1. What is a Confidence Interval?

A confidence interval is a range of values that is likely to contain a population parameter with a certain level of confidence. It provides an estimate of the uncertainty around a sample statistic.

2. How Does the Calculator Work?

The calculator uses the confidence interval formula:

Where:

• \( \bar{X} \) — Sample mean
• \( z \) — z-score corresponding to the desired confidence level
• \( SE \) — Standard error of the mean

Explanation: The formula calculates a range around the sample mean that likely contains the true population mean.

3. Importance of Confidence Intervals

Details: Confidence intervals provide more information than point estimates alone, indicating the precision of an estimate and the uncertainty associated with it.

4. Using the Calculator

Tips: Enter the sample mean, z-score corresponding to your desired confidence level (e.g., 1.96 for 95% CI), and the standard error of the mean.

5. Frequently Asked Questions (FAQ)

Q1: What are common z-values for confidence intervals?
A: Common values are 1.645 for 90% CI, 1.96 for 95% CI, and 2.576 for 99% CI.

Q2: How is standard error calculated?
A: Standard error = standard deviation / √(sample size). It measures the variability of the sample mean.

Q3: What does a 95% confidence interval mean?
A: It means that if we repeated the study many times, 95% of the calculated confidence intervals would contain the true population parameter.

Q4: When should I use a t-score instead of a z-score?
A: Use a t-score when the population standard deviation is unknown and the sample size is small (typically n < 30).

Q5: Can confidence intervals be used for hypothesis testing?
A: Yes, if a confidence interval does not contain the null hypothesis value, you can reject the null hypothesis at the corresponding significance level.