The one-sided one sample problem with bivariate data is considered. A conditionally distribution-free sign test is proposed for that problem. This test is related to Hodges test and can be seen as a union-intersection test. Moreover, it is valid under very mild assumptions and it can be easily implemented. An explicit formula for the exact null conditional distribution of the test statistic is derived. This conditional distribution can be used to compute exact conditional p-values. A simulation study compares the new test to some competitors including the likelihood ratio test. The results show that the new test is very competitive for a wide variety of distributional models.