1. What is a 95% Confidence Interval?

A 95% confidence interval (CI) is a range of values that you can be 95% certain contains the true mean of the population. It quantifies the uncertainty around the sample mean estimate.

2. How Does the Calculator Work?

The calculator uses the standard formula for 95% CI:

Where:

• \( \bar{x} \) — Sample mean
• \( \sigma \) — Standard deviation
• \( n \) — Sample size
• 1.96 — Z-score for 95% confidence

Explanation: The interval is centered at the sample mean and extends 1.96 standard errors in each direction.

3. Importance of Confidence Intervals

Details: Confidence intervals provide more information than point estimates alone by showing the precision of the estimate and the likely range of the true population parameter.

4. Using the Calculator

Tips: Enter the sample mean, standard deviation, and sample size. The calculator will compute the 95% confidence interval. Larger sample sizes yield narrower intervals.

5. Frequently Asked Questions (FAQ)

Q1: Why 95% confidence?
A: 95% is a commonly used confidence level that balances precision with reasonable certainty. Other levels (90%, 99%) can be used by changing the z-score.

Q2: What if my data isn't normally distributed?
A: For non-normal data with large samples (n > 30), the Central Limit Theorem applies. For small non-normal samples, consider non-parametric methods.

Q3: How does sample size affect the CI?
A: Larger samples produce narrower confidence intervals, indicating more precise estimates of the population mean.

Q4: What's the difference between SD and SE?
A: Standard deviation (SD) measures data variability, while standard error (SE = SD/√n) measures precision of the mean estimate.

Q5: Can I use this for proportions?
A: For proportions, use the binomial proportion confidence interval formula instead.