微信客服：xiaoxionga100
微信客服：ITCS521
MCD2080-无代写
时间：2023-05-19
BUSINESS STATISTICS - MCD2080
Question & Answer Booklet
EXAM DURATION: 2 hours and 10 minutes
During an examination, you must not have in your possession a book, notes, paper, calculator, pencil case, mobile
phone, electronic devices, smart watch, electronic pens or other material/item which has not been authorised for
the exam or specifically permitted as noted below. Any unauthorised material or item on your desk, chair or
person will be deemed to be in your possession. You are reminded that possession of unauthorised materials in
an examination is a discipline offence under Monash College regulations.
AUTHORISED MATERIALS
CALCULATORS (HP 10bII+ Financial Calculator) YES
OPEN BOOK NO
SPECIFICALLY PERMITTED ITEMS NO
INSTRUCTIONS TO CANDIDATES
• Questions should be answered in Question Booklet in the box provided.
• Write clearly. Marks cannot be given if your handwriting cannot be read.
THIS ENTIRE EXAMINATION PAPER MUST BE HANDED IN AT THE END OF THE EXAMINATION.
DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED TO DO SO.
Examiner Use Only
Question
Questions
Total Marks
1 2 3 4 5
Mark /22 /23.5 /18.5 /13.5 /22.5 /100
Candidates must complete this section if required to write answers within this paper
STUDENT
ID:
DESK NUMBER:
Trimester One 2023 Sample Exam
INSTRUCTIONS TO CANDIDATES:
Answer ALL questions in this examination paper.
Paper is out of 100 marks
All answers must be written on blank sheets of paper which you upload to the e-assessment platform
at the conclusion of your exam.
Please write legibly. If we cannot read your writing, then we cannot give you any marks. You must
make sure your writing can be easily understood.
Where you are asked to perform calculations, you should write out the solution as an equation
containing the appropriate numerical values from within the question and perform the calculation.
Data Used
Question 1 & 2
Here we look at some analysis on a Computer Technology Company (TechCom) employee and their
experience, education and their annual salary. In addition, the company examines various departments
and their relationship with the employee profiles. The data is based on the records from 2003 to 2010.
Question 3
The data in the file “US Income.xlsx” captures the US annual income. We want to find how
individuals’ income is distributed between a few characteristics.
Question 4
The Data is about a direct marketer of electronic equipment and wants to investigate the efficacy in
their company named HyTex. HyTex sent catalogues to the customers and the question might be that,
if it is sending the catalogues to the right customers and if not, to whom should it send the catalogues
to. The file “Catalogue Marketing.xlsx” contains customer demographic attributes including the
Marital Status of the customer and the Region they live in.
Question 5
The Data is about Australian production of electricity from Quarter 1 2010 to Quarter 3 2018. The
data contains quarterly electricity production in million KWH (m.KWH).
Use the data to answer the following questions.
MCD2080 T1 2023 Exam Sample Page 2 of 18
Question 1 [2 + 2 + 2 + 4 + 1 + 1 + 3 + 1 + 1 + 5 = 22 marks]
a) Shown below is the table illustrating the number of employees from two different
depart5ments: Production and Engineering (P&E) and Purchasing by gender and the
educational attainment (in years).
Use Exhibit 1 below to answer the following questions.
Exhibit 1
Department Production and Engineering
Department Purchasing
Count of Employee Gender Count of Employee Gender
Education Female Male Grand Total Education Female Male Grand Total
0 4 1 5 0 2
2
2 3 1 4 2 4 4 8
4 27 22 49 4 20 14 34
6 8 9 17 6 10 8 18
8 1 2 3 8 4 1 5
Grand Total 43 35 78 Grand Total 40 27 67
Using the two pivot tables in Exhibit 1,
(i) Calculate the proportion of the female and the proportion of the male employees from the
P&E department. Show all workings to 4 decimal places.
(ii) Similarly, calculate the proportion of the female and male employees from the Purchasing
department. Show all workings to 4 decimal places.
(iii) From part (i) and (ii), compare the percentage of the employees from the two departments.
MCD2080 T1 2023 Exam Sample Page 3 of 18
b) Next, we want to examine the variable of employee’s experience and the distribution of
employees. Pivot tables (Exhibit 2) below show the employee experience from P&E and
Purchasing departments.
