The oracle problem is addressed for random testing and testing of randomized software. The presented Statistical Oracle is a Heuristic Oracle using statistical methods, especially statistical tests. The Statistical Oracle is applicable in case there are explicit formulae for the mean, the distribution, and so on, of characteristics computable from the test result. However, the present paper only deals with the mean. As with the Heuristic Oracle, the decision of the Statistical Oracle is not always correct. An example from image analysis is shown, where the Statistical Oracle has successfully been applied.