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A double sample test for a hypothesis concerning the mean mu of a normal random variable with unknown variance sigma[sup 2] is presented in this note. This test is an alternative to the usual single sample t test 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. A table is included which is a tabulation of the rejection and acceptance points for various sample sizes and alpha = .05 and alpha = .01. Additional tables are included which give some power values and expected sample sizes for the new test and Owen's test. These power values are compared with power values of various single sample t tests. Conclusions about desirable sample sizes are presented for both the new test and Owen's test. [ABSTRACT FROM AUTHOR]

The problem of iterated tests of hypotheses has been treated from the standpoint of multiple decision theory. Under the assumption that there is a UMP test (not necessarily similar) for each component hypothesis, a procedure has been developed which ensures an upper bound for various probabilities of misclassification and which maximizes the probabilities of correct classification in some class. [ABSTRACT FROM AUTHOR]