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STAT 409
Examples for 10/14/2009
Fall 2009
Matched Pair Comparison:
Pair
Difference
1
X
1
Y
1
D
1
= X
1
– Y
1
2
X
2
Y
2
D
2
= X
2
– Y
2
•
•
•
•
•
•
•
•
•
•
•
•
n
X
n
Y
n
D
n
= X
n
– Y
n
Assume that the differences
D
i
= X
i
– Y
i
are a random sample from normal distribution with
mean
δ
and standard deviation
σ
D
.
To test the hypothesis
H
0
:
δ
=
δ
0
,
use the test statistic
n
s
t
D
0
D
δ

=
.
n
– 1 degrees
of freedom
1.
Dr. Statman claims that his new revolutionary dietandexercise plan allows participants
to lose, on average, one pound per day (i.e., 7 pounds per week).
Eight participants were
weighed in the beginning of the program, and then again a week later.
The results were
as follows:
Participant
1
2
3
4
5
6
7
8
Weight Before
213
222
232
201
230
188
218
182
Weight After
207
220
224
198
219
183
220
175
Pounds Lost
6
2
8
3
11
5
–
2
7
Recall that
D = 5 pounds, and
s
D
= 4 pounds.
Is there enough evidence to conclude that
the average weight loss is less that 7 pounds per week?
(Use
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This note was uploaded on 10/12/2011 for the course STATISTICS stat 410 taught by Professor Stepanov during the Spring '11 term at University of Illinois, Urbana Champaign.
 Spring '11
 Stepanov
 Normal Distribution

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