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The Final Exam of Probability & Statistics (II)
Department of Information Management
Date: 22 June 2005
09:30~11:30
NOTICE!
 You can use the calculator for some complicated computations. However, the Notebook
computers, PDAs, and Smart phones will not be allowed.
 Answer the following questions in the closed-book context and honesty.
 Any evidence of cheating will result in a failing grade for the course.
1.
Twenty overweight individuals including ten women and ten men were randomly and equally assigned
to one of two diets. The left side of following table contains the after-10-week weight loss of diet
experiment. Please fill the right side ANOVA statistics. (2%×13) (a) Test the hypothesis of no
interaction effect between gender and diet. (3%) (b) Test the hypothesis of no gender effect on the
weight loss. (3%) (c) Test the hypothesis of no gender effect on the weight loss. (3%)
Degree of
Sources
SS
MS
F
Gender
Diet formula
freedom
A`
Men
Women
B
7.6
8.8
12.5
16.1
18.6
19.5
17.6
16.8
13.7
21.5
22.2
23.4
24.2
32.2
9.4
30.1
24.2
9.5
14.6
11.2
_
SSc
a
c
g
k
SSr
b
d
h
l
SSint
111.8645
e
i
m
SSe
706.172
f
j
SSt
935.3655
_
_
_
_
x... =17.685, x1.. =15.27, x 2.. =20.1, x.1. =17.5, x.2. =17.87
2.
An Experiment designed to study the relationship between hypertension and cigarette smoking yielded
the following data. Test the hypothesis that whether or not an individual has hypertension is
independent of how much that person smokes. (20%)
Nonsmoker Moderate smoker Heavy Smoker
Hypertension
20
38
28
No hypertension
50
27
18
3. An engineering firm wants to select one from two computer systems and submits eight designed
problems to these two systems in order to compare the performance. The following table contains the
processing time for the eight problems. Please determine the p-value of the sign test when testing the
hypothesis that there is no difference in the distribution of the time it takes the two types of computer
systems to solve problems. (20%)
Design problems
1
2
3
4
5
6
7
8
Time with Computer A
15
32
17
26
42
29
22
48
Time with Computer B
22
29
1
23
46
25
19
47
4. Please compare the two-way ANOVA test and the independence test of Contingency table. You can
address your argument from the perspective of data collection and dependent variable. (10%)
5. Please propose a nonparametric hypothesis testing method to test the symmetric property of
distribution. You have to describe the modeling processes of this approach in details. (10%)
6. The following signals represent the gold medal (M) and the failure record (F) of an athlete in the 20
games. If you want to adopt the Runs test to verify the effect of random luck, how many runs are there
in the 20 games? (5%)
M-F-M-M-F-M-F-M-M-M-F-M-F-M-M-F-M-F-M-M
Reference: F0.05,1,19= 4.381, F0.05,1,16= 4.494, F0.05,2,16=3.634,x20.05,1= 3.841459, x20.05,2= 5.991465,
x20.05,3= 7.814728
Name:
a
h
1.
2.
3
4
5
6
b
i
Student ID:
c
j
d
k
Final Exam of Probability & Statistics (II)
e
F
g
l
m