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 estimate.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The interval width depends on sample size and variability. Larger samples and lower variability produce narrower intervals.

3. Importance of Confidence Intervals

Details: CIs provide more information than point estimates alone, showing 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 calculator will output the 95% CI and margin of error.

5. Frequently Asked Questions (FAQ)

Q1: Why 95% confidence?
A: 95% is a conventional standard that balances precision with reliability. It means if you repeated the study 100 times, the CI would contain the true mean in ~95 cases.

Q2: 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.

Q3: What if my data isn't normally distributed?
A: For small non-normal samples, consider non-parametric methods or transformation. For proportions, use the binomial CI formula.

Q4: How does sample size affect the CI?
A: Larger samples produce narrower CIs (more precise estimates). The width decreases with the square root of n.

Q5: What's the difference between CI and standard deviation?
A: SD measures data variability, while CI quantifies uncertainty in the mean estimate. CI incorporates both SD and sample size.