  We present the results of two tests where a sample of human participants were
asked to make judgements about the conceptual combinations {\it The Animal
Acts} and {\it The Animal eats the Food}. Both tests significantly violate the
Clauser-Horne-Shimony-Holt version of Bell inequalities (`CHSH inequality'),
thus exhibiting manifestly non-classical behaviour due to the meaning
connection between the individual concepts that are combined. We then apply a
quantum-theoretic framework which we developed for any Bell-type situation and
represent empirical data in complex Hilbert space. We show that the observed
violations of the CHSH inequality can be explained as a consequence of a strong
form of `quantum entanglement' between the component conceptual entities in
which both the state and measurements are entangled. We finally observe that a
quantum model in Hilbert space can be elaborated in these Bell-type situations
even when the CHSH violation exceeds the known `Cirel'son bound', in contrast
to a widespread belief. These findings confirm and strengthen the results we
recently obtained in a variety of cognitive tests and document and image
retrieval operations on the same conceptual combinations.
