ABSTRACT
X¯ ln
( X¯ θ0
) + (1 − X¯ ) ln
( 1 − X¯ 1 − θ0
)]
that
Wˆ = [
(X¯ − θ0)√ X¯ (1 − X¯ )/n
]2 ,
and that
Sˆ = [
(X¯ − θ0)√ θ0(1 − θ0)/n
]2 .
As an example, let X1, X2, . . . , Xn constitute a random sample of size n from a N(μ, σ2) parent population. Consider testing the composite null hypothesis
H0 : μ = μ0, 0 < σ2 < +∞, versus the composite alternative hypothesis H1 : μ = μ0, 0 < σ2 < +∞. Note that this test is typically called a test of H0 : μ = μ0 versus H1 : μ = μ0.
