1. What is a 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
• \( z \) — Z-score for desired confidence level
• \( SD \) — Standard deviation of the sample
• \( n \) — Sample size

Explanation: The formula calculates the margin of error (the term after the ±) which is then added and subtracted from the sample mean to create the interval.

3. Importance of Confidence Intervals

Details: Confidence intervals provide more information than point estimates alone. They indicate the precision of an estimate and help assess the clinical or practical significance of results.

4. Using the Calculator

Tips: Enter the sample mean, appropriate z-score for your desired confidence level (1.96 for 95% CI), standard deviation, and sample size. All values must be valid (n > 0).

5. Frequently Asked Questions (FAQ)

Q1: What z-score should I use?
A: Common z-scores are 1.645 (90% CI), 1.96 (95% CI), and 2.576 (99% CI). Choose based on your desired confidence level.

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

Q3: How does sample size affect the CI?
A: Larger samples produce narrower confidence intervals, indicating more precise estimates.

Q4: What's the difference between CI and margin of error?
A: The margin of error is half the width of the confidence interval (the part after the ±).

Q5: When should I use t-score instead of z-score?
A: Use t-scores when the population standard deviation is unknown and sample size is small (typically n < 30).