Confidence interval

A range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter. Because of their random nature, it is unlikely that two samples from a given population will yield identical confidence intervals. But if you repeated your sample many times, a certain percentage of the resulting confidence intervals would contain the unknown population parameter. The percentage of these confidence intervals that contain the parameter is the confidence level of the interval.

For example, suppose you want to know the average amount of time it takes for an automobile assembly line to complete a vehicle. You take a sample of completed cars, record the time they spent on the assembly line, and use the 1-sample t procedure to obtain a 95% confidence interval for the mean amount of time all cars spend on the assembly line.  Because 95% of the confidence intervals constructed from all possible samples will contain the population parameter, you conclude that the mean amount of time all cars spend on the assembly line falls between your interval's endpoints, which are called confidence limits.

Creating confidence intervals is analogous to throwing nets over a target with an unknown, yet fixed, location. Consider the graphic below, which depicts confidence intervals generated from 20 samples from the same population. The black line represents the fixed value of the unknown population parameter; the blue confidence intervals contain the value of the population parameter; the red confidence interval does not.