Consider two independent normal samples with equal variances, as in Exercise 8.41. Consider testing H0 - μx - μY ‰¤ - δ or μx - μY ‰¥ - δ versus H1: - δ (a) Show that the size a LRT of H+0 :μx - μY ‰¥ δ versus H+0 : μx - μY > -δ rejects H-0 if

(b) Find the size a LRT of H+0 : μx - μY ‰¥ δ versus H* : μX - μY (c) Explain how the tests in (a) and (b) can be combined into a level a test of H0 versus H1.
(d) Show that the test in (c) is a size a test.
This procedure is sometimes known as the two one-sided tests procedure and was derived by Schuirmann (1987) (see also Westlake 1981) for the problem of testing bioequivalence. See also the review article by Berger and Hsu (1996) and Exercise 9.33 for a confidence interval counterpart.

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2 ta+m-2,a