Let constants c1 and c2 satisfy Pr(X2, (n0)≤c1)=Pr(X2(n0)≥c2)=α/2 and c1<c2, where X2(n0) is distributed as a chi-square distribution with degrees of freedom n0. In this paper we give a proof of the inequality n0 log (c2/c1)/(c2-c1)>1. This inequality is related with the condition for improving on an equal-tails confidence interval of normal variance.
