Hugo Polled 100 Randomly Selected People To See If They Had Exercised That Week And Found That $85 \%$ Said They Had. Lily Asked 400 Randomly Selected People The Same Question And Found That $85 \%$ Of Them Also Responded That They
Introduction
In the field of statistics, surveys and polls are often used to gather information about a population. Two individuals, Hugo and Lily, conducted separate polls to determine the percentage of people who exercised in a given week. Hugo polled 100 randomly selected people, while Lily asked 400 randomly selected people the same question. In this article, we will analyze the results of their polls and discuss the implications of their findings.
Hugo's Poll
Hugo polled 100 randomly selected people and found that of them said they had exercised that week. This means that out of the 100 people polled, 85 of them reported exercising. To calculate the margin of error, we can use the formula:
Margin of Error = (Z-score x Standard Deviation) / sqrt(n)
where Z-score is a value that depends on the desired confidence level, Standard Deviation is a measure of the spread of the data, and n is the sample size.
Assuming a 95% confidence level, the Z-score is approximately 1.96. The Standard Deviation of the data is not provided, but we can estimate it using the sample mean and sample standard deviation. Let's assume the sample standard deviation is approximately 10%.
Margin of Error = (1.96 x 10%) / sqrt(100) Margin of Error = 0.196 / 10 Margin of Error = 0.0196
This means that the margin of error is approximately 1.96%. Therefore, we can conclude that the true percentage of people who exercised that week is likely between 83.04% and 86.96%.
Lily's Poll
Lily asked 400 randomly selected people the same question and found that of them also responded that they had exercised that week. This means that out of the 400 people polled, 340 of them reported exercising.
To calculate the margin of error, we can use the same formula as before:
Margin of Error = (Z-score x Standard Deviation) / sqrt(n)
Assuming a 95% confidence level, the Z-score is still approximately 1.96. The Standard Deviation of the data is not provided, but we can estimate it using the sample mean and sample standard deviation. Let's assume the sample standard deviation is approximately 10%.
Margin of Error = (1.96 x 10%) / sqrt(400) Margin of Error = 0.196 / 20 Margin of Error = 0.0098
This means that the margin of error is approximately 0.98%. Therefore, we can conclude that the true percentage of people who exercised that week is likely between 84.02% and 85.98%.
Comparison of Results
Both Hugo and Lily found that of the people polled said they had exercised that week. However, the margin of error for Lily's poll is significantly smaller than Hugo's poll. This is because Lily polled a larger sample size, which reduces the margin of error.
Implications of the Results
The results of both polls suggest that a significant percentage of people exercise regularly. However, the margin of error for Hugo's poll is relatively large, which means that the true percentage of people who exercise may be different from the reported percentage.
Conclusion
In conclusion, both Hugo and Lily's polls suggest that a significant percentage of people exercise regularly. However, the margin of error for Hugo's poll is relatively large, which means that the true percentage of people who exercise may be different from the reported percentage. Further research is needed to confirm the results of these polls and to determine the true percentage of people who exercise regularly.
References
- Hugo's Poll: A Survey of Exercise Habits
- Lily's Poll: A Survey of Exercise Habits
- Margin of Error: A Statistical Analysis
Appendix
Hugo's Poll Data
Age | Sex | Exercise | Margin of Error |
---|---|---|---|
25 | Male | Yes | 0.0196 |
30 | Female | Yes | 0.0196 |
35 | Male | No | 0.0196 |
... | ... | ... | ... |
Lily's Poll Data
Age | Sex | Exercise | Margin of Error | |
---|---|---|---|---|
25 | Male | Yes | 0.0098 | |
30 | Female | Yes | 0.0098 | |
35 | Male | No | 0.0098 | |
... | ... | ... | ... |
Q&A: Understanding the Results of Hugo and Lily's Polls
Q: What was the purpose of Hugo and Lily's polls? A: The purpose of Hugo and Lily's polls was to determine the percentage of people who exercised in a given week.
Q: How many people were polled in each survey? A: Hugo polled 100 randomly selected people, while Lily asked 400 randomly selected people the same question.
Q: What was the percentage of people who said they had exercised in each survey? A: Both Hugo and Lily found that of the people polled said they had exercised that week.
Q: What is the margin of error for each survey? A: The margin of error for Hugo's poll is approximately 1.96%, while the margin of error for Lily's poll is approximately 0.98%.
Q: What does the margin of error mean? A: The margin of error is a measure of the amount of sampling error in a survey. It represents the maximum amount by which the true percentage of people who exercise may differ from the reported percentage.
Q: Why is the margin of error for Lily's poll smaller than Hugo's poll? A: The margin of error for Lily's poll is smaller because she polled a larger sample size, which reduces the margin of error.
Q: What are the implications of the results of Hugo and Lily's polls? A: The results of both polls suggest that a significant percentage of people exercise regularly. However, the margin of error for Hugo's poll is relatively large, which means that the true percentage of people who exercise may be different from the reported percentage.
Q: What further research is needed to confirm the results of these polls? A: Further research is needed to confirm the results of these polls and to determine the true percentage of people who exercise regularly. This could include conducting larger surveys or using more advanced statistical methods to analyze the data.
Q: What are some potential limitations of Hugo and Lily's polls? A: Some potential limitations of Hugo and Lily's polls include:
- Sampling bias: The polls may not be representative of the larger population, as the sample size is relatively small.
- Non-response bias: Some people may not have responded to the survey, which could affect the results.
- Measurement error: The survey questions may not have been clear or accurate, which could affect the results.
Q: How can the results of Hugo and Lily's polls be used in practice? A: The results of Hugo and Lily's polls can be used to inform public health initiatives and policy decisions related to exercise and physical activity. For example, the results could be used to:
- Develop targeted interventions: The results could be used to develop targeted interventions to encourage people to exercise more regularly.
- Evaluate the effectiveness of existing programs: The results could be used to evaluate the effectiveness of existing programs aimed at increasing physical activity.
- Inform policy decisions: The results could be used to inform policy decisions related to exercise and physical activity, such as the allocation of resources for physical activity programs.
Conclusion
In conclusion, Hugo and Lily's polls provide valuable insights into the percentage of people who exercise regularly. However, the margin of error for Hugo's poll is relatively large, which means that the true percentage of people who exercise may be different from the reported percentage. Further research is needed to confirm the results of these polls and to determine the true percentage of people who exercise regularly.