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IOE 265 Fall 2007 2
nd
Exam (80 minute exam)
November 19, 2007
1.
This is a
closed book
exam. But
one page of double sided notes
is allowed.
2.
Calculators are allowed.
3.
Work all problems on this exam and staple together with your answer sheets.
4.
Sign the Honor Code below
after the exam.
I have neither given nor received any aid on this examination, nor have I
concealed any violation of the Honor Code
Name(print):
____________________________
Student ID:
____________________________
Signature, Date: ___________________________
===============================================================
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Part I. Multiple choice questions (3 points each, total 15 points)
(Please read all answers and select the most appropriate one as your answer.
The score is based on the letter you put in the answer space)
1.
A random sample of size n=9 is taken from a normal distribution with mean 15 and
variance 25.
What is the probability that the sample variance is greater than 5.16?
a.
>.995
b.
<.005
c.
.01
d.
.99
Answer: __________
2.
What is the probability, P(t), that t
v=10
 < 1.0?
a.
P(t)<0.2
b.
0.2<P(t)<0.5
c.
0.5<P(t)<0.8
d.
P(t)>0.8
Answer: __________
3.
The Bureau of Meteorology of the Australian Government provided the mean annual
rainfall (in millimeters) in Australia 1983–2002 as follows
499.2, 555.2, 398.8, 391.9, 453.4, 459.8, 483.7, 417.6, 469.2, 452.4, 499.3, 340.6,
522.8, 469.9, 527.2, 565.5, 584.1, 727.3, 558.6
If one wants to construct a 99% confidence interval for the mean annual rainfall, the
statistics needed is:
a.
t
0.025, 18
b.
Z
0.025
c.
t
0.05, 18
d.
Z
0.05
Answer: __________
4.
If the histogram of data is obtained as below, which Boxplot is most likely to be
drawn from the same dataset?
4
3
2
1
0
1
2
20
15
10
5
0
Frequency
Histogram
Answer: __________
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a.
2
1
0
1
2
Boxplot
b.
4
3
2
1
0
1
2
3
Boxplot
c.
2
1
0
1
2
3
Boxplot
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d.
5.0
2.5
0.0
2.5
5.0
Boxplot
5.
If the normal probability plot is obtained below, what type of distribution does it
indicate?
a.
Lighttailed distribution
b.
Normal distribution
c.
A distribution with right skew
d.
Heavytailed distribution
Answer: __________
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Part II True/False Problems: please circle one correct answer
(3 points each, total 15 points)
1
.
Box plots can be used to simultaneously display several feature of a sample, such as
center, spread, departure from symmetry, and identification of outliers.
True
False
2
. If the Chisquared statistic is equal to the sum of the squares of
k
standard normal
random variables, then the statistic has
k1
degrees of freedom.
True
False
3
. Maximum likelihood estimators are usually preferred to the method of moments
because they are asymptotically normal and efficient.
True
False
4
. Assume that X is a distribution with mean
μ
and variance
σ
x
2
.
If we transform the data
as Y=X+5, then
σ
y
2
>
σ
x
2
.
True
False
5
. The sample standard deviation, s, is an unbiased measure of the population standard
deviation,
σ
.
True
False
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Part III Short Problems
(5 points for each answer, total 70 points)
Please write down the procedures.
You may get partial credit even if you
did not get the final correct solution. Box your answer.
1
. Suppose that X and Y are discrete random variables and have the following joint
distribution function:
X
1
2
3
Marginal of Y
1
0.3
0.15
2
0.15
0.05
3
0.05
0.05
0.1
Y
Marginal of X
0.3
a.
Complete the table above.
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This note was uploaded on 01/18/2009 for the course IOE 265 taught by Professor Jin during the Winter '07 term at University of Michigan.
 Winter '07
 Jin

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