  A microscopic confirmation of the fractional statistics of the {\em
quasiparticles} in the fractional quantum Hall effect has so far been lacking.
We calculate the statistics of the composite-fermion quasiparticles at
$\nu=1/3$ and $\nu=2/5$ by evaluating the Berry phase for a closed loop
encircling another composite-fermion quasiparticle. A careful consideration of
subtle perturbations in the trajectory due to the presence of an additional
quasiparticle is crucial for obtaining the correct value of the statistics. The
conditions for the applicability of the fractional statistics concept are
discussed.
