A double sample test for a hypothesis concerning the mean μ of a normal random variable with unknown variance σ2is presented in this note. This test is an alternative to the usual single samplettest and is made by taking samples at two stages. After the first sample has been observed the hypothesis is rejected, accepted or a second sample is taken. This double sample test is a modification of a double sample test suggested by D. Owen. However, for the test being suggested here if the second sample is taken the information from the first sample is used in making the final decision.