1. What Is A 95% Confidence Interval?

A 95% confidence interval 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 and uncertainty associated with a sample statistic.

2. How Does The Calculator Work?

The calculator uses the standard confidence interval formula:

Where:

• \( Mean \) — The sample mean
• \( SD \) — The sample standard deviation
• \( n \) — The sample size
• \( 1.96 \) — The z-score for 95% confidence level

Explanation: The formula calculates the range within which the true population mean is likely to fall, with 95% confidence, based on your sample data.

3. Importance Of Confidence Intervals

Details: Confidence intervals are crucial in statistical analysis as they provide a range of plausible values for population parameters, offering more information than a simple point estimate. They help researchers understand the precision of their estimates and the uncertainty inherent in sample data.

4. Using The Calculator

Tips: Enter the sample mean, standard deviation, and sample size. All values must be valid (n > 0, SD ≥ 0). The calculator will provide the 95% confidence interval for the population mean.

5. Frequently Asked Questions (FAQ)

Q1: Why use 1.96 in the formula?
A: 1.96 is the z-score that corresponds to 95% confidence level in a standard normal distribution. It represents the number of standard deviations from the mean that contain 95% of the data.

Q2: When should I use a t-score instead of a z-score?
A: Use a t-score when the sample size is small (typically n < 30) and/or when the population standard deviation is unknown. For larger samples, the z-score provides a good approximation.

Q3: What does a narrower confidence interval indicate?
A: A narrower confidence interval indicates more precise estimate of the population parameter, usually resulting from a larger sample size or smaller variability in the data.

Q4: Can confidence intervals be used for proportions?
A: Yes, but the formula differs slightly. For proportions, the standard error is calculated as √[p(1-p)/n], where p is the sample proportion.

Q5: What if my confidence interval includes zero?
A: If a confidence interval for a difference between means includes zero, it suggests that there may be no statistically significant difference between the groups at the 95% confidence level.