ECO220 Quiz #1 (Jun. 4, 2009)
Page 1 of 8
Instructor: Prof. Murdock
Duration: 60 minutes
Format: 20 multiple-choice questions. Record answers on pink SCANTRON form. Correct
answers worth 5 points each and incorrect answers worth 0 points. 100 total possible points.
Allowed aids: A non-programmable calculator and attached aid sheets.
Instructions:
•
Answers must be properly recorded on the pink SCANTRON form to earn marks
•
Print your LAST NAME and INITIALS in the boxes AND darken each letter in the
corresponding bracket below each box; Sign your name in the SIGNATURE box
•
Print your 9 digit STUDENT NUMBER in the boxes AND darken each number in the
corresponding bracket below each box
•
Your FORM NUMBER is 01
•
Use only a pencil or blue or black ball point pen
o Pencil strongly recommended because it can be erased
•
Make dark solid marks that fill the bubble completely
•
Erase completely any marks you want to change
•
Crossing out a marked box is not acceptable and is incorrect
•
If more than one answer is selected then that question earns 0 points
ECO220 Quiz #1 (Jun. 4, 2009)
Page 2 of 8
(1) For a random sample of 50 grandfathers, a researcher records whether or not he is retired and
whether or not he is a widower. These are _________ data that contain _________ variables.
(A) panel; interval
(B) panel; nominal
(C) time series; nominal
(D) cross-sectional; interval
(E) cross-sectional; nominal
Density
► Questions (2) – (3): Consider the following graphical description of a variable X for random
sample. The sample is taken from a population that has a mean of -5.
n: 250, mean: -6.3, sd: 8.6
.05
.04
.03
.02
.01
0
-20
-10
0
10
X
(2) Sampling error explains why ___________.
(A) the sample mean is negative
(B) the shape is not perfectly bell-shaped
(C) the sample standard deviation is less than 10
(D) more than half of the data are negative numbers
(E) the sample mean is less than the population mean
(3) Approximately how many observations fall within the modal class?
(A) 7
(B) 13
(C) 26
(D) 38
(E) 76
ECO220 Quiz #1 (Jun. 4, 2009)
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(4) A sample has a sample mean of 10 and a sample standard deviation of 2. Which of the
following is NOT possible?
(A) 0 percent of observations lie between 8 and 12
(B) 80 percent of observations lie between 4 and 16
(C) 90 percent of observations lie between 6 and 14
(D) 99.7 percent of observations lie between 6 and 14
(E) 100 percent of observations lie between 8 and 12
► Questions (5) – (6): Consider this tabulation of an interval variable from a random sample.
x |
Freq.
Percent
Cum.
------------+----------------------------------0 |
9
7.32
7.32
1 |
14
11.38
18.70
2 |
11
8.94
27.64
3 |
13
10.57
38.21
4 |
12
9.76
47.97
5 |
6
4.88
52.85
6 |
11
8.94
61.79
7 |
12
9.76
71.54
8 |
16
13.01
84.55
9 |
13
10.57
95.12
10 |
6
4.88
100.00
------------+----------------------------------Total |
123
100.00
(5) What informal inference should you make about the shape of the distribution?
(A) it is tri-modal
(B) it is symmetric
(C) it is bell-shaped
(D) it is positively skewed
(E) it is negatively skewed
(6) What is the 95th percentile?
(A) 8
(B) 8.5
(C) 9
(D) 9.5
(E) 10
ECO220 Quiz #1 (Jun. 4, 2009)
Page 4 of 8
(7) You wish to describe the relationship between minutes spent studying and marks on a short
quiz. You know that there are significant decreasing marginal returns to studying. Which is the best
approach to describe this relationship?
(A) draw two histograms
(B) construct a scatter diagram
(C) construct a cross-tabulation
(D) use the least squares method
(E) calculate the coefficient of determination
(8) If the coefficient of correlation is -1 then which of the following is true?
Statement 1: The coefficient of determination is 1
Statement 2: There is no scatter in the scatter diagram
Statement 3: The least squares slope is a negative number
(A) Only 2
(B) Only 3
(C) Only 1 and 2
(D) Only 2 and 3
(E) All three: 1, 2 and 3
► Question (9): Consider the following graph of a random sample with 1000 observations.
