  Of existing entanglement witnesses that utilize only collective measurements
of a spin ensemble, not all can detect genuine multipartite entanglement (GME),
and none can detect Greenberger-Horne-Zeilinger (GHZ) states beyond the
tripartite case. We fill this gap by introducing an entanglement witness that
detects GME of spin ensembles, whose total spin is half-integer, using only
collective spin measurements. Our witness is based on a nonclassicality test
introduced by Tsirelson, and solely requires the measurement of total angular
momentum along different directions. States detected by our witness are close
to a family of GHZ-like states, which includes GHZ states of an odd number of
spin-half particles. We also study the robustness of our witness under
depolarizing noise, and derive exact noise bounds for detecting noisy GHZ
states.
