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:

• \( \bar{x} \) — Sample mean
• \( s \) — Sample standard deviation
• \( n \) — Sample size
• 1.96 — Z-score for 95% confidence level

Explanation: The formula calculates the margin of error using the standard error of the mean and then creates an interval around the sample mean.

3. Importance Of Confidence Intervals

Details: Confidence intervals provide more information than point estimates alone. They indicate the precision of an estimate and the uncertainty around it, which is crucial for making informed decisions in research and data analysis.

4. Using The Calculator

Tips: Enter the sample mean, sample standard deviation, and sample size. All values must be valid (n > 0, standard deviation ≥ 0). The calculator assumes a normal distribution or a sufficiently large sample size (n ≥ 30).

5. Frequently Asked Questions (FAQ)

Q1: Why use 1.96 in the formula?
A: 1.96 is the z-score that corresponds to the 95% confidence level in a standard normal distribution.

Q2: When should I use a t-score instead of a z-score?
A: Use a t-score when the sample size is small (n < 30) and 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 interval indicates more precise estimates, typically resulting from larger sample sizes or smaller variability in the data.

Q4: Can I calculate confidence intervals for other confidence levels?
A: Yes, by replacing 1.96 with the appropriate z-score (e.g., 1.645 for 90% CI, 2.576 for 99% CI).

Q5: What are the assumptions for this calculation?
A: The calculation assumes that the sample is random, observations are independent, and the sampling distribution of the mean is approximately normal.