Intervallschätzung

Intervallschätzung, also known as confidence interval estimation, is a statistical method used to estimate an unknown population parameter based on a sample of data. Instead of providing a single point estimate, it offers a range of plausible values for the parameter. This range is called an interval.

The construction of an interval estimate involves a confidence level, typically expressed as a percentage (e.g., 95% or 99%). This confidence level quantifies the probability that the interval will contain the true population parameter if the sampling process were repeated many times. A 95% confidence interval means that if we were to take numerous samples and construct an interval for each, approximately 95% of these intervals would capture the true population parameter.

The width of the confidence interval is influenced by several factors. A larger sample size generally leads to a narrower interval, indicating a more precise estimate. A higher confidence level, conversely, results in a wider interval, as a broader range is needed to be more certain of capturing the true value. The variability within the sample data, often measured by the standard deviation, also plays a role; higher variability leads to wider intervals.

Confidence intervals are widely used in various fields, including medicine, social sciences, and engineering, to report the uncertainty associated with parameter estimates derived from sample data. They provide a more complete picture than point estimates alone by acknowledging and quantifying the inherent variability in statistical inference.