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Midterm 1
STAT 5601
Fall 2010
This paper contains 40 points. Show the details of your calculations for
full credit.
Name:
SID:
Consider the following data:
7
,
10
,
6
,
6
,
3
,
10
,
19
.
1. Obtain the empirical distribution function (edf) based on the above
data. You may either present it as a probability mass function or cumu
lative distribution function in a table, or draw a plot of the cumulative
distribution function.
[10 points]
2. Find the vectors of rank and order statistics from the above data.
[5 points]
3. What is the median in this data?
[2 points]
1
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View Full Document 4. Find the
trimmed mean
(ˆ
μ
LTS
) from the above data that achieves 20%
breakdown value. Justify your answer in one or two sentences.
[8 points]
5. Assume that the above data is an
i.i.d.
sample from a continuous dis
tribution
F
which has
median
(
F
) =
θ
. We want to test the null
hypothesis
H
0
:
θ
= 5 against the alternative
H
1
:
θ
n
= 5. Obtain
the values of the signed rank test statistic and the sign test statistic
for the above test. [Hint: First subtract the value of
θ
under the null
hypothesis from each observation.] The formula for both test statistics
are given at the end of this exam paper.
[10 points]
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This note was uploaded on 02/24/2011 for the course STAT 5601 taught by Professor Staff during the Fall '06 term at Minnesota.
 Fall '06
 Staff
 Statistics

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