In this paper, we propose a new class of two-sample U-statistics based on the mid-range for testing the location parameter. The asymptotic distribution of the test statistics is developed. The performance of test is evaluated, relative to existing tests, under a variety of situations.  For the test to have maximum efficiency, an optimality criterion is developed to choose the suitable sub-sample size. We describe a simulation study to find the power and estimated level of significance for various underlying distributions. The test is also illustrated with the help of a data example.

location parameter, sub-sample, mid-range, asymptotic distribution, simulation study.