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 for 95% confidence interval:

Where:

• Mean — The sample mean
• SD — Standard deviation of the sample
• n — Sample size
• 1.96 — The z-score for 95% confidence

Explanation: The formula calculates the margin of error (1.96 × standard error) and adds/subtracts it 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 the estimate and the likely range of the true population parameter.

4. Using the Calculator

Tips: Enter the sample mean, standard deviation, and sample size. All values must be valid (n > 0, SD ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: Why 95% confidence?
A: 95% is a commonly used confidence level that provides a good balance between precision and reliability in most research contexts.

Q2: What if my sample size is small (n < 30)?
A: For small samples, consider using a t-distribution instead of z-scores, especially when the population standard deviation is unknown.

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

Q4: Can I calculate CIs for other confidence levels?
A: Yes, by changing the multiplier (1.96). For 90% CI use 1.645, for 99% CI use 2.576.

Q5: What does it mean if my CI includes zero?
A: For difference measures, a CI including zero suggests the observed effect may not be statistically significant at the 5% level.