X
0
2
4
6
8
10
(9) Which would NOT be a plausible inference about the population?
(A) it is positively skewed
(B) the mean is less than 2
(C) the median is less than 2
(D) the range is greater than 6
(E) the interquartile range is roughly 2
ECO220 Quiz #1 (Jun. 4, 2009)
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► Questions (10) – (11): Consider this STATA summary of a variable X in a random sample.
x
------------------------------------------------------------Percentiles
Smallest
1%
-11
-13
5%
-8
-13
10%
-7
-12
Obs
1092
25%
-5
-12
Sum of Wgt.
1092
50%
-2
75%
90%
95%
99%
1
3
4
7
Largest
9
9
9
10
Mean
Std. Dev.
-2.028388
3.964568
Variance
Skewness
Kurtosis
15.7178
.0458465
2.733145
(10) How many observations fall within 3 standard deviations of the mean?
(A) 1088
(B) 1089
(C) 1090
(D) 1091
(E) 1092
(11) Based on an analysis of this STATA summary, which of the following is true?
Statement 1: The 95th percentile is 4
Statement 2: There is negative skew
Statement 3: Sampling error cannot reasonably explain why the mean is smaller than the median
(A) Only 1
(B) Only 2
(C) Only 3
(D) Only 1 and 2
(E) Only 1 and 3
ECO220 Quiz #1 (Jun. 4, 2009)
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► Questions (12) – (13): Consider the following quotation taken from a 2008 report from Common
Core entitled STILL AT RISK: What Students Don’t Know, Even Now, by Frederick M. Hess
(http://www.commoncore.org/_docs/CCreport_stillatrisk.pdf).
METHODOLOGY. Twelve hundred questionnaires were completed in the first two
weeks of January 2008 using a targeted sample base of 32,000 records purchased
from Scientific Telephone Samples (STS), the premiere telephone sampling
organization in the United States. The targeted list was part of a nationwide
database of over 1.6 million 17-year-olds compiled by STS. Based on the sample
size, the sampling margin of error in this effort is plus or minus three percent.
…
Administering the test as a telephone survey rather than in school to a national
sample of students poses particular challenges of ensuring that the sample is
nationally representative. For instance, the introduction of call-screening, multiple
phone lines, and widespread use of mobile phones have altered the population
sampled randomly by [calling a sample of land-lines]. Moreover, as of 2005, three
percent of the population in the United States did not have a working telephone in
their household, and at least 12.8 percent of Americans had cell phones only.
(12) What is the response rate?
(A) less than 0.01
(B) 0.0200
(C) 0.0375
(D) 0.2000
(E) 0.3750
(13) Analyzing the information in the quotation you should conclude that which of the following
problems is likely?
Problem 1: Selection bias
Problem 2: Endogeneity bias
Problem 3: Non-response error
Problem 4: Increased sampling error because of cluster sampling
Problem 5: Non-representative results because of stratified sampling
(A) Only 3
(B) Only 1 and 3
(C) Only 3 and 5
(D) Only 1, 3 and 5
(E) Only 2, 3 and 4
ECO220 Quiz #1 (Jun. 4, 2009)
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(14) Which of the following can an ogive help you approximate?
Item 1: the 75th percentile
Item 2: the interquartile range
Item 3: whether the variance is large or small
(A) Only 1
(B) Only 3
(C) Only 1 and 2
(D) Only 2 and 3
(E) All three: 1, 2 and 3
► Question (15): Consider the following table of joint probabilities.
Industry
Number of
Employees
Construction
Manufacturing
Retail
Under 20
0.2307
0.0993
0.5009
20 – 99
0.0189
0.0347
0.0876
100 or more
0.0019
0.0147
0.0113
(15) If you know a firm is not in construction, what is the chance it has under 20 employees?
(A) 0.0827
(B) 0.6002
(C) 0.7514
(D) 0.7693
(E) 0.8019
(16) Consider two random variables X and Y. They have different variances and different means.
Which of these statements is true?
