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
let Y denote the sample average from a random sample with mean μ
Which of the following statements is true for W1 and W2 ?
Both are biased estimators of 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.
let Y denote the sample average from a random sample with mean μ
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
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
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:
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:
What signs do you expect for β1 and β2 ?
Both should be positive.
β1 should be positive but β2 should be negative
β1 should be negative but β2 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:
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:
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:
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 interacting effect on log(aveincome)
An interacting 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 many 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 inventory will be postponed.
(一) 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%)
(二) What is the p-value of the data in (一)? (5%)
(三) 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%)
(四) If the true proportion is 0.05, what is the probability that the inventory will be
postponed? (6%)
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