How many voters should be sampled 95 % for a confidence interval? Round up to a whole number. A poll reported a approval rating  36% for a politician with a margin of error of  1 percentage point.

To determine the required sample size for a confidence interval, you can use the following formula for estimating proportions:

\[
n = \left( \frac{Z^2 \cdot p \cdot (1-p)}{E^2} \right)
\]

Where:
- \( Z \) is the Z-score for a 95% confidence level (which is 1.96),
- \( p \) is the estimated proportion of the population, which is 36% or 0.36,
- \( E \) is the margin of error, which is 1% or 0.01.

Let's calculate the sample size:

\[
n = \left( \frac{1.96^2 \cdot 0.36 \cdot (1-0.36)}{0.01^2} \right)
\]

I'll compute that for you.The required sample size for the poll to achieve a 95% confidence interval with a 1 percentage point margin of error is approximately **8,852** voters.

Would you like more details or have any further questions?

Here are 5 related questions to expand on this concept:
1. How does the margin of error affect the required sample size?
2. What is the significance of the 95% confidence level in polls?
3. How would the sample size change with a different margin of error?
4. Why is it necessary to round up the sample size in such calculations?
5. How does the estimated proportion (36% in this case) influence the sample size?

**Tip**: A larger sample size reduces the margin of error, increasing the accuracy of poll results.

How many voters should be sampled 95 % for a confidence interval? Round up to a whole number. A poll reported an approval rating of 36% for a politician with a margin of error of 1 percentage point.

Learn how to determine the sample size needed to estimate voter approval ratings with a 95% confidence interval and a 1% margin of error. This guide uses a 36% approval rating and walks through the statistical formula step-by-step. Suitable for college-level statistics students.

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