1. What is 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 quantifies the uncertainty around the sample mean estimate.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( mean \) — Sample mean (value)
• \( std \) — Sample standard deviation (value)
• \( n \) — Sample size (dimensionless)
• 1.96 — Z-score for 95% confidence

Explanation: The interval is centered around the sample mean, with the width determined by the standard deviation and sample size.

3. Importance of Confidence Interval

Details: Confidence intervals provide more information than point estimates alone, showing 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, std ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: Why 1.96 in the formula?
A: 1.96 is the z-score that captures 95% of the area under the normal distribution curve (2.5% in each tail).

Q2: When is this formula appropriate?
A: When the sample size is ≥30 or the population is normally distributed and σ is known.

Q3: What if my sample size is small?
A: For n < 30, use the t-distribution with n-1 degrees of freedom instead of the z-score (1.96).

Q4: How does sample size affect CI?
A: Larger sample sizes produce narrower confidence intervals, indicating more precise estimates.

Q5: Can CI be used for hypothesis testing?
A: Yes, if a 95% CI doesn't contain the null hypothesis value, you can reject the null at p < 0.05.