Question: 11. Let Xl . . .. ' X, and YI. . . y be samples from Na. ( 2 ) and N(1j, ( 2 ).

11. Let Xl . . .. ' X", and YI•. . .• y" be samples from Na. ( 2 ) and N(1j, ( 2 ). The UMP unbiased test for testing 71 - = 0 can be obtained through Problems 5 and 6 by making an orthogonal transformation from (Xl •. . .• X"" YI, · · . •Y,,) to (ZI" '" Z", +,,) such that ZI = (Y-X)/V(1!m) + (lin). Z2 = (Lx, + EY,)I/m + n.

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