19 m Let the observations from treatment 1 be denoted X₁, X2,..., X, and the observations from treatment 2 be denoted Y₁, Y2,..., Y. Let the sample means and the sample standard devia- tions of the X's and Y's be denoted as X, Y, Sx, and Sy, respectively. The two-sample t- statistic is defined as where t= X-Y Sp√1/m+1/n (m-1)S+(n-1)S Sp = m+n-2 t Express & in terms of T₁ =ΣX,, T=ΣY, +ΣY, and T. =Σx? +ΣY?. Since T and T are fixed for any permutation of the data, then is a function of T₁. Show that t is a monotone function of T₁, and hence conclude that permutation tests based on 7, and t are equivalent.