Contents of similar 4 bottles of water are 8.8, 9.2, 8.5, and 9.0. Find the
median.
8.8
8.9
9.0
8.875
None of the above
Two lottery tickets are drawn from 10 for first and second prizes. The total
number of sample points is given by:
380
0.9
90
45
None of the above
From 5 economists and 3 physicists, the possible number of committees
that can be formed consisting of 3 economists and 2 physicists is given by:
10
20
30
60
None of the above
Consider that there are three machines which produce
the total amount of a product in a firm, and denote each machine as A, B, and
C. A produces 20% of the total amount in a firm, while B produces 30% and C
produces 50 of it. However, we know that 5%, 4% and 2% of the product
produced by A, B, and C, respectively, is the defective product. Suppose that
you randomly pick one from the total.
The probability of the defective product is:
0.012
0.12
0.1
0.032
None of the above.
Consider that there are three machines which produce
the total amount of a product in a firm, and denote each machine as A, B, and
C. A produces 20% of the total amount in a firm, while B produces 30% and C
produces 50 of it. However, we know that 5%, 4% and 2% of the product
produced by A, B, and C, respectively, is the defective product. Suppose that
you randomly pick one from the total.
The probability of the defective product produced by A is given by:
3/8
5/16
0.12
3/16
None of the above
Contents of similar 7 bottles of water are 10, 5, 7, 8, 9, 9, and 6. Find the
mode.
6
7
8
9
10
Suppose that people in Chicago consisted of 40 percent Republicans and 60
percent Democrats (not actual figures). If 10% of the Republicans and 70%
of the Democrats voted for an incumbent Senator “A”, what is the
probability that a person in Chicago who voted for the incumbent Senator
“A” was a Democrat?
0.91
0.42
0.46
0.28
None of the above
Which of the following statements is true for W1 and W2 ?
Both are biased estimators for μ for a small n .
W1 is a biased estimator of μ for a small n but W2 is an unbiased
estimator of μ for a small n .
Both are unbiased estimators of μ for a small n .
None of the above.
Which of the following statements is true for W1 and W2 ?
W1 is inconsistent but W2 is consistent.
W1 is inconsistent and W2 is also inconsistent.
W1 is consistent but W2 is inconsistent.
W1 is consistent and W2 is also consistent.
None of the above.
Suppose that X and Y have the following joint
probability function where X takes 2 or 4 while Y takes 1, 3, or 5:
The expected value of XY 2 is given by:
30.5
62.5
48.5
35.2
None of the above
Suppose that X and Y have the following joint
probability function where X takes 2 or 4 while Y takes 1, 3, or 5:
The mean of X is given by:
3
3.2
3.5
4.5
None of the above
V
W
Both, We cannot say either one is better.
Not enough information to conclude
consider a following relation between consumption and
income estimated by using OLS:
When you calculate the residuals, the sum should be:
Close to zero
Always positive
Always negative
Positive or negative
None of the above
consider a following relation between consumption and
income estimated by using OLS:
The MPC will be much larger than APC.
Both will be closer.
The APC will be larger than MPC.
None of the above
Let rent be the average monthly rent on an apartment in a
university town in Taiwan. Let pop be the total population in a city in Taiwan,
aveincome be the mean city income, and studentpop the number of students as
a percent of the total population in a city. One possible model to investigate a
relation among those variables is:
log(rent) = β 0 +β1 log(pop) +β 2 log(aveincome) + β 3(studentpop) +ε
Suppose that you would like to know whether the size of the student
relative to the population influence the monthly rent. What are the null
and alternative hypotheses?
H0 : β3 > 0 , H1 : β3 < 0
H0 : β3 = 0 , H1 : β3 > 0
H0 : β3 = 0 , H1 : β3> 0
H0 : β3 = 0 , H1 : β3 ≠ 0
None of the above
Let rent be the average monthly rent on an apartment in a
university town in Taiwan. Let pop be the total population in a city in Taiwan,
aveincome be the mean city income, and studentpop the number of students as
a percent of the total population in a city. One possible model to investigate a
relation among those variables is:
log(rent) = β 0 +β1 log(pop) +β 2 log(aveincome) + β 3(studentpop) +ε
What signs do you expect for β1 and β 2 ?
Both should be positive.
β1 should be positive but β 2 should be negative.
β1 should be negative but β 2 should be positive.
Both should be negative.
Let rent be the average monthly rent on an apartment in a
university town in Taiwan. Let pop be the total population in a city in Taiwan,
aveincome be the mean city income, and studentpop the number of students as
a percent of the total population in a city. One possible model to investigate a
relation among those variables is:
log(rent) = β 0 +β1 log(pop) +β 2 log(aveincome) + β 3(studentpop) +ε
The total population does not have any influence on the rent.
β1 is statistically different from zero.
The average income does have any influence on the rent.
β1 is statistically less than zero.
None of the above.
Let rent be the average monthly rent on an apartment in a
university town in Taiwan. Let pop be the total population in a city in Taiwan,
aveincome be the mean city income, and studentpop the number of students as
a percent of the total population in a city. One possible model to investigate a
relation among those variables is:
log(rent) = β 0 +β1 log(pop) +β 2 log(aveincome) + β 3(studentpop) +ε
A 10% increase in the average income is associated with about a 5.5%
increase in rent.
A 10% increase in the average income is associated with about a 55%
increase in rent.
A 10 increase in the average income is associated with about a 0.55%
increase in rent.
A 1% increase in the average income is associated with about a 5.5%
increase in rent.
None of the above
Let rent be the average monthly rent on an apartment in a
university town in Taiwan. Let pop be the total population in a city in Taiwan,
aveincome be the mean city income, and studentpop the number of students as
a percent of the total population in a city. One possible model to investigate a
relation among those variables is:
log(rent) = β 0 +β1 log(pop) +β 2 log(aveincome) + β 3(studentpop) +ε
A 50 point ceteris paribus increase in studentpop is predicted to
increase rent by 25%.
A 50 point ceteris paribus increase in studentpop is predicted to
increase rent by 0.25%.
A 25 point ceteris paribus increase in studentpop is predicted to
increase rent by 1.25%.
A 25 point ceteris paribus increase in studentpop is predicted to
increase rent by 0.125%.
None of the above.
now you estimated a new model as:
What effect does the term, studentpop, have?
An increasing effect on log(rent)
A diminishing effect on log(rent)
An increasing effect on log(aveincome)
An increasing effect on log(pop)
None of the above
now you estimated a new model as:
At what point does the marginal effect of studentpop on log(rent) become
negative?
0.041
48.24
0.00007
24.12
None of the above
A university library ordinarily has a complete shelf inventory done once
very year. Because of new shelving rules instituted the previous year, the
head librarian feels that it may be possible to save money by postponing
the inventory. The librarian decides to select at random 800 books from the
library’s collection and have them searched in a preliminary manner. If
evidence indicates strongly that the true proportion of misshelved or
unlocatable books is less than 0.02, then the inventor will be postponed.
a. Among the 800 books searched, 12 were misshelved or unlocatable.
Test the relevant hypothesis and advise the librarian what to do. Use
α = 0.05 . (8%)
b. What is the p-value of the data in (a)? (5%)
c. If the true proportion of misshelved and lost books is actually 0.01,
what is the probability that the inventory will be unnecessarily taken?
(6%)
d. If the true proportion is 0.05, what is the probability that the inventory
will be postponed? (6%)
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