Question: 9. Let X; j (j= 1, .. . ,mj ) and Y;k (k= 1,. .. ,n;) be independently normally distributed with common variance a2 and

9. Let X; j (j= 1, .. . ,mj ) and Y;k (k= 1,. .. ,n;) be independently normally distributed with common variance a2 and means E(X;j) = and E(Y;) = t + !!.. . Then the UMP invariant test of H :!!.. = 0 is given by (110) with 8 = !!.., 80 = 0 and m ; n; L X;j + E (Y;k - 8) ,;_1 k -l N; t=-- m ·n L -'-'(Y;.- X; .) ; N; 8= -- m .n . E-'-' ; N; where N; = m, + n..

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