What is a confidence interval and how is it used?

What is a confidence interval and how is it used?

A confidence interval is a range of values used to estimate the true value of a population parameter. It provides an interval estimate that is likely to contain the parameter with a certain level of confidence, often expressed as a percentage.

How do you calculate a confidence interval?

To calculate a confidence interval, you typically use the formula: CI = ar{x} ± Z * (σ/√n), where ar{x} is the sample mean, Z is the Z-score corresponding to your desired confidence level, σ is the standard deviation, and n is the sample size.

What does the confidence level represent?

The confidence level represents the probability that the confidence interval contains the true population parameter. For example, a 95% confidence level means that if you were to take 100 different samples and compute a confidence interval for each sample, about 95 of the intervals would contain the true parameter.

Can confidence intervals be used for proportions?

Yes, confidence intervals can also be calculated for proportions. The formula is slightly different, typically using the sample proportion and the standard error of the proportion.