Based on years of experience, an economics professor knows that on the first principles of economics exam of the semester 13% of students will receive an A, 22% will receive a B, 35% will receive a C, 20% will receive a D, and the remainder will earn an F. Assume a 4 point grading scale A = 4, B = 3, C = 2, D = 1, and F = 0. Define the random variable GRADE = 4, 3, 2, 1, 0 to be the grade of a randomly chosen student. What is the expected value of GRADE? A. 2.08 B. 10 C. 1
In each question, select ONE response from the provided alternative responses.
Based on years of experience, an economics professor knows that on
the first principles of economics exam of the semester 13% of students
will receive an A, 22% will receive a B, 35% will receive a C, 20%
will receive a D, and the remainder will earn an F. Assume a 4 point
grading scale A = 4, B = 3, C = 2, D = 1, and F = 0. Define the
random variable GRADE = 4, 3, 2, 1, 0 to be the grade of a randomly
chosen student. What is the
A. 2.08
B. 10
C. 1
32. Suppose Y = 3X + 2. Given that E (X) = 8 and V ar (X) = 4, what is
V ar (Y )?
A. 36
B. 26
C. 38
Compute the
given the joint
X
1 2
Y 0 0.70 0.00
1 0.00 0.30
A. 0.6
B. 1
6
C. 0.21
The following is a random sample of seven (x, y) pairs of data points:
(1, 5) (3, 7) (4, 6) (5, 8) (7, 9) (3, 6) (5, 7)
Use the data points to attempt Questions 34 − 37.
34. Compute the sample covariance.
A. 2
B. 14
C. 2.3333
What are the standard deviations for X and Y ?
A. SX = 1.9149 and SY = 1.3452
B. SX = 3.6667 and SY = 1.8095
C. SX = 1.7728 and SY = 1.2454
Compute the correlation coefficient.
A. 0.9586
B. 0.3517
C. 0.9059
37. We would like to test, at the 5% level of significance, the null hypothesis
that the population correlation coefficient is zero against the alternative
hypothesis that it is positive. What is the critical value of the test
statistic?
A. 2.015
B. 2.571
C. 3.365
7
38. You are given the following summary data based on a sample of 5
observations on two variables, X and Y .
XX = 19,
XY = 37,
XXY = 193,
XX
2 = 103.
The summary data is based on the levels of the variables, and not
deviations from the sample means. We would like to regress Y on X.
What is the estimated slope coefficient?
A. 1.8738
B. 1.7013
C. 0.9351
39. Reconsider the data given in Question 38. Suppose we would like to fit
a model without an intercept. What is the estimated slope coefficient?
A. 0.9351
B. 1.7013
C. 1.8738
40. Based on a sample of 5 observations, the following regression model
was estimated:
Yb = −7.5714 + 1.7013X
. What is the interpretation of the estimated slope coefficient?
A. When X = 0, Y = −7.5714, on average.
B. A percentage increase in X leads to an increase in Y by 1.7013%,
on average.
C. A unit increase in X leads to an increase in Y by 1.7013 units, on
average.
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