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Sample Midterm
ECO 4000, Baruch College
Instructions: There is a total of 20 questions. Mark all your answers clearly on the
scantron. No points will be given for work on the scratch paper or the exam paper. Make
sure you answer all questions.
- The probability of an event A or B (Pr( A or B )) to occur equals
A) Pr( A ) × Pr( B ).
B) Pr( A ) + Pr( B ) if A and B are mutually exclusive.
C)
Pr
Pr
A
B
D) Pr( A ) + Pr( B ) even if A and B are not mutually exclusive.
- An estimator
ˆ Y
of the population value
Y
is more efficient when compared to another
estimator
Y
, if
A) E (
ˆ Y
) > E (
Y
B) it has a smaller variance.
C) its c.d.f. is flatter than that of the other estimator.
D) both estimators are unbiased, and var(
ˆ Y
) < var(
Y
- The expected value of a discrete random variable
A) is the outcome that is most likely to occur.
B) can be found by determining the 50% value in the c.d.f.
C) equals the population median.
D) is computed as a weighted average of the possible outcome of that random variable, where
the weights are the probabilities of that outcome.
- Let Y be a random variable. Then the standard deviation of Y equals
A)
2
) Y
E Y
.
B)
Y
E Y
.
C)
2
Y
E Y
.
D)
Y
E Y .
- The conditional distribution of Y given X = x , Pr( Y = y |X= x ), is
A)
Pr
Pr
Y y
X x
B)
1
Pr ,
l
i
i
X x Y y
C)
Pr ,
Pr
X x Y y
Y y
D)
Pr ,
Pr
X x Y y
X x
- Among all unbiased estimators that are weighted averages of Y 1
,..., Y
n
, is
A) the only consistent estimator of μ Y
B) the most efficient estimator of μ
Y
C) a number which, by definition, cannot have a variance.
D) the most unbiased estimator of μ
Y
- When the sample size n is large, the 90% confidence interval for is
A) ± 1.96 SE ( ).
B) ± 1.64 SE ( ).
C) ± 1.64σ Y
D) ± 1.96.
- To standardize a variable you
A) subtract its mean and divide by its standard deviation.
B) integrate the area below two points under the normal distribution.
C) add and subtract 1.96 times the standard deviation to the variable.
D) divide it by its standard deviation, as long as its mean is 1.
- Assume that Y is normally distributed N ( μ , σ
). Moving from the mean ( μ ) 2.58 standard
deviations to the left and 2.58 standard deviations to the right, then the area under the normal
p.d.f. is
A) 0.
B) 0.
C) 0.
D) 0.
A manufacturer claims that a certain brand of VCR player has an average life expectancy of 5
years and 6 months with a standard deviation of 1 year and 6 months. Assume that the life
expectancy is normally distributed.
- Based on the information above, when selecting one VCR player at random what is the
probability of its life expectancy being greater than seven years?
A) 0.
B) 0.
C) 0.
D) 0.
- Based on the information above, if a random sample of size 25 with an average of six years
and a standard deviation of two years was collected, what is the 95% confidence interval for
the average life?
A) (5.37, 6.83)
B) (5.27,6.73)
C) (5.17,6.83)
D) (5.32,6.68)
- When there are ∞ degrees of freedom, the t
∞
distribution
A) can no longer be calculated.
B) equals the standard normal distribution.
C) has a bell shape similar to that of the normal distribution, but with "fatter" tails.
D) equals the
2
X distribution.
Let X denote the grade in your econometrics course and Y the grade in your finance course.
Assume that you assign the following subjective probabilities for your final grade in your
econometrics course (the standard GPA scale of 4 = A to 0 = F applies).
Grade P(X) P(Y|X=C) P(X|Y=C)
A 0.20 0.1 0.
B 0.50 0.3 0.
C 0.20 0.2 0.
D 0.08 0.1 0.
F 0.02 0.3 0.
- Given the information above, suppose you obtained a C in finance, then what is the expected
grade in econometrics?
A) 2.
B) 1.
C) 2.
D) 2.
- Given the information above, suppose you obtained a C in econometrics, then what is the
expected grade in finance?
A) 1.
B) 2.
C) 2.
D) It cannot be computed
Suppose in a sample of 64 students the average grade in the statistics exam was 50, the standard
deviation was 16. After a couple of tutoring sessions, the instructor believes the students’ true
exam mean should be about 54. However he doubts that results, hence he wants to conduct a
statistical test to see if the true mean is different than 54:
- What is the correct H 0 and H A of the problem above?
A) H
0 : μ=54 , H A : μ<
B) H
0 : μ =54 , H A : μ≠
C) H
0
: μ≠54 , H A
: μ<
D) H
0 : μ≠54 , H A : μ>
- What is the result of the hypothesis test above at alpha=5%?
A) Do not Reject the Null
B) Reject the Null
C) Not enough information to answer this question
D) None of the above
