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(Solved): 8.6-5. Let x_(1),x_(2),dots,x_(n) be a random sample from the normal distribution N(\mu ,36). (a) Sh ...
8.6-5. Let x_(1),x_(2),dots,x_(n) be a random sample from the
normal distribution N(\mu ,36).
(a) Show that a uniformly most powerful critical region
for testing H_(0):\mu =50 against H_(1):\mu <50 is given by
C_(2)={\bar{x} :\bar{x} <=c}.
(b) With this result and that of Example 8.6-4, argue that
a uniformly most powerful test for testing H_(0):\mu =50
against H_(1):\mu !=50 does not exist.