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's calculated from the sample mean and standard error.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The interval gives the range within which we expect the population mean to lie with 95% confidence.

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 and standard error. The standard error must be greater than 0. The calculator will output the 95% confidence interval.

5. Frequently Asked Questions (FAQ)

Q1: Why 1.96 for 95% confidence?
A: 1.96 is the z-score that captures 95% of the area under a normal distribution curve (±1.96 standard deviations from the mean).

Q2: What if my data isn't normally distributed?
A: For non-normal data with large samples (n > 30), the Central Limit Theorem makes this approximation reasonable. For small non-normal samples, consider bootstrap methods.

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

Q5: When should I use confidence intervals?
A: Always report CIs alongside point estimates to show the precision of your estimates and facilitate comparison between studies.