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 your sample mean estimate.

2. How Does the Calculator Work?

The calculator uses the standard formula for 95% CI:

Where:

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

Explanation: The interval is centered at the sample mean and extends equally in both directions based on the standard error (SD/√n) multiplied by the z-score for 95% confidence.

3. Importance of Confidence Intervals

Details: Confidence intervals provide more information than just a point estimate. They show the precision of your 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. The sample size must be ≥2. The standard deviation must be ≥0.

5. Frequently Asked Questions (FAQ)

Q1: Why 95% confidence?
A: 95% is a commonly used confidence level that provides a good balance between precision and reliability. Other levels (90%, 99%) can be used depending on the context.

Q2: What does 95% confidence mean?
A: If you repeated your study many times, 95% of the calculated confidence intervals would contain the true population mean.

Q3: When is this formula appropriate?
A: For normally distributed data or large samples (n > 30) due to the Central Limit Theorem. For small samples with non-normal distributions, consider t-distribution.

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

Q5: Can I use this for proportions?
A: For proportions, use a different formula that accounts for binomial distribution characteristics.