  The Full Bayesian Significance Test (FBST) for precise hypotheses was
presented by Pereira and Stern [Entropy 1(4) (1999) 99-110] as a Bayesian
alternative instead of the traditional significance test using p-value. The
FBST is based on the evidence in favor of the null hypothesis (H). An important
practical issue for the implementation of the FBST is the determination of how
large the evidence must be in order to decide for its rejection. In the
Classical significance tests, it is known that p-value decreases as sample size
increases, so by setting a single significance level, it usually leads H
rejection. In the FBST procedure, the evidence in favor of H exhibits the same
behavior as the p-value when the sample size increases. This suggests that the
cut-off point to define the rejection of H in the FBST should be a sample size
function. In this work, the scenario of Linear Regression Models with known
variance under the Bayesian approach is considered, and a method to find a
cut-off value for the evidence in the FBST is presented by minimizing the
linear combination of the averaged type I and type II error probabilities for a
given sample size and also for a given dimension of the parametric space.
