We propose that the formation of beliefs be treated as statistical hypothesis tests, and we label such beliefs inferential expectations. If a belief is overturned through the build-up of evidence, agents are assumed to switch to the rational expectation. Rational expectations are shown to be a special (limiting) case of inferential expectations, with the test size ‘a’ becoming a metric for rationality. We present the results of an experiment that supports inferential expectations. When inferential expectations are built into a Dornbusch-style model of the exchange rate, regression tests of Uncovered Interest Parity and the rational expectations version of the term structure both display downward bias in the slope coefficient.