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 provides an estimate of the precision of your sample mean.

2. How Does the Calculator Work?

The calculator uses the standard formula:

Where:

• \( \text{mean} \) — Sample mean
• \( SE \) — Standard error of the mean
• 1.96 — Z-score for 95% confidence level

Explanation: The interval is constructed by adding and subtracting 1.96 standard errors from the sample mean. This creates a range that would contain the true population mean in 95% of samples.

3. Importance of Confidence Intervals

Details: Confidence intervals provide more information than p-values alone. They indicate both the size of the effect and the precision of the estimate, helping researchers assess clinical or practical significance.

4. Using the Calculator

Tips: Enter the sample mean and standard error. The standard error should be > 0. The calculator will output the lower and upper bounds of the 95% CI.

5. Frequently Asked Questions (FAQ)

Q1: Why 95% confidence?
A: 95% is a conventional standard that balances precision with reasonable certainty. Other confidence levels (90%, 99%) can be used depending on the context.

Q2: What if my data isn't normally distributed?
A: For non-normal data or small samples, consider using bootstrap methods or non-parametric alternatives.

Q3: How is standard error calculated?
A: Standard error is typically calculated as \( SE = \frac{SD}{\sqrt{n}} \), where SD is standard deviation and n is sample size.

Q4: What's the difference between CI and prediction interval?
A: A CI estimates where the population mean lies, while a prediction interval estimates where future observations will fall.

Q5: Can I use this for proportions?
A: For proportions, different methods (like Wilson score interval) may be more appropriate, especially with extreme proportions.