1. A poll of 2,500 people shows that 50% approve of a smoking ban in bars and restaurants. What is the margin of error, assuming a 95% confidence level? What is the confidence interval?
1. A poll of 2,500 people shows that 50% approve of a smoking ban in bars and restaurants. What is the margin of error, assuming a 95% confidence level? What is the confidence interval?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Poll Analysis**
1. A poll of 2,500 people shows that 50% approve of a smoking ban in bars and restaurants. What is the margin of error, assuming a 95% confidence level? What is the confidence interval?
**Explanation:**
To calculate the margin of error (MOE) and confidence interval for this poll, use the following steps:
1. **Determine the sample proportion (p):** In this case, p = 0.50 (50% approval).
2. **Calculate the standard error (SE):**
SE = sqrt[(p(1-p))/n]
Where n is the sample size (2,500 in this case).
SE = sqrt[(0.50 * 0.50) / 2,500]
SE = sqrt[0.25 / 2,500]
SE = sqrt[0.0001]
SE = 0.01
3. **Find the Z-score for a 95% confidence level:**
Typically, the Z-score is 1.96 for a 95% confidence level.
4. **Calculate the Margin of Error (MOE):**
MOE = Z * SE
MOE = 1.96 * 0.01
MOE = 0.0196 or 1.96%
5. **Determine the Confidence Interval:**
Lower limit = p - MOE = 0.50 - 0.0196 = 0.4804 or 48.04%
Upper limit = p + MOE = 0.50 + 0.0196 = 0.5196 or 51.96%
Thus, the confidence interval is 48.04% to 51.96%. This means we can be 95% confident that the true proportion of people who approve of the smoking ban is between 48.04% and 51.96%.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c8f01e2-a14e-48cc-8752-a6869fe4cc3e%2F6353be35-f5ca-4f02-b578-4a37cb2c7938%2Feazat0k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Poll Analysis**
1. A poll of 2,500 people shows that 50% approve of a smoking ban in bars and restaurants. What is the margin of error, assuming a 95% confidence level? What is the confidence interval?
**Explanation:**
To calculate the margin of error (MOE) and confidence interval for this poll, use the following steps:
1. **Determine the sample proportion (p):** In this case, p = 0.50 (50% approval).
2. **Calculate the standard error (SE):**
SE = sqrt[(p(1-p))/n]
Where n is the sample size (2,500 in this case).
SE = sqrt[(0.50 * 0.50) / 2,500]
SE = sqrt[0.25 / 2,500]
SE = sqrt[0.0001]
SE = 0.01
3. **Find the Z-score for a 95% confidence level:**
Typically, the Z-score is 1.96 for a 95% confidence level.
4. **Calculate the Margin of Error (MOE):**
MOE = Z * SE
MOE = 1.96 * 0.01
MOE = 0.0196 or 1.96%
5. **Determine the Confidence Interval:**
Lower limit = p - MOE = 0.50 - 0.0196 = 0.4804 or 48.04%
Upper limit = p + MOE = 0.50 + 0.0196 = 0.5196 or 51.96%
Thus, the confidence interval is 48.04% to 51.96%. This means we can be 95% confident that the true proportion of people who approve of the smoking ban is between 48.04% and 51.96%.
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