A Note on Optimal Intervals in Normal Populations

Abstract

In the setting of one and two normal populations, the shortest confidence interval (SCI) involving location parameters coincides with the classic equal-tails confidence interval (ETCI). However, for confidence intervals involving scale parameters, the ETCI fails to provide the SCI and results can differ notably. In order to obtain such SCIs, either constrained optimization problems or nonlinear systems of equations have to be solved. In this setting, two tables are provided to find the SCIs at 95% confidence, which can be then used in classrooms to compare the results with the ETCIs usually obtained by the students and provided by the statistical software.