Data Analysis

Sample Midterm I
Econ 3790: Statistics for Business and Economics
Instructor: Yogesh Uppal
You are allowed to use a standard size (8.5*11) cheat sheet and a simple calculator. Please write all the answers with a
BALL-POINT PEN or an INK PEN. If you have any questions during the exam, please raise your hand. GOOD LUCK!!! I am sure you guys will do great.
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question and write it in the space given next to the question number. Each multiple choice question is worth 1 point.
____

____

____

____

____

1. In a questionnaire, respondents are asked to mark their gender as male or female. Gender is an example of the
a. ordinal scale
b. nominal scale
c. ratio scale
d. interval scale
2. Data obtained from a nominal scale
a. must be alphabetic
b. can be either numeric or nonnumeric
c. must be numeric
d. must rank order the data
3. In a post office, the mailboxes are numbered from 1 to 4,500. These numbers represent
a. qualitative data
b. quantitative data
c. either qualitative or quantitative data
d. since the numbers are sequential, the data is quantitative
4. A tabular summary of a set of data showing the fraction of the total number of items in several classes is a
a. frequency distribution
b. relative frequency distribution
c. frequency
d. cumulative frequency distribution
5. A tabular method that can be used to summarize the data on two variables simultaneously is called
a. simultaneous equations
b. crosstabulation
c. a histogram
d. an ogive
Exhibit 1-1
A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

Graduate School
Yes
No
Total

Undergraduate Major
Business
Engineering
70
84
182
208
252
292

Others
126
130
256

Total
280
520
800

____

____

____

____

6. Refer to Exhibit 1-1. What percentage of the students does not plan to go to graduate school?
a. 280
b. 520
c. 65
d. 32
7. Refer to Exhibit 1.1. What percentage of the students' undergraduate major is engineering?
a. 292
b. 520
c. 65
d. 36.5
8. Refer to Exhibit 1-1. Of those students who are majoring in business, what percentage plans to go to graduate school? a. 27.78
b. 8.75
c. 70
d. 72.22
9.  is an example of a
a. population parameter
b. sample statistic
c. population variance
d. mode
Exhibit 1-2
The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated. mean = 160 mode = 165 median = 170

range = 60 variance = 324

____ 10. Refer to Exhibit 1-2. The coefficient of variation equals
a. 0.1125%
b. 11.25%
c. 203.12%
d. 0.20312%
____ 11. Refer to Exhibit 1-2. The distribution of weights in the above sample is
a. positively skewed
b. negatively skewed
c. symmetric
d. None of the above
____ 12. Refer to Exhibit 1-2. The 50th percentile is
a. 160
b. 165
c. 170
d. cannot be answered give the amount of information.

____ 13. Refer to Exhibit 1-2. What is the difference between the largest value and the smallest value of the data?
a. 160
b. 60
c. 40
d. None of the above
____ 14. Refer to Exhibit 1-2. The standard deviation of the above data is
a. 20
b. 18
c. 16
d. 14
____ 15. Events A and B are mutually exclusive. Which of the following statements is also true?
a. A and B are also independent.
b. P(A  B) = P(A)P(B)
c. P(A  B) = P(A) + P(B)
d. P(A  B) = P(A) + P(B)
____ 16. A method of assigning probabilities based upon judgment is referred to as the
a. relative method
b. probability method
c. classical method
d. subjective method
____ 17. The multiplication law is potentially helpful when we are interested in computing the probability of
a. mutually exclusive events
b. the intersection of two events
c. the union of two events
d. conditional events
____ 18. If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A  B) =
a. 0.76
b. 1.00
c. 0.24
d. 0.20
____ 19. An experiment consists of four outcomes with P(E1) = 0.2, P(E2) = 0.3, and P(E3) = 0.4. The probability of outcome E4 is
a. 0.500
b. 0.024
c. 0.100
d. 0.900
____ 20. An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is a
a. discrete random variable
b. continuous random variable
c. complex random variable
d. simplex random variable

____ 21. An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment.
The random variable in this experiment is a
a. discrete random variable
b. continuous random variable
c. complex random variable
d. simplex random variable

Exhibit 1.3
The probability distribution for the number of goals the Lions soccer team makes per game is given below.
Number
Of Goals
0
1
2
3
4

Probability
0.05
0.15
0.35
0.30
........

____ 22. Refer to Exhibit 1.3. Fill in the probability of 4 goals per game.
a. 0.25
b. 0.35
c. 1.2
d. 0.15
____ 23. Refer to Exhibit 1.3. The expected number of goals per game is
a. 0
b. 1
c. 2, since it has the highest probability
d. 2.35
____ 24. Refer to Exhibit 1.3. The standard deviation of number of goals per game is
a. 1.06
b. 2.06
c. 3.06
d. 4.06
____ 25. Refer to Exhibit 1.3. What is the probability that in a given game the Lions will score at least 1 goal?
a. 0.20
b. 0.55
c. 1.0
d. 0.95
Exhibit 1.4
The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week.
Define the random variable X to be the number of days Pete catches fish.
____ 26. Refer to Exhibit 1.4. The probability that Pete will catch fish on exactly one day is
a. .008
b. .096
c. .104
d. .8

____ 27. Refer to Exhibit 1.4. The probability that Pete will catch fish on one day or less is
a. .008
b. .096
c. .104
d. .8
____ 28. Refer to Exhibit 1.4. The expected number of days Pete will catch fish is
a. .6
b. .8
c. 2.4
d. 3
____ 29. Refer to Exhibit 1.4. The variance of the number of days Pete will catch fish is
a. .16
b. .48
c. .8
d. 2.4
____ 30. Refer to Exhibit 1.4. The standard deviation of the number of days Pete will catch fish is
a. 0.59
b. 0.69
c. 0.79
d. 0.89
Problem
31. The following data show the yearly salaries of football coaches at some state supported universities.

University
A
B
C
D
E
F
G
H

Salary
(in $1,000)
53
44
68
47
62
59
53
94

For the above sample, determine the following measures.
a. The mean yearly salary
b. The standard deviation
c. The mode
d. The median
e. The 70th percentile. Please interpret your answer.
32. Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A) The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is
0.11. The probability of getting Merit scholarship or Athletic scholarship or both is 0.3.
a. What is the probability that you will receive a Merit scholarship?
b. Are events A and M mutually exclusive? Why or why not? Explain.
c. Are the two events A, and M, independent? Explain, using probabilities.
d. What percent of Athletic scholars received merit scholarships?

33. A survey of a sample of business students resulted in the following information regarding the genders of the individuals and their selected major.
Selected Major
Gender
Male

Management
40

Marketing
10

Others
30

Total
80

Female

30

20

70

120

Total

70

30

100

200

a.
b.
c.
d.

What is the probability of selecting an individual who is majoring in Marketing?
What is the probability of selecting an individual who is majoring in Management, given that the person is female?
Given that a person is male, what is the probability that he is majoring in Management?
What is the probability of selecting a male individual?

Sample Midterm I
Answer Section
MULTIPLE CHOICE
1.
2.
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30.

ANS:
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B
B
A
B
B
C
D
A
A
B
B
C
B
B
C
D
B
C
C
A
B
D
D
A
D
B
C
C
B
B

PROBLEM
31. ANS:
a.
b.
c.
d.
e.

60
15.8
53
56
62. 70% of the universities pay their football coaches yearly salaries less than or equal to
$62,000.

32. ANS:
a. 0.23
b. No, because P(A  M)  0
c. No, because P(A  M)  P(A) P(B)
d. 61.1%
33. ANS:
a.
b.
c.
d.

0.15
0.25
0.50
0.40