Exhibit 2
Department Production and Engineering
Department Purchasing
Count of Employee Gender
Count of Employee Gender
Prior Experience
(years)
Female Male Grand
Total
Prior Experience
(years)
Female Male Grand
Total
0-4 21.79% 15.38% 37.18%
0-4 25.37% 17.91% 43.28%
5-9 21.79% 7.69% 29.49%
5-9 14.93% 10.45% 25.37%
10-14 11.54% 17.95% 29.49%
10-14 14.93% 11.94% 26.87%
15-20 0.00% 3.85% 3.85%
15-20 4.48% 0.00% 4.48%
Grand Total 55.13% 44.87% 100.00%
Grand Total 59.70% 40.30% 100.00%
Based on the above reported probabilities, discuss how the employees prior experience affects
the distribution of the employees as their experience increases. Give examples.
c) The pivot table below (Exhibit 3) gives the employee’s prior experience by employees’ gender
for all company’s departments.
Exhibit 3: % of Grand Total
Department (All)
Count of Employee Gender
Prior Experience (years) Female Male Grand Total
0-4 23.04% 15.69% 38.73%
5-9 18.14% 9.80% 27.94%
10-14 13.73% 14.22% 27.94%
15-20 3.43% 1.96% 5.39%
Grand Total 58.33% 41.67% 100.00%
From this Exhibit 3, answer the following questions.
(i) What does the value 5.39 present?
(ii) Explain the meaning of the value 9.80%.
d) Below is a chart of showing the distribution of employees’ salaries by their prior experience for
MCD2080 T1 2023 Exam Sample Page 4 of 18
all departments.
Exhibit 4.
For the following questions, refer to above Exhibit 4.
(i) Does the prior experience really matter in terms of employee’s salary? Discuss giving the
evidence in terms of values and the percentage estimates.
(ii) Which range of years of experience has the highest percentage of group of annual salaries?
State the salary group and the percentage as well.
(iii) Which is the most salary group with the most years of experience?
What percentage is that group?
0%
20%
40%
60%
80%
100%
0-4 5-9 10-14 15-20
C
o
u
n
t
(%
)
Prior Experience (Years)
Employees' salaries by prior experience
0-50 50-100 100-150 150-200
MCD2080 T1 2023 Exam Sample Page 5 of 18
e) The pivot table below (Exhibit 5), examines the distribution of employees’ salaries by their prior
experience for all departments.
Exhibit 5
Department All
Count of Employee Annual Salary ($'000)
Prior Experience (years) 0-50 50-100 100-150 150-200 Grand Total
0-4 45 32 2
79
5-9 5 47 4 1 57
10-14
36 21
57
15-20
3 7 1 11
Grand Total 50 118 34 2 204
Here we want to find out if the employees’ prior years of experience is independent of their annual
salaries. From Exhibit 5, write down a probability statement that would support that relationship If
these two variables were independent.
MCD2080 T1 2023 Exam Sample Page 6 of 18
Question 2 [3 + 2 + 2.5 + 4 + 5 + 3 + 4 = 23.5 marks]
a) Summary statistics and the distribution of the employees’ salaries for all departments are
provided below (Exhibit 6).
Exhibit 6
Statistics Annual Salary ($'000)
Mean 71.27
Median 68.40
Standard Deviation 30.25
Minimum 12.40
Maximum 163.90
Count 204.00
Range 151.50
First Quartile 51.55
Third Quartile 86.98
Interquartile Range (IQR) 35.43
Coefficient of Variation (CV) 42.45%
Exhibit 7
(i) What type of chart given in the Exhibit 7
Give three essential items/elements that will improve this type of chart.
0
10
20
30
40
50
60
70
0-20 20-40 40-60 60-80 80-100 100-120 120-140 140-160 160-180
Total
Total
MCD2080 T1 2023 Exam Sample Page 7 of 18
(ii) Using Exhibit 6 and 7, describe the shape of the “Annual Salaries” of the employees.
(iii) It is hard to state the mode in the continuous data. However, from Exhibit 7 what would be
the annual salaries modal class?
Obtain the percentage of this modal class. Show your calculations.
(iv) Using Exhibit 7 interpret in context the central tendency of the annual salaries.
(v) To describe the variation of data, we use Range, interquartile range (IQR) and coefficient of
variation (CV).
From Exhibit 7, illustrate how we calculate Range, IQR and CV
Give interpretations for two of any of these three measures.
MCD2080 T1 2023 Exam Sample Page 8 of 18
b) To use the Empirical Rule we assume the data is approximately normally distributed. If this
rule is applied to the employee’s annual salaries, use Exhibit 7 to answer the following
questions.
(i) Calculate the annual salary that 2.5% of employees who receive a salary equal to or lower
than this value. Show your workings.
(ii) What is an approximate probability of a randomly selected employee who receive a salary
between $41,022 and $101,527?
