In this paper, we apply the theory of hypothesis testing to the steganalysis, or detection of hidden data, in the least significant bit (LSB) of a host image. The hiding rate (if data is hidden) and host probability mass function (PMF) are unknown. Our main results are as follows. (a) Two types of tests are derived: a universal (over choices of host PMF) method that has certain asymptotic optimality properties, and methods that are based on knowledge or estimation of the host PMF, and hence an appropriate likelihood ratio (LR). (b) For known host PMF, it is shown that the composite hypothesis testing problem corresponding to an unknown hiding rate reduces to a worst-case simple hypothesis testing problem. (c) Using the results for known host PMF, practical tests based on estimation of the host PMF are obtained. These are shown to be superior to the state of the art in terms of receiver operating characteristics as well as self-calibration across different host images. Estimators for the hiding rate are also developed.