A multiple test of a mean parameter, λ, in the Poisson model is considered using the Bayes factor. Under noninformative improper priors, the intrinsic Bayes factor(IBF) or Berger and Pericchi(1996) and the fractional Bayes factor(FBF) of O`Hagan(1995) called as the default or automatic Bayes factors are used to select one among three models, M_1 : λ< λ_0, M_2 :λ= λ_0, M_3 : λ> λ_0. Posterior probability of each competitive model is computed using the default Bayes factors. Finally, theoretical results are applied to simulated data and real data.