  We present a class of observables which are suitable for determining the
fidelity of a state to the multipartite Greenberger-Horne-Zeilinger (GHZ)
state. Given an expectation value of an observable belonging to the class, we
give a simple formula that gives a lower bound and an upper bound for the
fidelity. Applying the formula to the GHZ-state preparation experiment by Pan
{\it et al}. {[Nature (London) {\bf 403}, 515 (2000)]}, we show that the
observed state lies outside of the class of biseparable mixed three-qubit
states. We also show that for this class of operators, adopting the principle
of minimum variance {[Phys. Rev. A {\bf 60}, 4338 (1999)]} in the state
estimation always results in the state with the minimum fidelity.
