1.645 1.960 = 2.576 Jump to level 1 A poll reported 42% support for a statewide election with a margin of error of 2.13 percentage points. How many voters should be sampled for a 99% confidence interval? Round up to the nearest whole number. Ex: 1234 voters Check Next 3 Allen Brexit poll: Six months on Brits stand by EU referendum decision, ONN, 19 December 2016,
1.645 1.960 = 2.576 Jump to level 1 A poll reported 42% support for a statewide election with a margin of error of 2.13 percentage points. How many voters should be sampled for a 99% confidence interval? Round up to the nearest whole number. Ex: 1234 voters Check Next 3 Allen Brexit poll: Six months on Brits stand by EU referendum decision, ONN, 19 December 2016,
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Poll and Sample Size Calculation
**Problem Statement:**
A poll reported **42%** support for a statewide election with a margin of error of **2.13** percentage points.
**Question:**
How many voters should be sampled for a **99% confidence interval**? Round up to the nearest whole number.
**Input Field:**
\[ \text{Ex: 1234 voters} \]
**Buttons:**
1. Check
2. Next
**Steps to Calculate Sample Size:**
1. Identify the reported support percentage (proportion).
2. Determine the margin of error.
3. Utilize the z-value for the desired confidence level (e.g., 2.576 for 99% confidence).
4. Apply the sample size formula for proportions.
**Formula:**
\[ n = \left( \frac{Z^2 \cdot p \cdot (1-p)}{E^2} \right) \]
Where:
- \( n \) is the sample size
- \( Z \) is the z-value (2.576 for 99% confidence)
- \( p \) is the proportion (0.42 in this case)
- \( E \) is the margin of error (0.0213 in this case)
This exercise helps understand the process of determining sample sizes for surveys or polls to ensure a defined confidence level and margin of error.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F061c5e53-6155-4c0d-9250-b0bc13e2d85b%2F4f35cb9d-29b8-405d-9c96-f1385803243d%2F3rid95_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Poll and Sample Size Calculation
**Problem Statement:**
A poll reported **42%** support for a statewide election with a margin of error of **2.13** percentage points.
**Question:**
How many voters should be sampled for a **99% confidence interval**? Round up to the nearest whole number.
**Input Field:**
\[ \text{Ex: 1234 voters} \]
**Buttons:**
1. Check
2. Next
**Steps to Calculate Sample Size:**
1. Identify the reported support percentage (proportion).
2. Determine the margin of error.
3. Utilize the z-value for the desired confidence level (e.g., 2.576 for 99% confidence).
4. Apply the sample size formula for proportions.
**Formula:**
\[ n = \left( \frac{Z^2 \cdot p \cdot (1-p)}{E^2} \right) \]
Where:
- \( n \) is the sample size
- \( Z \) is the z-value (2.576 for 99% confidence)
- \( p \) is the proportion (0.42 in this case)
- \( E \) is the margin of error (0.0213 in this case)
This exercise helps understand the process of determining sample sizes for surveys or polls to ensure a defined confidence level and margin of error.
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