Let X = ( X 1 , X n ) be a random sample from N( 1 , 2 ) and let Y = ( Y 1 , Y m ) be a random…
Let X = (X1, Xn) be a random sample from N(1, 2) and let Y =
(Y1, Ym) be a random sample from N(2, 2). Suppose that we
to test H0: 1 = 2 versus Ha: 1 _= 2.
(a) Show that the likelihood function _(X,Y) is a monotone
function of T 2,
where T is the two-sample t-statistic that
uses the pooled estimator S2
p of the common variance 2.
(b) Let S2 1 be the sample variance for the Xi ’s. Let W =(¯Y –X − 0)/S1,
where_0 is a constant. Find a constant K such that KWhas the noncentral
t-distribution. Give the degrees of freedom and
noncentrality parameter _.