Using the methods developed by Fewster and colleagues, we derive a quantum inequality for the free massive spin- 3 2 Rarita-Schwinger fields in four dimensional Minkowski spacetime. Our quantum inequality bound for the Rarita-Schwinger fields is weaker, by a factor of 2, than that for the spin- 1 2 Dirac fields. This fact along with other quantum inequalities obtained by various other authors for the fields of integer spin (bosonic fields) using similar methods lead us to conjecture that, in flat spacetime, separately for bosonic and fermionic fields, the quantum inequality bound gets weaker as the number of degrees of freedom of the field increases. A plausible physical reason might be that the more field degrees of freedom, the more freedom one has to create negative energy, therefore the weaker the quantum inequality bound.