QBA Assignment 1
Due Date: Monday, February 21, 2022
Khalifa Dzhamaludinov – 00089183
Ilker Kaya
Questions (Questions 1 to 5 will be graded)
1. (20 points) The marks of 320 students on an economics midterm test were recorded in
dataset Xr03-17 (inside folder ch03 xlsx under Data folder on iLearn). Describe this data
in a frequency distribution, and relative frequency distribution table and use a histogram
to summarize these data. Describe the modality and symmetry of the graph and interpret
your findings by using the information on the histogram. (Please use 10 points increments
and create a total of 8 classes on your histogram).
Frequency
100
90
80
70
60
50
40
30
20
10
0
30
40
50
60
70
80
90
100
In terms of describing the modality of the histogram, we can see that it is bimodal, we have 2
groups, which are the groups in the high 80s-90s and the 50s. Therefore, we can identify 2 peaks
in 2 separate groups, the first peak being the peak in the 90s, and the second one being in the 50s.
In terms of symmetry, the histogram is symmetrical, this means that hypothetically, if we were to
put a line in the middle of the histogram, both sides will be similar in shape or have similar
characteristics. In this case, if we were to divide the 2 groups, we will find that they have similar
trends, that there is a peak in the middle and the following peaks are lower. The overall shape is
similar but the magnitude of frequency is different, however the magnitude of the frequency is not
the main concern when looking at symmetry.
Interpreting the results from the relative frequency table and the histogram, we can see that
majority of the students either did well or did poorly, hence why there are 2 groups. More than
50% of the population got higher than 80 and around 20% got less than 50, the rest are spread out.
One can assume that population did well considering that a lot of people got good grades, however,
it is concerning that there is a peak in the 50s. The fact that there are 2 groups and peaks when it
comes to grades means that there are 2 ends of the spectrum.
2. (20 points) Use dataset Xr03-50 (inside folder ch03 xlsx under Data folder on iLearn). In
a business school where calculus is a prerequisite for the statistics course, a sample of 15
students was drawn. The marks for calculus and statistics were recorded for each student.
By using the dataset,
a. Plot a scatter diagram for this data showing the relationship between the two variables. Show
all relevant information on the graph (the graph should look professional).
Statistics
Relationship Between Calculus and Statistics Grades
100
95
90
85
80
75
70
65
60
55
50
50
55
60
65
70
75
80
85
90
95
100
Calculus
b. What does the graph tell you about the relationship between the marks in calculus and
statistics?
From this scatter plot we are able to identify a positive linear relationship between the 2 variables.
This means that as one variable increases or decreases, the other follows through with it and goes
in the same direction. Thus, the trend here is that people who performed well in calculus tended to
do better in statistics.
3. (20 points) Use dataset Xr02-42 (inside folder ch02 xlsx under Data folder on iLearn). The
dean of a business school was looking for ways to improve the quality of the applicants to
its MBA program. In particular, she wanted to know whether the undergraduate degree of
applicants differed among her school and the three nearby universities with MBA
programs. She sampled 100 applicants of her program and an equal number from each of
the other universities. She recorded their undergraduate degrees (1 = BA, 2 = BEng, 3 =
BBA, 4 = other) as well the university (codes 1, 2, 3, and 4). Use a tabular technique (crossclassification table and graph) to determine whether the undergraduate degree and the
university each person applied to appear to be related.
It seems that from the bar chart, the students’ undergraduate degrees do appear to be related to the
universities that they apply to. People with an undergraduate degree in The Arts (BA – Blue) and
Business Administration (BBA – Green) tend to have been the majority applying to these
universities offering MBA programs. Students with an undergraduate in Engineering (BEng – Red)
and Other (Purple) have contributed less to the university’s applications. We can deduce the fact
that the majority of their applicants are BA and BBA students, therefore, the dean of the business
school should cater to these students as she now better understands the dynamic and demographic
of her business school and other universities in the area offering MBA programs.
4. (20 points) A smartphone was found to have two types of minor faults. The probability
that a smartphone has a type 1 defect is 0.3, and the probability that it has a type 2 defect
is 0.4. Also, the probability that it has both faults is 0.15. Find the probabilities of the
following events:
A = An item has either a type 1 defect or a type 2 defect.
A = 0.3 + 0.4 - 0.15 = 0.55 = 55%
B = An item does not have either of the defects.
B = 1 - (0.3 + 0.4 + 0.15) = 0.15 = 15%
C = An item has defect 1, but not defect 2.
C = 0.3 - 0.15 = 0.15 = 15%
5. (20 points) A business manager analyzed his company’s most recent sales and
determined the relationship between the way the customers saw/heard their advertisement
and the gender of the customers. The joint probabilities in the following table were
estimated.
a. If the customer is a female, what is the probability that she saw the ad on TV?
0.3 / 0.45 x 100 = 66% chance
b. If the customer saw the ad in newspaper, what is the probability that the customer is a
male?
0.25/0.30 = 5/6 x 100 = 83% chance
c. What is the probability that the customer is a female?
0.45/1 = 45/100 x 100 = 45% chance
d. What is the probability that the customer is a male and heard the ad on the radio?
0.05/0.50 x 100 = 10% chance
e. Are being a female and seeing the ad in newspaper dependent?
P(female and newspaper) = 0.05
P(female) x P(newspaper) = 0.45 x 0.30
P(female and newspaper) ≠ P(female) x P(newspaper) = NOT DEPENDANT