Statistics 403 Problem Set 11
Due in lab on Friday, December 10th
1. Suppose we are conducting a study to assess whether heavy drinking is associated with the development
of pancreatic cancer. We identify 50 pancreatic cancer cases from a medical center and determine which
among them are heavy drinkers. We also identify 50 agematched people without pancreatic cancer
and determine which among them are heavy drinkers. As a result, we obtain the following table
PC
Not PC
HD
19
9
Not HD
31
41
(a) What is the pvalue for the null hypothesis that there is no association between heavy drinking
and the occurance of pancreatic cancer?
Solution:
The log odds ratio is
log(19) + log(41)

log(9)

log(31)
≈
1
.
03
.
The standard error of this estimate is
p
1
/
19 + 1
/
41 + 1
/
9 + 1
/
31
≈
0
.
47
.
The standardized log odds ratio (Zscore) is 1
.
03
/
0
.
47
≈
2
.
2.
Thus the pvalue is
P
(

Z

>

Z
obs
) = 2
P
(
Z <

2
.
2)
≈
0
.
03
.
(b) Construct a 95% confidence interval for the population log odds ratio.
Solution:
The 95% CI is the estimate plus or minus two times its standard error, thus the
CI is
(1
.
03

2
·
0
.
47
,
1
.
03 + 2
·
0
.
47) = (0
.
09
,
1
.
97)
.
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 Winter '12
 KerbyShedden
 Statistics, Null hypothesis, Statistical hypothesis testing, Pancreatic Cancer, 80%

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