Skip to content
Q113Section C (Part C)113 of 120

Wilcoxon rank-sum statistic for sample sizes 7 and 9

Let (X1,X2,…,X7)(X_1,X_2,\dots,X_7) and (Y1,Y2,…,Y9)(Y_1,Y_2,\dots,Y_9) be two independent random samples from the continuous distribution functions F(x−μ)F(x-\mu) and F(x−θ)F(x-\theta), respectively, where FF, μ\mu and θ\theta are all unknown. Further, let μ\mu be the unique median of F(x−μ)F(x-\mu) and θ\theta be the unique median of F(x−θ)F(x-\theta). Let RiR_i be the rank of YiY_i in the combined sample, i=1,2,…,9i=1,2,\dots,9. For testing H0:μ=θH_0:\mu=\theta against H1:μ>θH_1:\mu>\theta, the test statistic T=∑i=19RiT=\sum_{i=1}^9R_i is proposed. Then, which of the following statements are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Options

Select every correct option, then submit.