ST 708, Fall 2008 Homework 4, due 10/7/08
Chapter 4, pages 149-159
• # 1. Do part (d). You have already done parts (a) – (c) in the previous homework.
• # 3. Do parts (d), (e), and (f). You have already done parts (a) and (b) and started
part (d) in the previous homework. Make sure to use the correct answer from the
previous homework for the null hypothesis in part (d).
• # 6.
• # 10.
You should complete #1 and #3 by hand. For #6 and #10, you may use SAS, but be
sure to clearly describe where in the output you found the answers to each part.
Additional Problem:
1. Consider the model with three predictors plus an intercept, where the resulting
design matrix is full rank.
Each of the following sets of hypotheses can be written in the form 0:HK m
β
′
=
vs. :
a
HK m
β
′≠, with
(
)
rK k
′
=
. For each of them state K
′
, m, and k.
a. 01 2
:2H
β
β
= vs. 12
:2
a
H
β
β
≠
.
b. 01 2
:22H
β
β
== vs. 0
: Not
a
HH.
c. 0:H The mean response when 10X
=
, 21X
=
, and 30X= is 5 vs.
0
: Not
a
HH.
For each of the following, state the null hypothesis that you would be testing, and
what the full and reduced models would be. Also state K
′
, m, and k.
d.
()
01 23
,|,R
β
βββ
.
e.
()
123 0
,,|R
β
ββ β
.
f.
()
123
|,R
β
ββ
.
