Homework 7 – STAT 543
Due Friday, March 9 by 5:00 pm (TA’s office);
you also may turn in the assignment in class on the same Friday
Distance students: Due Friday, March 16 by 5:00 pm (TA’s email)
1.
(a) Problem 8.13(a)-(c), Casella and Berger (2nd Edition)
(b) In place of Problem 8.13(d), consider the following test:
½
√
1
if X(1) > 1 − 0.05 or X(2) > 1
φ3 (X1 , X2 ) =
0
otherwise
where X(1) , X(2) are the min,max
Find the size of this test and the power function for θ > 0. Then, graph the power functions
of φ3 and φ2 to determine which test is more powerful. (It’s enough to graph over the range
θ ∈ [0, 1.2].)
2. Problem 8.14, Casella and Berger (2nd Edition)
3. Problem 8.15, Casella and Berger (2nd Edition)
1