Confidence Interval
A confidence interval (CI) is a statistical tool used to estimate the range within which a population parameter, such as a mean or proportion, is likely to fall. It provides a measure of uncertainty around a sample statistic, allowing researchers to infer conclusions about a larger group based on a smaller sample.
The confidence interval is typically expressed as a range (e.g., 5 to 10) and is associated with a confidence level, commonly set at 95% or 99%. A 95% confidence interval means that if we were to take 100 different samples and compute a CI for each sample, approximately 95 of those intervals would contain the true population parameter.
To calculate a confidence interval for a population mean, you generally use the formula:
CI = x̄ ± z * (σ/√n)
- x̄ = sample mean
- z = z-score corresponding to the desired confidence level
- σ = standard deviation of the population
- n = sample size
When the population standard deviation is unknown, the t-distribution is often used instead of the z-distribution, especially with smaller sample sizes.
Confidence intervals are widely used in various fields, including medicine, social sciences, and economics, to convey the reliability and precision of statistical estimates. However, it’s important to note that a CI does not guarantee that the true parameter lies within the interval; it merely provides a degree of certainty based on the sample data.