(a) Consider testing the hypotheses
H_(0):\lambda =0 versus
H_(1):\lambda =1 at the 0.05 level of significance using
Y=-lnx as the test statistic.
Given:
P(Y<=y)={(0 if y<=0,),(1-e^(-y(\lambda +2)) if 0<=y<\infty .):}
(i) Determine the critical value,
c, of the test that rejects
H_(0) if
y=-lnx<=c. What is the power of the test at
\lambda =1 ?
(3+4)