5.1.6 Confidence intervals and tests for the correlation coefficient

5.1.6 Confidence intervals and tests for the correlation coefficient

In statistics, it is called confidence interval to a pair or several pairs of numbers between which it is estimated that there will be a certain unknown value with a certain probability of success. Formally, these numbers determine a range, which is calculated from data from a sample, and the unknown value is a population parameter.

The probability of success in the estimation is represented by 1 - α and is called confidence level. In these circumstances, α is the so-called random error or level of significance, that is, a measure of the possibilities of failure in the estimation by such an interval.

Use the confidence interval to evaluate the estimation of the population parameter. For example, a manufacturer wants to know if the average length of the pencils he produces is different from the target length. The manufacturer takes a random sample of pencils and determines that the average length of the sample is 52 millimeters and the confidence interval of 95% is (50.54). Therefore, you can be 95% sure that the average length of all pencils is between 50 and 54 millimeters.