  Confidence intervals are assessed according to two criteria, namely expected
length and coverage probability. In an attempt to apply the decision-theoretic
method to finding a good confidence interval, a loss function that is a linear
combination of the interval length and the indicator function that the interval
includes the parameter of interest has been proposed. We consider the
particular case that the parameter of interest is the normal mean, when the
variance is unknown. Casella, Hwang and Robert, Statistica Sinica, 1993, have
shown that this loss function, combined with the standard noninformative prior,
leads to a generalized Bayes rule that is a confidence interval for this
parameter which has "paradoxical behaviour". We show that a simple modification
of this loss function, combined with the same prior, leads to a generalized
Bayes rule that is the usual confidence interval i.e. the "paradoxical
behaviour" is removed.
