ABSTRACT
From (7.13) and (7.14) the likelihood ratio test criterion for testing H0: µ= µ0 is given by
The right-hand side of (7.15) follows from Exercise 1.12. Since ? is a monotonically
decreasing function of the likelihood ratio test of H0; µ=µ0 when S is unknown rejects H0 whenever
where c is a constant depending on the level of significance a of the test. Note In connection with tests we shall use c as the generic notation for the
significance point of the test. From (6.60) the distribution of
is given by
where d2=N(µ-µ0)'S - 1 (µ-µ0). This is often called the distribution of T
2 with N-1
degrees of freedom. Under H0, µ=µ0, d 2=0, and (T2/(N-1))× ((N-p)/p) is distributed
as central F with parameter (p, N-p). Thus for any
