1. What is Confidence Interval?

A confidence interval (CI) is a range of values that's likely to include a population parameter with a certain degree of confidence. It provides an estimated range of values which is likely to include an unknown population parameter.

2. How Does the Calculator Work?

The calculator uses the confidence interval formula:

Where:

• \( \bar{X} \) — Sample mean
• \( Z \) — Critical value from normal distribution (e.g., 1.96 for 95% CI)
• \( SD \) — Standard deviation
• \( n \) — Sample size

Explanation: The formula calculates the range around the sample mean that likely contains the true population mean, with the width depending on the desired confidence level and sample variability.

3. Importance of Confidence Interval

Details: Confidence intervals provide more information than point estimates alone by indicating the precision of an estimate and the uncertainty around it. They are essential for statistical inference and hypothesis testing.

4. Using the Calculator

Tips: Enter the sample mean, critical Z-value (1.96 for 95% CI, 2.576 for 99% CI), standard deviation, and sample size. All values must be valid (n > 0, SD ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What Z-value should I use?
A: Common values are 1.645 (90% CI), 1.96 (95% CI), and 2.576 (99% CI). These come from the standard normal distribution.

Q2: How does sample size affect the CI?
A: Larger sample sizes produce narrower confidence intervals, indicating more precise estimates.

Q3: What if my data isn't normally distributed?
A: For non-normal data with large samples (n > 30), the Central Limit Theorem applies. For small samples, consider non-parametric methods.

Q4: What's the difference between CI and margin of error?
A: Margin of error is half the width of the confidence interval.

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