INFERENCE STATISTICS

Example 51 Suppose that the following random sample data was generated by the location model given by (3.17) where 61, 62, ..., 620 are iid with median 0. We consider the exact and asymptotic (although n = 20 is not large) sign tests for Ho : 0 = 0.618 versus H1 : 0 ) . 000001 . 000019 .000181 .001087 .004621 .014786 . 036964 . 073929 .120134 .160179 P(S 0.05. Hence we fail to reject Ho. . The asymptotic (large sample although n = 20 is not large) tests statistic is 2(s - n/2) 2(9 - 10) 2 = = -0.4472 > -1.645. Vn V20 Hence we again fail to reject Ho.QUESTION 4 [19] Consider the following random sample data which is assumed to have been generated by the location model given by Xi = 0 + ci (i = 1, 2, ..., 13) where 61, 62, ..., 613 are iid with median 0. -6.125 1.000 2.000 0.750 2.925 3.500 5.125 1.750 3.625 7.000 3.000 9.375 -7.500 Use: (a) the exact; and (b) the large sample sign tests to test the hypotheses Ho : 0 = 2 versus H1 : 0 > 2 at the 0.05 level of significance. Hint: See Example 51 in the Study Guide