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STAT 428
Spring 2010
Homework #6
Apr 7
Homework 6
Due in class on Friday, Apr 16.
1.
(Diaconis and Sturmfels, 1985) The following table shows data gathered to test the hypothesis
of association between birthday and deathday. The table records the month of birth and death
for 82 descendants of Queen Victoria. A widely stated claim is that birthdaydeathday pairs are
associated. The table is available at:
http://www.stat.uiuc.edu/˜yuguo/stat428/labs/table.txt
Implement the exact test to test the null hypothesis that birthday and deathday are independent.
One way to deFne
p
value for exact test is
p
value =
s
T
∈
Ω
1
{
p
(
T
)
≤
p
(
T
0
)
}
p
(
T
)
.
where
T
0
is the observed table above, and Ω is the set of 12
×
12 contingency tables with the
same row sums and column sums as
T
0
. Here
p
(
T
) is deFned as
p
(
T
)
∝
1
p
12
i
=1
p
12
j
=1
t
ij
!
,
T
∈
Ω
,
where
t
ij
is the (
i, j
)th entry of the table. Estimate the
p
value and give the standard error of
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This note was uploaded on 10/24/2010 for the course STAT 428 taught by Professor Chen during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Chen

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