Abstract
The paper describes various criteria for the construction of confidence intervals based on the control of the error of overestimation or underestimation of a parameter and on the pre-determined precision of the parameter estimation. The respective constructions are illustrated by confidence intervals for the parameters of the normal distribution. Examples presented in the paper show the influence of some selected criteria on the formula of the appropriate confidence interval. The performed calculations show the dependence of the width of a given interval on the size of the sample, and vice versa – the size of the sample on the pre-determined width of this interval. The problem of selecting the sample size with a predetermined precision of the estimation was presented taking into account solutions that do not depend on the estimated values of the unknown parameter. The aim of the study is to show how the problem of confidence intervals construction can be presented more comprehensively in statistical education.
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