Survey on Politics In a study, 68% of 903 randomly selected adults said they believe the Republicans favor the rich. If the margin of error was 2 percentage points, what was the confidence level used for the proportion? Round the intermediate calculations to four decimal places, round the z value to two decimal places, and round the final answer to the nearest whole number. The confidence level is
Survey on Politics In a study, 68% of 903 randomly selected adults said they believe the Republicans favor the rich. If the margin of error was 2 percentage points, what was the confidence level used for the proportion? Round the intermediate calculations to four decimal places, round the z value to two decimal places, and round the final answer to the nearest whole number. The confidence level is
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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![**Survey on Politics**
In a study, 68% of 903 randomly selected adults said they believe the Republicans favor the rich. If the margin of error was 2 percentage points, what was the confidence level used for the proportion?
Round the intermediate calculations to four decimal places, round the z value to two decimal places, and round the final answer to the nearest whole number.
[Input Box]
The confidence level is [ ]%.
---
**Explanation of Calculations:**
To find the confidence level, you need to calculate the z-score corresponding to the given margin of error and sample proportion. Then, translate the z-score to a percentage representing the confidence level.
1. **Sample Proportion (p-hat):** 0.68
2. **Sample Size (n):** 903
3. **Margin of Error (E):** 0.02 (2 percentage points)
**Formula for Margin of Error:**
\[ E = z \times \sqrt{\frac{p(1-p)}{n}} \]
Where:
- \( p \) is the sample proportion (0.68)
- \( n \) is the sample size (903)
**Steps:**
1. Calculate the standard error (SE) using \( \sqrt{\frac{p(1-p)}{n}} \).
2. Solve for z using the margin of error formula.
3. Convert the z-value to a confidence level percentage.
**Rounding Instructions:**
- Intermediate calculations to four decimal places.
- z value to two decimal places.
- Final answer to the nearest whole number.
Remember to use z-tables or statistical software to convert the computed z-value to its corresponding confidence level.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3510745c-b224-4e3c-988a-4a06d65307ae%2F6d8400a3-7692-47bd-b5d3-4c1c0f74c841%2F46z33f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Survey on Politics**
In a study, 68% of 903 randomly selected adults said they believe the Republicans favor the rich. If the margin of error was 2 percentage points, what was the confidence level used for the proportion?
Round the intermediate calculations to four decimal places, round the z value to two decimal places, and round the final answer to the nearest whole number.
[Input Box]
The confidence level is [ ]%.
---
**Explanation of Calculations:**
To find the confidence level, you need to calculate the z-score corresponding to the given margin of error and sample proportion. Then, translate the z-score to a percentage representing the confidence level.
1. **Sample Proportion (p-hat):** 0.68
2. **Sample Size (n):** 903
3. **Margin of Error (E):** 0.02 (2 percentage points)
**Formula for Margin of Error:**
\[ E = z \times \sqrt{\frac{p(1-p)}{n}} \]
Where:
- \( p \) is the sample proportion (0.68)
- \( n \) is the sample size (903)
**Steps:**
1. Calculate the standard error (SE) using \( \sqrt{\frac{p(1-p)}{n}} \).
2. Solve for z using the margin of error formula.
3. Convert the z-value to a confidence level percentage.
**Rounding Instructions:**
- Intermediate calculations to four decimal places.
- z value to two decimal places.
- Final answer to the nearest whole number.
Remember to use z-tables or statistical software to convert the computed z-value to its corresponding confidence level.
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