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?

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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%.
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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