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% confidence interval:

Where:

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

Explanation: The interval provides a range of plausible values for the population mean. The width of the interval depends on the sample size and variability.

3. Importance of Confidence Intervals

Details: Confidence intervals are more informative than simple point estimates because they provide both an estimate of the effect size and the precision of that estimate.

4. Using the Calculator

Tips: Enter the sample mean, standard deviation, and sample size. All values must be valid (n > 0, SD ≥ 0). The result will show the lower and upper bounds of the 95% CI.

5. Frequently Asked Questions (FAQ)

Q1: Why 95% confidence?
A: 95% is a conventional level that balances precision with reasonable certainty. Other common levels are 90% and 99%.

Q2: What does 95% confidence mean?
A: If we repeated the sampling many times, 95% of the calculated CIs would contain the true population mean.

Q3: When is this formula appropriate?
A: For normally distributed data with known standard deviation, or when sample size is large (n > 30) due to Central Limit Theorem.

Q4: What if my data isn't normally distributed?
A: For small non-normal samples, consider non-parametric methods or transformation of data.

Q5: How does sample size affect the CI?
A: Larger samples produce narrower CIs (more precise estimates), while smaller samples yield wider intervals.