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11. Likehood Ratio and Other Tests  517

                           Now, we combine (11.3.5)-(11.3.6) to express the likelihood ratio as






                           with  from (11.3.4) and reject H  if and only if ? is small. Thus, we decide as
                                                       0
                           follows:



                           where k(> 0) is a generic constant. Again, let us utilize (11.2.4) and write






                           which implies that





                           In other words, the “small” values of
                              will correspond to the “large” values of

                                Thus, we can rewrite the test (11.3.8) as follows:





                           where k(> 0) is an appropriate number.















                                    Figure 11.3.1. Two-Sided Student’s t  Rejection Region
                                                                   v
                                       Where the Degree of Freedom Is v = n  + n  - 2
                                                                        1   2
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