Statement 1: V[X – Y] = V[X + Y] if X and Y are not related
Statement 2: V[X – Y] > V[X + Y] if X and Y are positively correlated
Statement 3: V[X – Y] < V[X + Y] if X and Y are negatively correlated
(A) Only 1
(B) Only 3
(C) Only 1 and 2
(D) All three: 1, 2 and 3
(E) None of the three are true
ECO220 Quiz #1 (Jun. 4, 2009)
Page 8 of 8
(17) Consider the following joint probability table of two random variables that contain interval data.
What is the coefficient of correlation?
X
Y
0
1
0
0.25
0.25
1
0.25
0.25
(A) 0.00
(B) 0.20
(C) 0.25
(D) 0.50
(E) 1.00
► Questions (18) – (20): In an academic year at a very large university 10% of students take 3
courses, 30% take 4 courses, 40% take 5 courses, and 20% take 6 courses.
(18) What is the population standard deviation?
(A) 0.6 courses
(B) 0.7 courses
(C) 0.8 courses
(D) 0.9 courses
(E) 1.0 courses
(19) If in addition to a $250 flat registration fee the university charges $1,000 per course what is
the population mean revenue per student?
(A) $4,950
(B) $5,250
(C) $5,550
(D) $5,850
(E) $6,150
(20) If two students are randomly selected what is the chance that one is taking 4 or fewer courses
and one is taking 5 or more courses?
(A) 24%
(B) 25%
(C) 48%
(D) 50%
(E) 100%
Your form number is 01. Complete the FORM box at the top right of your pink SCANTRON form.
N
n
∑ xi
Population
Mean:
μ = i =1
N
N
Population
Variance:
Population s.d.:
X = i =1
n
n
∑ ( xi − μ )
∑ (xi − X )
2
σ = i =1
2
∑ xi
Sample
Mean:
N
σ = σ2
Population coefficient of variation:
CV =
2
Sample
Variance:
s = i =1
Sample s.d.:
s = s2
σ
μ
2
n −1
Sample coefficient of variation:
N
Population
covariance:
∑ ( xi − μ X )( yi − μY )
σ XY = i =1
Population coefficient
of correlation:
Sample coefficient of
correlation:
ρ=
r=
N
σ XY
σ XσY
s XY
s X sY
P( A | B) =
Multiplication
Rule:
Expected
Value:
s
X
Sample
covariance:
s XY
∑ (xi − X )( yi − Y )
s XY = i =1
n −1
n
n
⎡
⎤
x
y
∑
∑
i
i
⎥
1 ⎢n
i =1 i =1
x
y
=
−
⎥
⎢∑ i i
n − 1 ⎢i =1
n
⎥
⎣
⎦
Complement Rules:
P( A and B )
P( B)
P( AC ) = 1 − P ( A)
P( A and B ) = P ( A | B ) P ( B )
E[ X ] = μ = ∑ xp( x)
all x
Covariance:
cv =
n
Sample
covariance
(shortcut):
Conditional Probability:
2
⎛n x⎞
⎜∑ ⎟
1 n 2 ⎝ i =1 i ⎠
[ ∑ xi −
]
=
n − 1 i =1
n
Addition
Rule:
Variance:
P ( AC | B ) = 1 − P ( A | B )
P( A or B ) = P ( A) + P ( B ) − P ( A and B )
V [ X ] = E[( X − μ ) 2 ] = σ 2 = ∑ ( x − μ) 2 p ( x)
all x
E[( X − μ X )(Y − μY )] = σ XY = ∑ ∑ ( x − μ X )( y − μY ) p ( x, y )
all x all y
Laws of Expected Value:
Laws of Variance:
E[c] = c
E[X+c] = E[X] + c
E[cX] = cE[X]
E[a+bX+cY] = a + bE[X] + cE[Y]
V[c] = 0
COV[X, c] = 0
V[X+c] = V[X]
COV[a+bX, c+dY] = bdCOV[X,Y]
V[cX] = c2V[X]
V[a+bX+cY] = b2V[X] + c2V[Y] + 2bcCOV[X,Y]
Laws of Covariance: