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STATISTICS FOR SOCIAL & BEHAVIORAL SCIENCES
MID TERM 1 – September 30, 2014

This midterm is made of 5 problems on 9 numbered pages, for a total of
26 points.

You have 70 minutes (one hour and 10 minutes) to complete this quiz.

Write your name at the top of this sheet and on every page.

Circle the only right answer. There is one right answer exactly unless
indicated (first question of problem 3).

Non-communicating calculators are recommended (no 3g, wifi, LTE, 2g,
EDGE, even in airport mode). The calculator’s memory should not contain
the course’s statistical formulas.

Please perform this mid term 1 in silence.

If stuck on one question, move on ! There are easy and tough questions
on this midterm, so keep going!

This is a closed book midterm. Notes are not allowed.

If in doubt about a question, write on the answer sheet provided and move
on. The rule is that I will not provide clarifications during the exam.

This midterm should be enjoyable: good luck !
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Problem 1 – New York City Crime (4 points)
A researcher in Mayor Bloomberg’s data team (Paul) performs a linear
regression of neighborhood crime (y, in number of reported crimes) on
neighborhood median income (x, in thousands of dollars) only. He observes
crime yi and income xi for each neighborhood i.
Paul finds that the linear relationship is yi = 2000 – 30 xi + ei. He finds that the r
squared of the linear regression is 0.82 (or 82%).
Which of the following statements is true?
a. A increase in neighborhood median income by $1,000 is associated with a
reduction in crime of 30 crimes.
b. A increase in neighborhood median income by $1,000 is associated with a
reduction in crime of 30,000 crimes.
c. A increase in neighborhood median income by $1,000 is associated with a
increase in crime of 30,000 crimes.
d. A increase in neighborhood median income by $1,000 is associated with a
decrease in crime of 30,000 crimes.
Which of the following statements is true?
a. The predicted number of
of $40,000 is 80.
b. The predicted number of
of $40,000 is 800.
c. The predicted number of
of $40,000 is 8.
d. The predicted number of
of $40,000 is 2000.
crimes for a neighborhood with a median income
crimes for a neighborhood with a median income
crimes for a neighborhood with a median income
crimes for a neighborhood with a median income
Which of the following statements is true?
a. The correlation between neighborhood
income is 1.
b. The correlation between neighborhood
income is -1.
c. The correlation between neighborhood
income is positive or zero.
d. The correlation between neighborhood
income is negative (but not zero).
crime and neighborhood median
crime and neighborhood median
crime and neighborhood median
crime and neighborhood median
Which of the following statements is true?
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a. The Total Sum of Squares is equal to 82% of the Explained Sum of
Squares.
b. The Explained Sum of Squares is equal to 82% of the Total Sum of
Squares.
c. The Sum of Squared Errors is equal to 82% of the Total Sum of Squares.
d. The Total Sum of Squared Errors is equal to 82% of the Sum of Squared
Errors.
Problem 2 – Singapore Connection (5 points)
The Economic Development Board of Singapore (EDB) collected data on
individuals’ education level. It collected data for a sample of N=1,219 individuals,
and observes, for each individual, the number of years of education from age 6.
We note this variable xi, measured from 0 years of education (did not go to
school, for one individual in the sample) to the maximum of 26 years of education
for the most highly educated individual in the sample. The mean of x in the
sample is 16 years of education.
Which of the following statements is true?
a.
b.
c.
d.
e.
x is a categorical nominal variable.
x is a categorical ordinal variable.
x is a categorical continuous variable.
x is a quantitative nominal variable.
x is a quantitative discrete variable.
Which of the following statements is true?
a.
b.
c.
d.
the interquartile range of x is strictly higher than 26.
the interquartile range of x is equal to 26.
the interquartile range of x is lower or equal to 26.
none of the above.
The EDB then finds that the distribution is right-skewed. Which of the following
statements is true?
a. The standard deviation of x is higher than 2.
b. The median of x is strictly greater than 16.
c. The median of x is strictly lower than 16.
The population of Singapore is 5.4M inhabitants. The sample was drawn by
simple random sampling. Therefore, which of the following is true:
a. The sample does not suffer from response bias.
b. The sample does not suffer from nonresponse bias.
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c. The sample does not suffer from sampling bias.
d. The sample does not suffer from sampling error.
The mean of x in the sample is:
a.
b.
c.
d.
a parameter
a residual
a statistic
a sum of squares
Problem 3 – Friendships at NYU Prague (5 points)
Anton Dzerkovic, a professor of Sociology, spent 2 years at NYU Prague. He
collected data for a sample of 324 students willing to participate. For each
student i, Prof. Dzerkovic asked the student how many friends he had (x i). Prof.
Dzerkovic could not verify the answers’ accuracy. All students of the sample
