9.2.16. Let X1, X2, ..., Xn and Y1, Y2,..., Ym be indepen dent random samples drawn from normal distributions with means ux and my, respectively, and with the same known variance o'. Use the generalized likelihood ratio criterion to derive a test procedure for choosing between Ho: ux = My and Hi: ux * MY.Ho = MX = MY LUX;M, 6) = (8() e 20, (X -M) HI : MX # My L (Y ) M, 6 ) = (0/ ) e- 25- #, (xi-M L = L ( X , M , 6 ) x L ( X ; M , 6 ) -(1276) 25- (E (xi- NX) + (y;-1x) ) MX = X+ 9 HE( Xi - ( X4 7 ) ) + mi ( Yi - ( x + F )) L ( H. )= T mth 2 m th FILE (Xi- (X +P))' + (Y-(x + F)) ) e L U41 ) = men - math e ath L ( H . ) (Xi - IX + 8))+, = (X- (8 + F1 )') P = (X = K. ) $ ( x ,y ) = $ 1 * + F > K. r , x + Y = K , otherwise EH. ( $ (x ) ) = a Critical region : 1 X P ( x + Y Z k, ) = d W= {Xty = (UX+ MY ) + (#+in la))) P ( X + F - (MAX+MY) > K, - (HX+MY) ) = ad JAtm where $" ( a ) is tabulated value of 2- score P(2 2 KI- ( MX+ My) = d K - (xthy) = $"(d ) In + m K , = (uxt My ) + JT + m x Q (xx1 )