  The Cosmic X-ray Background (CXB) is the total emission from past accretion
activity onto supermassive black holes in active galactic nuclei (AGN) and
peaks in the hard X-ray band (30 keV). In this paper, we identify a significant
selection effect operating on the CXB and flux-limited AGN surveys, and outline
how they must depend heavily on the spin distribution of black holes. We show
that, due to the higher radiative efficiency of rapidly-spinning black holes,
they will be over-represented in the X-ray background, and therefore could be a
dominant contributor to the CXB. Using a simple bimodal spin distribution, we
demonstrate that only 15 per cent maximally-spinning AGN can produce 50 per
cent of the CXB. We also illustrate that invoking a small population of
maximally-spinning black holes in CXB synthesis models can reproduce the CXB
peak without requiring large numbers of Compton-thick AGN. The spin bias is
even more pronounced for flux-limited surveys: 7 per cent of sources with
maximally-spinning black holes can produce half of the source counts. The
detectability for maximum spin black holes can be further boosted in hard (>10
keV) X-rays by up to ~60 per cent due to pronounced ionised reflection,
reducing the percentage of maximally spinning black holes required to produce
half of the CXB or survey number counts further. A host of observations are
consistent with an over-representation of high-spin black holes. Future NuSTAR
and ASTRO-H hard X-ray surveys will provide the best constraints on the role of
spin within the AGN population.