Show your workings.
MCD2080 T1 2023 Exam Sample Page 9 of 18
Question 3 [1 + 3 + 4 + 2.5 + 2 + 6 = 18.5 marks]
a) Using the data “US Income.xlsx” let us define the following variables:
Income (Per Year) = Individual annual income ($).
Female = 1 if an individual is a female and 0 if a male
Proportion = values of 1’s
Using excel we obtain the regression of variable the “Female” on the variable “Proportion”. The out is
given below, Exhibit 8.
Exhibit 8
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.696105192
R Square 0.484562439
Adjusted R Square 0.484365743
Standard Error 0.499810773
Observations 5085
ANOVA
df SS MS F Significance F
Regression 1 1193.9618 1193.962 4779.464 0
Residual 5084 1270.0382 0.249811
Total 5085 2464
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 0 #N/A #N/A #N/A #N/A #N/A
Proportion 0.484562439 0.0070091 69.13367 0 0.470822 0.498303
Use the above Exhibit 8 to answer the following question
(i) State and interpret the coefficient of the “proportion” variable.
(ii) Calculate the male proportion and compare it with the female proportion.
(iii) State and interpret the 95% confidence interval for the proportion variable in Exhibit 8 in
context.
MCD2080 T1 2023 Exam Sample Page 10 of 18
b) (i) As we are dealing with the sample proportion, explain the concept of “repeated sampling” and
give a “mathematical” interpretation of the 95% confidence interval in Exhibit 7.
(ii) Explain what effect the sample size being decreased will have on the confidence interval in
Exhibit 1 if all other factors are assumed constant.
Explain your answer.
(iii) What would happen to the confidence interval in Exhibit 1 if we instead constructed a 90%
confidence level given that all other factors remain constant?
Explain your answer.
c) Next, we use Excel to obtain a regression of Income (Per Year) on Female. The output is given
below in the Exhibit 9.
Exhibit 9
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.05784
R Square 0.00335
Adjusted R Square 0.00315
Standard Error 35641.621
Observations 5085
ANOVA
df SS MS F Significance F
Regression 1 2.167E+10 2.17E+10 17.06242 3.68E-05
Residual 5083 6.457E+12 1.27E+09
Total 5084 6.479E+12
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 32600.080 696.184 46.827 0 31235.26 33964.9
Female -4131.135 1000.113 -4.131 3.68E-05 -6091.79 -2170.48
MCD2080 T1 2023 Exam Sample Page 11 of 18
Use the above Exhibit 9 to answer parts i, ii & iii
(i) State and give an interpretation of the intercept coefficient.
(ii) State and give an interpretation of the slope coefficient.
(iii) Carry out a hypothesis test to establish if the difference between the male and female annual
incomes is significant at 1% level of significance
Use the p-value approach and show all the steps.
MCD2080 T1 2023 Exam Sample Page 12 of 18
Question 4 [3 + 3.5 + 4.5 + 2.5 = 13.5 marks]
We want to explore the variables that might influence the amount the customer spends at HyTex on
purchases. We define the following variables:
Y variable:
AmountSpent = Total amount spent on purchases from HyTex ($).
X variables:
Male = 1 if a person is a male and 0 if female.
OwnHome = 1: if person owns home and 0 if renting.
Married = 1 if person is married and 0 otherwise.
Salary = Combined annual salary of person and spouse (if any).
Children = Number of children living with person.
Catalogs = Number of catalogs sent to person this year.
a) (i) First, carry out a correlation matrix of variable of “AmountSpent” on the above variables”.
Name that Exhibit 10.
Exhibit 10
Male OwnHome Married Salary Children Catalogs AmountSpent
Male 1
OwnHome 0.084433 1
Married 0.116057 0.264009 1
Salary 0.261492 0.460736 0.675633 1
Children -0.10547 -0.03227 0.00977 0.049663 1
Catalogs 0.087351 0.093132 0.13706 0.183551 -0.11346 1
AmountSpent 0.201687 0.350811 0.475879 0.699598 -0.2223 0.472644 1
(1 marks)
(ii) From Exhibit 10, which variable have the most influence and the least impacts on the
“AmountSpent”?
Sate and interpret one of these two values.
MCD2080 T1 2023 Exam Sample Page 13 of 18
b) Excel is used to regress “AmountSpent” on Male, OwnHome, Married, Salary, Children, and
Catalogues. The output is given below in the Exhibit 11.
