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STA 3024 Summer A 2011
Exam 1 (Form Code X)
Name:
UFID:
This is
75
minutes exam. You have to answer
20
multiple choice questions. Each question
is worth
5
points that makes the whole exam worth
100
points. There is only
one
correct
answer for each question. You need to
bubble the correct answer
on the scantron to get
credit. Only scantron and
not this exam
will be graded. You have to turn in both exam
and scantron. You can use a calculator but you cannot use any supplemented materials
not included in this exam.
•
On
this paper
, write your
name and UFID
. You also need to
sign and date this exam
below
.
•
On your
scantron
, bubble your
name, UFID, and exam Form Code
(please see upper right
corner of this page for your form code.) You also need to bubble your
section number
which
is
1053
. There are no special codes.
•
A formula sheet and chisquared table are provided on the last page.
On my honor I have neither received or given or planning to give any aid on this exam as
well as disclose its contents to the ones who is going to take it after me.
Name:
DATE:
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Data collection.
Imagine we want to know the average price of ”regular” gas in Gainesville,
FL. You and your friend have driven around to collect some data. You have collected information
from few gas stations and your friend has collected information from few gas stations that are
different from yours. Unfortunately, you have recorded only the average of your gas stations so
has your friend. Neither you nor your friend remembers sample sizes, so the only things known
are two sample means and nothing else. The goal is to recover the overall mean of all gas
stations that were sampled by both of you. Can we just take the mean of our two sample means
to get the overall mean? Please select the best possible answer. (HINT: Think about two generic
means
¯
X
=
1
n
∑
n
i
=1
X
i
and
¯
Y
=
1
m
∑
m
j
=1
Y
j
that correspond to our samples with sizes
n
and
m
respectively. I am asking you about the behavior of
1
2
(
¯
X
+
¯
Y
)
. Try too see what happens in
each scenario listed below. If you are confused and you cannot see the result analytically using
the specified formula you can try to consider the example with the actual arbitrary numbers
you pick as an elements of two samples. That will hopefully help you to identify the result.)
(A) Yes, we can always use the mean of sample means and it will always be equal to the overall
mean for the combined sample.
(B) No we cannot recover the overall sample mean in this way. We need to know all the
observations to do this.
(C) We can recover the overall mean this way
only
if the sample sizes are the same.
(D) We can recover the overall mean this way
only
if the sample means are the same.
•
We can recover the overall mean if
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 Summer '08
 TA
 Statistics

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