It is well known that there exist infinitely many (non homeomorphic) non-Haken closed hyperbolic 3-manifolds. These can be obtained for example doing Dehn surgery on the figure eight knot complement. However, these manifolds may contain embedded nonorientable closed surfaces.

So, my question is:

Are there infinitely many (non homeomorphic) non-Haken closed hyperbolic 3-manifolds, which does not contain embedded nonorientable closed surfaces?