1. What is a 99% Confidence Interval for Proportion?

A 99% confidence interval for a proportion provides a range of values within which we can be 99% confident that the true population proportion lies. It accounts for sampling variability in estimating proportions from sample data.

2. How Does the Calculator Work?

The calculator uses the normal approximation formula:

Where:

• \( p \) — Sample proportion (0 to 1)
• \( n \) — Sample size (≥1)
• 2.576 — Z-score for 99% confidence level

Explanation: The interval is centered at the sample proportion with a margin of error that depends on the sample size and variability of the proportion.

3. Importance of Confidence Intervals

Details: Confidence intervals provide more information than point estimates alone, indicating the precision of the estimate and the range of plausible values for the population parameter.

4. Using the Calculator

Tips: Enter the sample proportion (between 0 and 1) and sample size (≥1). For percentages, convert to proportion (e.g., 45% = 0.45).

5. Frequently Asked Questions (FAQ)

Q1: When is the normal approximation appropriate?
A: When both np and n(1-p) are ≥10. For small samples or extreme proportions, exact methods may be needed.

Q2: What does 99% confidence mean?
A: If we repeated the sampling many times, 99% of the calculated intervals would contain the true population proportion.

Q3: How does sample size affect the CI?
A: Larger samples produce narrower intervals (more precise estimates). The width is inversely proportional to √n.

Q4: What if my proportion is 0 or 1?
A: The formula breaks down at extremes. Consider Wilson score interval or exact binomial methods in these cases.

Q5: Why use 2.576 as the multiplier?
A: This is the z-score that captures 99% of the area under the standard normal curve (leaving 0.5% in each tail).