Exhibit 11
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8119
R Square 0.6592
Adjusted R Square 0.6571
Standard Error 562.7842
Observations 1000
ANOVA
df SS MS F Significance F
Regression 6 6.08E+08 1.01E+08 320.0627 4.4E-228
Residual 993 3.15E+08 316726
Total 999 9.23E+08
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -437.438 55.127 -7.935 5.65E-15 -545.618 -329.259
Male -42.069 37.388 -1.125 0.260773 -115.438 31.299
OwnHome 29.715 40.381 0.736 0.461984 -49.527 108.957
Married -24.390 48.662 -0.501 0.616327 -119.883 71.102
Salary 0.021 0.001 22.971 5.45E-94 0.019 0.022
Children -200.487 17.274 -11.606 2.71E-29 -234.386 -166.589
Catalogs 47.793 2.758 17.329 5.55E-59 42.381 53.205
(i) State and interpret the intercept.
(ii) State and interpret the coefficient of “Salary”.
MCD2080 T1 2023 Exam Sample Page 14 of 18
(iii) State and interpret the coefficient of “Catalogs”.
(iv) State and interpret the coefficient of “Married”.
(v) Use the model in Exhibit 2 above to predict the amount spent by the customer who is
female, who is renting, not married, with a salary of $100,000, no children and supplied with
35 catalogues
Show your working clearly.
MCD2080 T1 2023 Exam Sample Page 15 of 18
Question 5 [2 + 2.5 + 2 + 3 + 1.5 + 3.5 + 4 + 4 = 22.5 marks]
a) (i). Excel is used to construct a line graph of the electricity production over time. The output is
given below in the Exhibit 12.
Exhibit 12
(ii) State and discuss any three of the time series components that is obvious in the data
shown in Exhibit 12.
b) (i). Using Excel, an estimated model of a linear trend and quarterly seasonal dummies. Quarter
4 is used as a base quarter. Output is given in Exhibit 13 below.
To do that we need to define the following variables:
Y variable:
• elect_prod: = Australian quarterly production of electricity (million KWH).
X variables:
• Time: number of quarters since Q1 2010 to Q3 2018.
• Qrtr1: = 1 if the quarter is from January to March and 0 otherwise.
• Qrtr2: = 1 if the quarter is from April to June and 0 otherwise.
• Qrtr3: = 1 if the quarter is from July to September and 0 otherwise.
• Qrtr4: = 1 if the quarter is from October to December and 0 otherwise.
8000
9000
10000
11000
12000
13000
14000
15000
16000
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
E
le
ct
ri
ci
ty
P
ro
d
u
ct
io
n
(
m
.
K
W
H
)
Time (in quarters)
Australian Electricity Production
MCD2080 T1 2023 Exam Sample Page 16 of 18
Exhibit 13
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.96619
R Square 0.93353
Adjusted R Square 0.92467
Standard Error 321.63113
Observations 35
ANOVA
df SS MS F Significance F
Regression 4 43584008 10896002 105.3297 3.28E-17
Residual 30 3103398 103446.6
Total 34 46687405
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 10350.646 149.555 69.209 1.18E-34 10045.213 10656.079
Time, t 96.612 5.397 17.902 1.46E-17 85.591 107.634
Qrt1 -159.906 156.378 -1.023 0.31469 -479.272 159.460
Qrt2 371.037 156.285 2.374 0.02419 51.861 690.213
Qrt3 1079.795 156.378 6.905 1.15E-07 760.429 1399.161
(ii) State and interpret the coefficient of the intercept.
(iii) State and interpret the coefficient of time.
(iv) State and interpret the estimated coefficient for the months of January to March.
(v) From the above estimated model (Exhibit 2), state the quarter with the second highest
Electricity production.
State and Interpret it’s value.
MCD2080 T1 2023 Exam Sample Page 17 of 18
(vi) Carry out a hypothesis test to determine if the electricity production of the months of July
to September is different to that in the electricity production of the moths of October to
December.
Use a 1% level of significance and show all the steps.
(vii) Using the model in Exhibit 2, predict the Australia electricity production for Quarter 1 in
2019.
To do so:
• First, write down the value for the “Time” variable. [Hint: Time = 1 in Qtr1 2010]
• Second, write down the value for each of the Quarterly dummy variables for Quarter
1 2019.
• Third, write down the equation substituting these quarterly dummy values in the
model (equation) to predict the electricity production for Quarter 1 2019.
(viii) Lastly, we need to evaluate the accuracy of the above prediction, in part (v). The
electricity production over the period between quarter 1 2010 to quarter 3 2018 is
12,421.62 m.KWH.
With that in mind, discuss any two ways we can evaluate this model.
