  We report on a conceptually new test of the equivalence principle performed
by measuring the acceleration in Earth's gravity field of two isotopes of
strontium atoms, namely, the bosonic $^{88}$Sr isotope which has no spin vs the
fermionic $^{87}$Sr isotope which has a half-integer spin. The effect of
gravity upon the two atomic species has been probed by means of a precision
differential measurement of the Bloch frequency for the two atomic matter waves
in a vertical optical lattice. We obtain the values $\eta = (0.2\pm
1.6)\times10^{-7}$ for the E\"otv\"os parameter and
$k=(0.5\pm1.1)\times10^{-7}$ for the coupling between nuclear spin and gravity.
This is the first reported experimental test of the equivalence principle for
bosonic and fermionic particles and opens a new way to the search for the
predicted spin-gravity coupling effects.
