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Stat120C
Homework 1 (due Thursday April 10, 2008)
Instructor: Zhaoxia Yu
TA: Vinh Nyugen
Note
: Where appropriate, all relevant software code and output should be also handed in.
Problem 1.
(11.10 of Rice) Verify that the twosample
t
test at level
α
of
H
0
:
μ
X
=
μ
Y
versus
H
A
:
μ
X
6
=
μ
Y
rejects if and only if the conﬁdence interval for
μ
X

μ
Y
does not contain zero.
Problem 2.
(11.14 of Rice) Suppose that
X
1
,
· · ·
,X
n
are i.i.d.
N
(
μ,σ
2
). To test the null hypothesis
H
0
:
μ
=
μ
0
, the ttest is often used:
t
=
¯
X

μ
0
s
¯
X
Under
H
0
,
t
follows a
t
distribution with
n

1 df. Show that the likelihood ratio test of this
H
0
is equivalent
to the
t
test.
Problem 3.
(11.36 of Rice) Lin, sutton, and Qurashi (1979) compared microbiological and hydroxylamine
methods for the analysis of ampicillin dosages. In one series of experiments, pairs of tablets were analyzed
by the two methods. The data in the following table give the percentages of claimed amount of ampicillin
found by the two methods in several pairs of tablets. What are
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 Spring '08
 Yu

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