------------- END OF EXAM -------------
MCD2080 T1 2023 Exam Sample Page 18 of 18
Question & Answer Booklet
EXAM DURATION: 2 hours and 10 minutes
During an examination, you must not have in your possession a book, notes, paper, calculator, pencil case, mobile
phone, electronic devices, smart watch, electronic pens or other material/item which has not been authorised for
the exam or specifically permitted as noted below. Any unauthorised material or item on your desk, chair or
person will be deemed to be in your possession. You are reminded that possession of unauthorised materials in
an examination is a discipline offence under Monash College regulations.
AUTHORISED MATERIALS
CALCULATORS (HP 10bII+ Financial Calculator) YES
OPEN BOOK NO
SPECIFICALLY PERMITTED ITEMS NO
INSTRUCTIONS TO CANDIDATES
• Questions should be answered in Question Booklet in the box provided.
• Write clearly. Marks cannot be given if your handwriting cannot be read.
THIS ENTIRE EXAMINATION PAPER MUST BE HANDED IN AT THE END OF THE EXAMINATION.
DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED TO DO SO.
Examiner Use Only
Question
Questions
Total Marks
1 2 3 4 5
Mark /22 /23.5 /18.5 /13.5 /22.5 /100
Candidates must complete this section if required to write answers within this paper
STUDENT
ID:
DESK NUMBER:
Trimester One 2023 Sample Exam
INSTRUCTIONS TO CANDIDATES:
Answer ALL questions in this examination paper.
Paper is out of 100 marks
All answers must be written on blank sheets of paper which you upload to the e-assessment platform
at the conclusion of your exam.
Please write legibly. If we cannot read your writing, then we cannot give you any marks. You must
make sure your writing can be easily understood.
Where you are asked to perform calculations, you should write out the solution as an equation
containing the appropriate numerical values from within the question and perform the calculation.
Data Used
Question 1 & 2
Here we look at some analysis on a Computer Technology Company (TechCom) employee and their
experience, education and their annual salary. In addition, the company examines various departments
and their relationship with the employee profiles. The data is based on the records from 2003 to 2010.
Question 3
The data in the file “US Income.xlsx” captures the US annual income. We want to find how
individuals’ income is distributed between a few characteristics.
Question 4
The Data is about a direct marketer of electronic equipment and wants to investigate the efficacy in
their company named HyTex. HyTex sent catalogues to the customers and the question might be that,
if it is sending the catalogues to the right customers and if not, to whom should it send the catalogues
to. The file “Catalogue Marketing.xlsx” contains customer demographic attributes including the
Marital Status of the customer and the Region they live in.
Question 5
The Data is about Australian production of electricity from Quarter 1 2010 to Quarter 3 2018. The
data contains quarterly electricity production in million KWH (m.KWH).
Use the data to answer the following questions.
MCD2080 T1 2023 Exam Sample Page 2 of 18
Question 1 [2 + 2 + 2 + 4 + 1 + 1 + 3 + 1 + 1 + 5 = 22 marks]
a) Shown below is the table illustrating the number of employees from two different
depart5ments: Production and Engineering (P&E) and Purchasing by gender and the
educational attainment (in years).
Use Exhibit 1 below to answer the following questions.
Exhibit 1
Department Production and Engineering
Department Purchasing
Count of Employee Gender Count of Employee Gender
Education Female Male Grand Total Education Female Male Grand Total
0 4 1 5 0 2
2
2 3 1 4 2 4 4 8
4 27 22 49 4 20 14 34
6 8 9 17 6 10 8 18
8 1 2 3 8 4 1 5
Grand Total 43 35 78 Grand Total 40 27 67
Using the two pivot tables in Exhibit 1,
(i) Calculate the proportion of the female and the proportion of the male employees from the
P&E department. Show all workings to 4 decimal places.
(ii) Similarly, calculate the proportion of the female and male employees from the Purchasing
department. Show all workings to 4 decimal places.
(iii) From part (i) and (ii), compare the percentage of the employees from the two departments.
MCD2080 T1 2023 Exam Sample Page 3 of 18
b) Next, we want to examine the variable of employee’s experience and the distribution of
employees. Pivot tables (Exhibit 2) below show the employee experience from P&E and
Purchasing departments.
