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We purpose and analyze an off-line randomized sensor selection strategy for sequential hypothesis testing problem constrained with sensor measurement costs. Within the framework of Wald's approximation, the sequential probability ratio test (SPRT) with sensor selection is designed for minimizing the expected total measurement cost subject to reliability and sensor usage constraints. In the case of symmetric hypotheses, we introduce a quantity, called efficiency, of a sensor and show that it is critical to the sensor selection in SPRT. Furthermore, an algorithm with linear time complexity is proposed to obtain the optimal sensor selection probabilities.