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To calculate the required sample size for this poll, we can use the formula for sample size in proportion estimation:

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

where:
- \( Z \) is the Z-score corresponding to the desired confidence level (for 99% confidence, \( Z = 2.576 \)),
- \( p \) is the estimated proportion of people supporting the candidate. If we don't have a prior estimate, we use \( p = 0.5 \) to maximize the sample size,
- \( E \) is the margin of error, which is 1% or \( 0.01 \) in this case.

**Step-by-Step Calculation:**

1. **Identify the Z-score:** For a 99% confidence level, \( Z = 2.576 \).
2. **Assume proportion (p):** We use \( p = 0.5 \) as no prior data is given.
3. **Set margin of error (E):** \( E = 0.01 \).

Plugging in these values:

\[
n = \frac{(2.576)^2 \cdot 0.5 \cdot (1 - 0.5)}{(0.01)^2}
\]

Calculating each component:

\[
n = \frac{6.635 \cdot 0.5 \cdot 0.5}{0.0001}
\]
\[
n = \frac{1.65875}{0.0001}
\]
\[
n \approx 16587.5
\]

Since the sample size must be a whole number, we round up:

\[
n = 16588
\]

### Answer:
The required sample size is **16,588 people**.

Would you like more details on each step or further explanation? 

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Here are five related questions that expand on this concept:
1. How would the required sample size change if the confidence level were 95% instead of 99%?
2. What would happen to the sample size if we had a prior estimate that \( p = 0.6 \)?
3. How does the margin of error influence the sample size requirement?
4. Why do we use \( p = 0.5 \) when there is no prior data?
5. How is the Z-score determined for different confidence levels?

**Tip:** When estimating proportions, using \( p = 0.5 \) provides the largest possible sample size, ensuring the estimate remains valid even in the worst case.

A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 1% margin of error at a 99% confidence level, what size of sample is needed? Give your answer in whole people.

Learn how to calculate the required sample size for a poll with a 99% confidence level and a 1% margin of error. This guide includes a step-by-step solution using statistical formulas for sample size determination, ideal for students in undergraduate statistics or AP statistics.

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