Exhibit 2
Department Production and Engineering
Department Purchasing
Count of Employee Gender
Count of Employee Gender
Prior Experience
(years)
Female Male Grand
Total
Prior Experience
(years)
Female Male Grand
Total
0-4 21.79% 15.38% 37.18%
0-4 25.37% 17.91% 43.28%
5-9 21.79% 7.69% 29.49%
5-9 14.93% 10.45% 25.37%
10-14 11.54% 17.95% 29.49%
10-14 14.93% 11.94% 26.87%
15-20 0.00% 3.85% 3.85%
15-20 4.48% 0.00% 4.48%
Grand Total 55.13% 44.87% 100.00%
Grand Total 59.70% 40.30% 100.00%
Based on the above reported probabilities, discuss how the employees prior experience affects
the distribution of the employees as their experience increases. Give examples.
c) The pivot table below (Exhibit 3) gives the employee’s prior experience by employees’ gender
for all company’s departments.
Exhibit 3: % of Grand Total
Department (All)
Count of Employee Gender
Prior Experience (years) Female Male Grand Total
0-4 23.04% 15.69% 38.73%
5-9 18.14% 9.80% 27.94%
10-14 13.73% 14.22% 27.94%
15-20 3.43% 1.96% 5.39%
Grand Total 58.33% 41.67% 100.00%
From this Exhibit 3, answer the following questions.
(i) What does the value 5.39 present?
(ii) Explain the meaning of the value 9.80%.
d) Below is a chart of showing the distribution of employees’ salaries by their prior experience for
MCD2080 T1 2023 Exam Sample Page 4 of 18
all departments.
Exhibit 4.
For the following questions, refer to above Exhibit 4.
(i) Does the prior experience really matter in terms of employee’s salary? Discuss giving the
evidence in terms of values and the percentage estimates.
(ii) Which range of years of experience has the highest percentage of group of annual salaries?
State the salary group and the percentage as well.
(iii) Which is the most salary group with the most years of experience?
What percentage is that group?
0%
20%
40%
60%
80%
100%
0-4 5-9 10-14 15-20
C
o
u
n
t
(%
)
Prior Experience (Years)
Employees' salaries by prior experience
0-50 50-100 100-150 150-200
MCD2080 T1 2023 Exam Sample Page 5 of 18
e) The pivot table below (Exhibit 5), examines the distribution of employees’ salaries by their prior
experience for all departments.
Exhibit 5
Department All
Count of Employee Annual Salary ($'000)
Prior Experience (years) 0-50 50-100 100-150 150-200 Grand Total
0-4 45 32 2
79
5-9 5 47 4 1 57
10-14
36 21
57
15-20
3 7 1 11
Grand Total 50 118 34 2 204
Here we want to find out if the employees’ prior years of experience is independent of their annual
salaries. From Exhibit 5, write down a probability statement that would support that relationship If
these two variables were independent.
MCD2080 T1 2023 Exam Sample Page 6 of 18
Question 2 [3 + 2 + 2.5 + 4 + 5 + 3 + 4 = 23.5 marks]
a) Summary statistics and the distribution of the employees’ salaries for all departments are
provided below (Exhibit 6).
Exhibit 6
Statistics Annual Salary ($'000)
Mean 71.27
Median 68.40
Standard Deviation 30.25
Minimum 12.40
Maximum 163.90
Count 204.00
Range 151.50
First Quartile 51.55
Third Quartile 86.98
Interquartile Range (IQR) 35.43
Coefficient of Variation (CV) 42.45%
Exhibit 7
(i) What type of chart given in the Exhibit 7
Give three essential items/elements that will improve this type of chart.
0
10
20
30
40
50
60
70
0-20 20-40 40-60 60-80 80-100 100-120 120-140 140-160 160-180
Total
Total
MCD2080 T1 2023 Exam Sample Page 7 of 18
(ii) Using Exhibit 6 and 7, describe the shape of the “Annual Salaries” of the employees.
(iii) It is hard to state the mode in the continuous data. However, from Exhibit 7 what would be
the annual salaries modal class?
Obtain the percentage of this modal class. Show your calculations.
(iv) Using Exhibit 7 interpret in context the central tendency of the annual salaries.
(v) To describe the variation of data, we use Range, interquartile range (IQR) and coefficient of
variation (CV).
From Exhibit 7, illustrate how we calculate Range, IQR and CV
Give interpretations for two of any of these three measures.
MCD2080 T1 2023 Exam Sample Page 8 of 18
b) To use the Empirical Rule we assume the data is approximately normally distributed. If this
rule is applied to the employee’s annual salaries, use Exhibit 7 to answer the following
questions.
(i) Calculate the annual salary that 2.5% of employees who receive a salary equal to or lower
than this value. Show your workings.
(ii) What is an approximate probability of a randomly selected employee who receive a salary
between $41,022 and $101,527?
Show your workings.
