1. What is a 99% Confidence Interval?

A 99% confidence interval (CI) is a range of values that is likely to contain the true population parameter with 99% confidence. It is calculated from sample data and provides an estimate of the precision of a statistical measurement.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \bar{x} \) — Sample mean
• \( SE \) — Standard error of the mean
• 2.576 — Z-score for 99% confidence level

Explanation: The interval extends 2.576 standard errors on either side of the sample mean. This multiplier comes from the standard normal distribution and gives 99% coverage.

3. Importance of Confidence Intervals

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

4. Using the Calculator

Tips: Enter the sample mean and standard error. The standard error should be calculated as \( \sigma/\sqrt{n} \) where σ is the standard deviation and n is the sample size.

5. Frequently Asked Questions (FAQ)

Q1: Why use 2.576 for 99% CI?
A: This is the critical value from the standard normal distribution that leaves 0.5% in each tail (99% in the middle).

Q2: How does sample size affect the CI?
A: Larger samples produce narrower CIs (more precise estimates) because SE decreases with increasing n.

Q3: When is this formula appropriate?
A: For normally distributed data or large samples (n > 30) where the Central Limit Theorem applies.

Q4: What's the difference between 95% and 99% CI?
A: A 99% CI is wider (more conservative) than a 95% CI, reflecting greater confidence but less precision.

Q5: Can I use this for proportions?
A: For proportions, use \( \hat{p} \pm 2.576 \times \sqrt{\hat{p}(1-\hat{p})/n} \) where \( \hat{p} \) is the sample proportion.