test statistic D n i1 (Ri i)2 . Then small values of D

Chapter 15, Problem 15.9

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test statistic D n i1 (Ri i)2 . Then small values of D give support to Ha (e.g., the smallest value is 0 for R1 1, R2 2, . . . , Rn n), so H0 should be rejected in favor of Ha if d c. When H0 is true, any sequence of ranks has probability 1/n!. Use this to find c for which the test has a level as close to .10 as possible in the case n 4. [Hint: List the 4! rank sequences, compute d for each one, and then obtain the null distribution of D. See the Lehmann book (in the chapter bibliography), p. 290, for more information.]

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