Mathematics · Nonparametric Tests

Let X1, X2, ..., X7 and Y1, Y2, ..., Y9 be two independent random samples from continuous distribution functions F(x - θ) and F(x - μ), respectively, where F, θ, and μ are unknown. Further, let θ be the unique median of F(x - θ) and μ be the unique median of F(x - μ). Let Ri be the rank of Yi in the combined sample for i = 1, 2, ..., 9. For testing H0: μ = θ against H1: μ > θ, the test statistic T = ∑i=19 Ri is proposed. Which of the following statements is true?