The use of random numbers is pervasive in today's world. Random numbers have practical applications in such far-flung arenas as computer simulations, cryptography, gambling, the legal system, statistical sampling, and even the war on terrorism. Evaluating the randomness of extremely large samples is a complex, intricate process. However, the randomness of small samples can be investigated in the classroom with a relatively simple technique. This article demonstrates the technique of combining the results of two tests--(1) the test of the mean; and (2) the test of the distribution--by investigating some samples. The author explores an application of the technique and an illustration of the technique's limitation. In conclusion, a combination of two tests--one comparing a sample mean with its population mean and another comparing the sample's distribution with that of its population--can help assess whether a sample is likely to be random. (Contains 5 tables.)