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11. Likehood Ratio and Other Tests  511

                           Observe that













                           On the other hand, one has











                           Now, we combine (11.2.4) and (11.2.10)-(11.2.11) to express the likelihood
                           ratio




                           Now, we reject H  if and only if ? is small. Thus, we decide as follows:
                                          0

                           where k(> 0) is a generic constant. That is, we reject H  if and only if
                                                                         0
                           when properly scaled becomes too large or too small. The implementable
                           form of the level α LR test would then look like this:















                           Figure 11.2.2. Two-Sided Student’s t  Rejection Region
                                                          n–1
   529   530   531   532   533   534   535   536   537   538   539