Gültigkeitsintervalle

Gültigkeitsintervalle, also known as validity intervals or confidence intervals, are statistical measures used to estimate the range within which a population parameter is likely to fall. They are derived from sample data and provide a degree of uncertainty around the point estimate. For example, if a sample mean is used to estimate a population mean, the confidence interval gives a range of values that is likely to contain the true population mean.

The width of a confidence interval is influenced by the sample size, the variability of the data, and the desired level of confidence. A larger sample size or a lower level of confidence will result in a narrower interval, indicating greater precision. Conversely, a smaller sample size or a higher level of confidence will result in a wider interval, indicating greater uncertainty.

Confidence intervals are typically expressed as a range with a lower and upper bound, such as (a, b), where a and b are the limits of the interval. The level of confidence is often expressed as a percentage, such as 95% or 99%, indicating the probability that the interval contains the true population parameter.

In practice, confidence intervals are widely used in various fields, including science, engineering, and economics, to make inferences about population parameters based on sample data. They provide a more informative and nuanced understanding of the data compared to point estimates alone.