b. Since
1
mincfw_1, L(0 ) L( a ) , we have
maxcfw_1, L( a ) L(0 )
L(0 ) L(a ) k .
< k < 1 if and only if
c. The results are consistent with the NeymanPearson lemma.

Equivalently, this is
yi n ln 0
i1
a
n
1
1
ln k
a 0
1
c,
and c is chosen so that the test is of size (the chisquare distribution
can be used see Ex. 10.95).
b. Since the RR does not depend on a specific value of a < 0, it is a UMP
test.
10.105
2

a. The manager of the dairy is concerned with determining if there is a
difference in the two variances, so a twosided alternative should be used.
b. The salesman for company A would prefer Ha: 12 < 2 , since if this
2
hypothesis is accepted, the manager

The hypotheses are H0: 1 2 = 0 vs. Ha: 1 2 0.
a. The computed test statistic is, where s 2 10(52)2313(71) 62.74 , is given by
p
6469
= 1.57.
t
1 1
62.74
11 14
i. With 11 + 14 2 = 23 degrees of freedom, t.10 = 1.319 and
t.05 = 1.714. Thus, since we hav

f. This is because of part a.
g.-h. Answers vary.
10.18
H0: = 13.20, Ha: < 13.20. Using the large sample test for a mean, z =
2.53, and with = .01, z.01 = 2.326. So, H0 is rejected: there is evidence
that the company is paying substandard wages.
10.19
H0

MSPE PROGRAM
ECON 506 - FALL 2009
Solution to HW7
(The problem numbers refer to numbers in 7th edition)
Part B:
Use likelihood ratio test.
The observed test statistics is 2 ln (24/196) = 4.2
The sampling distribution is 2 with 1 degree of freedom. At for