MCD2080 T1 2023 Exam Sample Page 9 of 18
Question 3 [1 + 3 + 4 + 2.5 + 2 + 6 = 18.5 marks]
a) Using the data “US Income.xlsx” let us define the following variables:
Income (Per Year) = Individual annual income ($).
Female = 1 if an individual is a female and 0 if a male
Proportion = values of 1’s
Using excel we obtain the regression of variable the “Female” on the variable “Proportion”. The out is
given below, Exhibit 8.
Exhibit 8
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.696105192
R Square 0.484562439
Adjusted R Square 0.484365743
Standard Error 0.499810773
Observations 5085
ANOVA
df SS MS F Significance F
Regression 1 1193.9618 1193.962 4779.464 0
Residual 5084 1270.0382 0.249811
Total 5085 2464
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 0 #N/A #N/A #N/A #N/A #N/A
Proportion 0.484562439 0.0070091 69.13367 0 0.470822 0.498303
Use the above Exhibit 8 to answer the following question
(i) State and interpret the coefficient of the “proportion” variable.
(ii) Calculate the male proportion and compare it with the female proportion.
(iii) State and interpret the 95% confidence interval for the proportion variable in Exhibit 8 in
context.
MCD2080 T1 2023 Exam Sample Page 10 of 18
b) (i) As we are dealing with the sample proportion, explain the concept of “repeated sampling” and
give a “mathematical” interpretation of the 95% confidence interval in Exhibit 7.
(ii) Explain what effect the sample size being decreased will have on the confidence interval in
Exhibit 1 if all other factors are assumed constant.
Explain your answer.
(iii) What would happen to the confidence interval in Exhibit 1 if we instead constructed a 90%
confidence level given that all other factors remain constant?
Explain your answer.
c) Next, we use Excel to obtain a regression of Income (Per Year) on Female. The output is given
below in the Exhibit 9.
Exhibit 9
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.05784
R Square 0.00335
Adjusted R Square 0.00315
Standard Error 35641.621
Observations 5085
ANOVA
df SS MS F Significance F
Regression 1 2.167E+10 2.17E+10 17.06242 3.68E-05
Residual 5083 6.457E+12 1.27E+09
Total 5084 6.479E+12
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 32600.080 696.184 46.827 0 31235.26 33964.9
Female -4131.135 1000.113 -4.131 3.68E-05 -6091.79 -2170.48
MCD2080 T1 2023 Exam Sample Page 11 of 18
Use the above Exhibit 9 to answer parts i, ii & iii
(i) State and give an interpretation of the intercept coefficient.
(ii) State and give an interpretation of the slope coefficient.
(iii) Carry out a hypothesis test to establish if the difference between the male and female annual
incomes is significant at 1% level of significance
Use the p-value approach and show all the steps.
MCD2080 T1 2023 Exam Sample Page 12 of 18
Question 4 [3 + 3.5 + 4.5 + 2.5 = 13.5 marks]
We want to explore the variables that might influence the amount the customer spends at HyTex on
purchases. We define the following variables:
Y variable:
AmountSpent = Total amount spent on purchases from HyTex ($).
X variables:
Male = 1 if a person is a male and 0 if female.
OwnHome = 1: if person owns home and 0 if renting.
Married = 1 if person is married and 0 otherwise.
Salary = Combined annual salary of person and spouse (if any).
Children = Number of children living with person.
Catalogs = Number of catalogs sent to person this year.
a) (i) First, carry out a correlation matrix of variable of “AmountSpent” on the above variables”.
Name that Exhibit 10.
Exhibit 10
Male OwnHome Married Salary Children Catalogs AmountSpent
Male 1
OwnHome 0.084433 1
Married 0.116057 0.264009 1
Salary 0.261492 0.460736 0.675633 1
Children -0.10547 -0.03227 0.00977 0.049663 1
Catalogs 0.087351 0.093132 0.13706 0.183551 -0.11346 1
AmountSpent 0.201687 0.350811 0.475879 0.699598 -0.2223 0.472644 1
(1 marks)
(ii) From Exhibit 10, which variable have the most influence and the least impacts on the
“AmountSpent”?
Sate and interpret one of these two values.
MCD2080 T1 2023 Exam Sample Page 13 of 18
b) Excel is used to regress “AmountSpent” on Male, OwnHome, Married, Salary, Children, and
Catalogues. The output is given below in the Exhibit 11.