answered.
From the information provided in this text, which biases affect Prof.
Dzerkovic’s study (tick all that apply, + 1 for each correct answer, -1 for each
wrong answer)?
◻︎ Nonresponse bias.
◻︎ Response bias.
◻︎ Sampling bias.
Students had an average (i.e. mean) number of friends of 12, with a standard
deviation of 4 (social life is intense at NYU Prague!). The distribution of the
number of friends is bell-shaped. Therefore, applying the empirical rule, which is
the right statement?
a.
b.
c.
d.
e.
f.
Almost no student had more than 16 friends.
Almost no student had more than 22 friends.
Almost no student had more than 21 friends.
Almost no student had more than 24 friends.
Almost no student had more than 20 friends.
Almost no student had more than 17 friends.
Also, which is the right statement?
a. 63% of students had between 8 and 16 friends.
b. 67% of students had between 8 and 16 friends.
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c. 68% of students had between 8 and 16 friends.
d. 59% of students had between 8 and 16 friends.
e. 95% of students had between 8 and 16 friends.
Prof. Dzerkovic also collected data on each student’s time spent studying y i. He
found that the correlation between the time spent studying per week (in hours)
and the number of friends is -0.7, and that the standard deviation of the number
of hours spent studying per week is 3h. Therefore, in the linear relationship
yi = a + b xi + ei, the value of the slope b is:
a.
b.
c.
d.
e.
f.
0.425
-0.425
0.881
-0.525
0.525
-0.881
Also, a one standard deviation increase in the number of friends is associated
with a …… standard deviation decline in the number of hours studied per week:
a.
b.
c.
d.
e.
0.525
0.881
0.7
0.425
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Problem 4 – Rats in Space (6 points)
Prof. Gandhi is based in Bangalore. He sent 7 rats in a satellite to Mars, and the
satellite sends data on the rats’ stress level in the satellite. Each rat i=1,2,3,4,…,7
has a stress level xi measured as 0,1,2,3,4. 4 is the highest level of stress.
Prof. Gandhi drew the following contingency table based on his data:
Stress level
0
1
2
3
4
Number of rats
0
2
3
1
1
The median stress level is:
a. 0
b. 0.5
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c.
d.
e.
f.
g.
h.
i.
j.
1
1.5
2
2.5
3
3.5
4
4.5
The mode is:
a.
b.
c.
d.
e.
f.
0
1
2
3
4
5
The variable xi is:
a. categorical nominal
b. quantitative continuous
c. quantitative discrete
The mean of xi is:
a.
b.
c.
d.
e.
f.
g.
0.777
0.987
0.811
1.875
2.143
3.101
4.129
The standard deviation of xi is:
a.
b.
c.
d.
e.
0.990
0.777
0.117
0.228
0.617
Please round to the closest number with 3 digits after the
decimal. E.g. for 0.1230, 0.1231, 0.1232, 0.1233, 0.1234 write 0.123. For 0.1235
and above, write 0.124.
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The variance of xi is:
a. 0.980
b. 0.999
c. 0.920
Use the rounded number of the previous question for your
calculation, and round the obtained variance in the same way.
Problem 5 – Age and weekly earnings (6 points)
Statisticians at the U.S. Census bureau collected data on a sample of 645
individuals with their weekly earnings in $ and their age in years.
They draw the following scatterplot and plot the regression line.
They find the following linear relationship:
yi = 276 + 7 xi + ei
The Total Sum of Squares was 74,213,916 and the Sum of Squared Errors was
68,948,223. Therefore, the R squared of the regression is:
a. 92.9%
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b. 7.1%
c. 0.5%
d. 86.3%
The standard deviation of age is 23.8 years. Given the information provided in
this exercise, the standard deviation of weekly earnings is:
a.
b.
c.
d.
5,817.98$
625.24$
90.11$
2,201.12$
In the scatterplot, consider the only observation that has an age above 80. For
this observation,
a. the residual is positive
b. the residual is negative
c. the residual is zero
The regression line is the line that:
a. makes sure there is an equal number of points above and below the
regression line.
b. Maximizes the absolute deviation between the observations yi and the
regression line.
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c. Minimizes the absolute deviation between the observations yi and the
predicted observations y with a hat.
d. Minimizes the sum of the squared residuals.
e. Minimizes the total sum of squares.
The standard deviation of the errors ei is:
a.
b.
c.
d.
623.590
771.190
326.950
901.180
Rounding rule as in problem 4. Use N as the denominator in the formulas, as
in class.
(Slightly more difficult question, attempt if time remains, and do not get bogged
down). If the researcher had regressed age on income instead of income on age,
the slope would have been:
a.
b.
c.
d.
-1
5
0.010
-,10
END OF MIDTERM
Thank you for your answers.
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DRAFT – WRITE HERE – ONLY ANSWERS ON THE MCQ FORM ITSELF
WILL BE CONSIDERED (FIRST 9 PAGES)
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DRAFT – WRITE HERE – ONLY ANSWERS ON THE MCQ FORM ITSELF
WILL BE CONSIDERED (FIRST 9 PAGES)
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DRAFT – WRITE HERE – ONLY ANSWERS ON THE MCQ FORM ITSELF
WILL BE CONSIDERED (FIRST 9 PAGES)
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