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Kata Bognar
kbognar@ucla.edu
Economics 41
Statistics for Economists
UCLA
Fall 2010
Midterm 1
 suggested solutions by Yujing Xu 
Part I  Multiple Choice Questions (3 points each)
1. In statistics, a population consists of:
C
(a) all people living in a city
(b) all students in a class
(c)
all subjects or objects whose characteristics are being studied
(d) a selection of a limited number of elements
Explanation:
See deﬁnition in the handout.
2. The temperatures (in Fahrenheit) observed during seven days of summer in Los Angeles are 78,
99, 67, 91, 99, 75, and 85. The mean temperature for the summers in Los Angeles is 85 with a
variance of 144. Then the zscore associated with 67 degree is:
A
(a)
1.5
(b) 1.5
(c) 0.125
(d) 0.125
Explanation:
Recall that the zscore for observation
x
i
is
z
i
=
x
i

μ
σ
where
μ
and
σ
are the mean
and the standard deviation of the distribution. Hence,
z
i
=
67

85
√
144
=

1
.
5
.
3. A box contains a few red and a few white marbles. After randomly drawing two marbles from
this box, you observe their color. Which of the following is an example of a simple event?
C
(a) At most one marble is red.
(b) At least one marble is white.
(c)
Both marbles are white.
(d) Not more than one marble is red.
Explanation:
The outcome space in this experiment is
{
RR,RW,WW
}
,
where ‘R’ refers to a
red and ‘W’ refers to a white marble. The events described in (a), (b) and (d) occur for multiple
outcomes while (c) occurs only if
WW
is drawn.
C
4. You select one person from a group of eight males and two females. The two events a male is
selected and a female is selected are:
C
(a) independent
(b) equally likely
(c)
exhaustive
(d) none of the above
Explanation:
The two events are exhaustive, a person selected is either a male or a female. The
two events are exclusive, it is not possible to select a male and a female at the same time, therefore
they are not independent. The probability that a male is selected is 8
/
10 while the probability
that a female is selected is 2
/
10
,
hence the events are not equally likely.
5.
8
P
3
is equal to
C
(a) 56
1
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View Full Document(b) 512
(c)
336
(d) none of the above
Explanation:
By the permutation rule
8
P
3
=
8!
5!
= 336
.
6. A company has received application from 10 candidates for a ﬁnancial analyst position. One
candidate stands out and the other 9 seem to be equally qualiﬁed. The manager has decided to
select four of the candidates for an interview. She contacts the outstanding candidate and selects
three others randomly. Then the number of total selections possible is
D
(a) 720
(b) 504
(c) 120
(d)
84
Explanation:
Since the outstanding candidate is selected for sure, the number of total selection
is equal to the number of ways in which the manager can select 3 out of 9 candidates. Here the
order does not matter, so you have to use the combination rule:
9
C
3
=
9!
6!3!
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 Fall '07
 Guggenberger
 Economics

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