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 CI formula:

Where:

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

Explanation: The margin of error decreases with larger sample sizes and smaller standard deviations, resulting in narrower confidence intervals.

3. Importance of Confidence Intervals

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

4. Using the Calculator

Tips: Enter the sample mean, standard deviation, and sample size. All values must be valid (n ≥ 1, SD ≥ 0). The calculator assumes normally distributed data.

5. Frequently Asked Questions (FAQ)

Q1: Why use 1.96 for the z-score?
A: 1.96 corresponds to the 97.5th percentile of the standard normal distribution, capturing 95% of the data (2.5% in each tail).

Q2: What if my sample size is small (n < 30)?
A: For small samples, consider using the t-distribution (t-critical values) instead of z-scores, especially when population SD is unknown.

Q3: How to interpret a 95% CI?
A: If you repeated the study many times, 95% of the calculated CIs would contain the true population mean.

Q4: What affects the width of the CI?
A: Width increases with higher variability (SD) and decreases with larger sample sizes.

Q5: Can I use this for proportions?
A: For proportions, different formulas are needed (e.g., Wald, Wilson, or Clopper-Pearson intervals).