, which may have affected the accuracy of the results.
Limited data collection method: The data was collected through a random sampling, which may not have been representative of the population.
Limited demographic information: The study did not collect demographic information about the students, which may have affected the accuracy of the results.

Q: What are some potential applications of this study?

A: Some potential applications of this study include:

Informing park management decisions: The results of this study can be used to inform park management decisions, such as determining the allocation of resources and developing marketing campaigns.
Developing educational programs: The results of this study can be used to develop educational programs that promote awareness and appreciation of national parks.
Conducting further research: The results of this study can be used to inform further research on student preferences for national parks and other outdoor recreational activities.

Q: What are some potential future research directions?

A: Some potential future research directions include:

Conducting a larger study: Conducting a larger study with a more representative sample size and a more reliable data collection method.
Collecting demographic information: Collecting demographic information about the students to ensure that the sample is representative of the population.
Analyzing the results using more advanced statistical methods: Analyzing the results using more advanced statistical methods, such as regression analysis or clustering analysis.

Conclusion

In conclusion, random sampling can be a powerful tool for analyzing student preferences for national parks. By selecting a subset of students from the population, researchers can make inferences about the entire population. In this article, we answered some frequently asked questions about the study and provided additional insights into the results. We also discussed some potential applications and future research directions.