Exhibit 11
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8119
R Square 0.6592
Adjusted R Square 0.6571
Standard Error 562.7842
Observations 1000
ANOVA
df SS MS F Significance F
Regression 6 6.08E+08 1.01E+08 320.0627 4.4E-228
Residual 993 3.15E+08 316726
Total 999 9.23E+08
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -437.438 55.127 -7.935 5.65E-15 -545.618 -329.259
Male -42.069 37.388 -1.125 0.260773 -115.438 31.299
OwnHome 29.715 40.381 0.736 0.461984 -49.527 108.957
Married -24.390 48.662 -0.501 0.616327 -119.883 71.102
Salary 0.021 0.001 22.971 5.45E-94 0.019 0.022
Children -200.487 17.274 -11.606 2.71E-29 -234.386 -166.589
Catalogs 47.793 2.758 17.329 5.55E-59 42.381 53.205
(i) State and interpret the intercept.
(ii) State and interpret the coefficient of “Salary”.
MCD2080 T1 2023 Exam Sample Page 14 of 18
(iii) State and interpret the coefficient of “Catalogs”.
(iv) State and interpret the coefficient of “Married”.
(v) Use the model in Exhibit 2 above to predict the amount spent by the customer who is
female, who is renting, not married, with a salary of $100,000, no children and supplied with
35 catalogues
Show your working clearly.
MCD2080 T1 2023 Exam Sample Page 15 of 18
Question 5 [2 + 2.5 + 2 + 3 + 1.5 + 3.5 + 4 + 4 = 22.5 marks]
a) (i). Excel is used to construct a line graph of the electricity production over time. The output is
given below in the Exhibit 12.
Exhibit 12
(ii) State and discuss any three of the time series components that is obvious in the data
shown in Exhibit 12.
b) (i). Using Excel, an estimated model of a linear trend and quarterly seasonal dummies. Quarter
4 is used as a base quarter. Output is given in Exhibit 13 below.
To do that we need to define the following variables:
Y variable:
• elect_prod: = Australian quarterly production of electricity (million KWH).
X variables:
• Time: number of quarters since Q1 2010 to Q3 2018.
• Qrtr1: = 1 if the quarter is from January to March and 0 otherwise.
• Qrtr2: = 1 if the quarter is from April to June and 0 otherwise.
• Qrtr3: = 1 if the quarter is from July to September and 0 otherwise.
• Qrtr4: = 1 if the quarter is from October to December and 0 otherwise.
8000
9000
10000
11000
12000
13000
14000
15000
16000
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
Q
tr
4
Q
tr
1
Q
tr
2
Q
tr
3
E
le
ct
ri
ci
ty
P
ro
d
u
ct
io
n
(
m
.
K
W
H
)
Time (in quarters)
Australian Electricity Production
MCD2080 T1 2023 Exam Sample Page 16 of 18
Exhibit 13
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.96619
R Square 0.93353
Adjusted R Square 0.92467
Standard Error 321.63113
Observations 35
ANOVA
df SS MS F Significance F
Regression 4 43584008 10896002 105.3297 3.28E-17
Residual 30 3103398 103446.6
Total 34 46687405
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 10350.646 149.555 69.209 1.18E-34 10045.213 10656.079
Time, t 96.612 5.397 17.902 1.46E-17 85.591 107.634
Qrt1 -159.906 156.378 -1.023 0.31469 -479.272 159.460
Qrt2 371.037 156.285 2.374 0.02419 51.861 690.213
Qrt3 1079.795 156.378 6.905 1.15E-07 760.429 1399.161
(ii) State and interpret the coefficient of the intercept.
(iii) State and interpret the coefficient of time.
(iv) State and interpret the estimated coefficient for the months of January to March.
(v) From the above estimated model (Exhibit 2), state the quarter with the second highest
Electricity production.
State and Interpret it’s value.
MCD2080 T1 2023 Exam Sample Page 17 of 18
(vi) Carry out a hypothesis test to determine if the electricity production of the months of July
to September is different to that in the electricity production of the moths of October to
December.
Use a 1% level of significance and show all the steps.
(vii) Using the model in Exhibit 2, predict the Australia electricity production for Quarter 1 in
2019.
To do so:
• First, write down the value for the “Time” variable. [Hint: Time = 1 in Qtr1 2010]
• Second, write down the value for each of the Quarterly dummy variables for Quarter
1 2019.
• Third, write down the equation substituting these quarterly dummy values in the
model (equation) to predict the electricity production for Quarter 1 2019.
(viii) Lastly, we need to evaluate the accuracy of the above prediction, in part (v). The
electricity production over the period between quarter 1 2010 to quarter 3 2018 is
12,421.62 m.KWH.
With that in mind, discuss any two ways we can evaluate this model.
------------- END OF EXAM -------------
MCD2080 T1 2023 Exam Sample Page 18 of 18
