MID TERM TEST (26/12/2023)

Full name: Ong Gia Bội

Student’s ID: 2215027003
PART 1
Question 1. (40 points) The file CEO2016 includes the total compensation (in $millions) for
CEOs
of 200 S&P 500 companies and the one-year total shareholder return in 2016. For total
compensation:
a) Construct a frequency distribution and a percentage distribution.
b) Construct a histogram and a percentage polygon.
c) Construct a cumulative percentage distribution and plot an ogive.
d) Based on (a) through (c), what conclusions can you reach concerning CEO compensation in
2016?
e) Construct a scatter plot of total compensation and shareholder return in 2016. What is the
relationship between the total compensation and shareholder return in 2016?

a) Frequency distribution and percentage distribution:

Compensation of Frequenc Percentag
company y e (%)
1 but less than 10 41 20.5
10 but less than 20 108 54
20 but less than 30 38 19
30 but less than 40 8 4
40 but less than 50 3 1.5
More than 50 2 1

b) Histogram:
 Percentage Polygon:

percentage polygon
60

50

40

30

20

10

0
1 but less 10 but less 20 but less 30 but less 40 but less More than 50
than 10 than 20 than 30 than 40 than 50

c) cumulative percentage distribution:

cumulativ
Compensation of Frequenc Percentag e
company y e (%) percentag
e (%)
1 but less than 10 41 20.5 0
10 but less than 20 108 54 20.5
20 but less than 30 38 19 74.5
30 but less than 40 8 4 93.5
40 but less than 50 3 1.5 97.5
More than 50 2 1 99
Total 100
 cumulative percentage (%)
120

100

80

60

40

20

0
1 but less 10 but less 20 but less 30 but less 40 but less More than Total
than 10 than 20 than 30 than 40 than 50 50

Question 2. (20 points) The file Restaurants contains the cost per meal and the ratings of 50
center city and 50 metro area restaurants on their food, décor, and service (and their summated
ratings). Complete the following for the center city and metro area restaurants:
a) Construct the five-number summary of the cost of a meal.
b) Construct a boxplot of the cost of a meal. What is the shape of the distribution?
c) Compute and interpret the correlation coefficient of the summated rating and the cost of a
meal. d) What conclusions can you reach about the cost of a meal at center city and metro area
restaurants?
a)
Media
X min Q1 Q3 X max
n
The five-number
23 39 48 58 91
summary
b)
Q1 - x
16
min
<
x max -
33
Q3
Q2 - Q1 9
<
Q3 - Q2 10
Q2 - x
25 <
min
 X max -
43
Q2
The Shape of the distribution is Right-skewed

PART 2:
Question 3:
a) Call A as private sector, B as talent management.
P(A) = 347/536 = 0.6474
P(B) = 222/536 = 0.4142
P(A and B) = 156/536 = 0.291
P(A or B) = P(A) + P(B) – P(A and B) = 347/536 + 222/536 – 156/536 = 0.77
b) P( no cost management in public) = 72/536 = 0.1343
c) Call A as public sector, B as cost management.
P(A) = 189/536 = 0.3526
P(B) = 291/536 = 0.5429
P(A and B) = 72/536 = 0.1343
P(A and B) = P(A) + P(B) – P(A and B) = 189/536 + 291/536 – 72/536 = 0.7612
d)
P(public sector IN cost management is not a priority)
= P(public sector and cost management is not a priority) / P(cost management is not a
priority)
 = (72/536) / (291/536) =0.25
e) Event A and B are independent is P(A and B) = P(A) x P(B)
P( cost management is a priority and public sector) = 117/536 = 0.22
P(cost management is a priority) = 245/536 = 0.46
P(public sector) = 189/536 = 0.35
P(cost management is a priority) x P(public sector) = 0.46 x 0.35= 0.16
Thus we can see that P(cost management is a priority and public sector) / new P(cost
management is a priority) x P(public sector)
Thus cost management is a priority and sectors are not independent.
f) P ( private sector) = 347/536= 0.65
P (talent management is a priority) 222/536= 0.41
P(private sector and talent management is a priority) = 156/536 = 0.29
We can see that:
P(private sector and talent management is a priority) / new P ( private sector) x P ( talent
management is a priority )
Thus talent management is a priority and sectors are not independent.

Question 4:
The probability that a nonprofit marketer, known to have a documented content strategy in their
organization, rates their organization as effective in terms of use of content marketing is
approximately 69%.
*The probability that a nonprofit marketer has both a documented content marketing strategy and
rates their organization as effective in content marketing. This is given by the product of the two
percentages: 42% (documented strategy) x 26% (effective rating) = 10.92%.
*The probability that a non profit marketer has a documented content marketing strategy
regardless of their effectiveness rating. This includes both those who rate their organization as
effective and those who don't: 42% (documented strategy with effective rating) + 19%
(documented strategy without effective rating) = 61%.
*Finally, divide the probability calculated in step 1 by the probability calculated in step 2:
10.92% / 61% = 0.1797 = 17.97%, which is approximately 18%.
The question asks about the probability that the nonprofit marketer rates their organization as
effective given that they have a documented content strategy. Since the complementary
probability (non-effective rating) would be 100% - 18% = 82%, the probability of an effective
rating is approximately 82%.