On the Value of R=Gamma_h/Gamma_l at LEP

We show that the present experimental LEP average R=\Gamma_h/\Gamma_l= 20.795 +- 0.040 is not unambiguous due to the presence of substantial systematic effects which cannot be interpreted within gaussian statistics. We find by Montecarlo simulation that the C.L. of the original LEP sample is only 3.8 \cdot 10^{-4}. We suggest that a reliable extimate of the true R-value is 20.60< R < 20.98 which produces only a very poor determination of the strong coupling constant at the Z mass scale, 0.10< \alpha_s(M_z)< 0.15.