University of Queensland Compute the Values Statistics Questions

Trimester 3 20201305AFE Business Data Analysis
Problem-Solving Assignment
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Given Name: …………………………..
Student Number: ……………………
(Please ensure that you insert your student details above)
Important Notice:
As this is an individual assessment item, students MUST work on their own and present
their individual assignment submission. If found to have cheated, your submission would
receive a mark of zero for this assessment item. Note: University uses text-matching tools
to detect academic cheating, collusion and plagiarism.
Instructions:
Please do read all of these instructions carefully.
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Answer all questions
Worth 40 marks (40%)
Release date and time: Wednesday, 3 Feb 2021, 3.00pm
Due date and time: Friday, 5 Feb 2021, 3.00pm
Display all your working for questions where you need to do calculation. This is not
an Excel computing assignment. You need to display your manual calculation working.
Your final submission must be presented and submitted in a Word document in .doc
or .docx format. No pdfs or Excel files or other type of document format will be
accepted!
Students must complete the Academic Integrity digital cover sheet of this assessment
item, available under Assessment tab in the Learning@Griffith course site.
Students must submit the completed work through the submission link provided
under Assessment tab in the Learning@Griffith course site.
You are required to keep a hard copy and an electronic copy of your submitted
assignment to re-submit, in case the original submission is lost for some reason.
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Problem 1 – Efficiency analysis of workflow system
(8 marks)
John is the Chief Financial Officer of a very large software company that employs more than
5,000 programmers. He is committed to increase funding to the development of the
company’s new workflow system if at least 20% of his programmers agree that the system
significantly enhances their work efficiency. 700 programmers were randomly selected and
surveyed for this analysis. 175 programmers stated that they find the workflow system is
useful and boost their work efficiency. Estimate with 99% confidence the proportion of all of
the company’s programmers who find the new workflow system useful for their work
efficiency.
a) Suppose you were a researcher working for the data analytic department of the
company. Which formula would you select in solving the problem? Provide a brief
reason on your selection.
1 mark
b) Obtain the lower confidence limit and the upper confidence limit of the 99%
confidence interval estimate of the proportion of all the company’s programmers who
find the new workflow system useful for their work efficiency. Display working.
3 marks
c) Present an interpretation of the lower confidence limit and the upper confidence limit
obtained in part b) in the context of the problem.
1.5 marks
d) Based on the interval estimation you just conducted, present brief statements of two
or three sentences for John, the Chief Financial Officer. Should he allocate more
funding for the development of the company’s new workflow system? Yes or no?
Why?
1.5 marks
e) What would happen to the width of the interval when a lower sample size is used?
Assume all of the other variables to do the calculation of confidence interval held
constant.
1 mark
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Problem 2 – Used car price evaluation
(10 marks)
It is estimated that around 13% of the residents of Jakarta use cars to commute. Despite the
current Covid-19 pandemic, a large car dealership in the city reported that the demand for
used mid-size passenger sedans in the city has become stronger. The dealership further
claimed that the average selling price for used mid-size passenger sedans is now more than
$9,500. In verifying this, a random sample of 120 used mid-size passenger sedans is selected.
The average price calculated from the sample is $9,600. Assume that the population standard
deviation of the price is $1,200.
a) Suppose you were a junior business analyst working for the dealership. Assist the
dealership in performing a hypothesis test at a 10% level of significance to check
whether the dealership’s claim is supported. Display the six steps process (involving
drawing the rejection region/s and determining the critical value/s for the decision
rule) in performing the test.
6 marks
b) Specify the decision rule to use in the p-value method hypothesis testing. Calculate
the p-value of the test above. Display working.
2 marks
c) Which one of these two types of error (i.e Type I or Type II) you could make with the
conclusion you made in part a)? Briefly explain your selection.
1 mark
d) What is the required condition for ensuring that the sampling distribution of the
sample mean is approximately normally distributed? Check if the condition is satisfied
in the hypothesis testing that you just completed.
1 mark
Problem 3 – Consumer behaviour theory
(16 marks)
“Consumers are likely to purchase more of a good when the price of the good decreases, and
vice versa.”
As stated above, a marketing theory in the field of consumer behaviour believes that an
indirect relation is likely to exist between the price and the number of units purchased for
most of the goods and services. In examining this, you were commissioned as a student in
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the Business Data Analysis course to conduct a mock market research surveying a sample of
potential customers in purchasing a hypothetical new product. You randomly selected 16 of
your fellow students as the potential customers for the product. You questioned them on the
number of units they were likely to purchase for a given price that you set. The data you
collected from the mock survey are displayed below. You are tasked in performing the
relevant inferential analyses on the relation between the two concerned variables by
addressing the below set of questions.
Potential
Customer
Set Price
Number of units
purchased
in $
Matt
13
21
Kim
15
15
Ken
13.5
21
Tom
15
13
Tim
16.5
14
Anne
13.5
22
Will
14
19
Joe
14.2
17
Jim
16.5
13
Naomi
17
13
Mike
17.2
14
Megan
18
15
Jennie
20
17
Andy
21
14
Bill
19
17
Tony
19.5
16
a) Which of the two concerned variables is the dependent variable? Which one is the
independent variable? Give an explanation of the rationale of the selection of the
dependent and independent variables.
(1 mark)
b) The following sums have been computed:
∑ 𝑋𝑖 = 262.9
∑ 𝑌𝑖 = 261 ∑ 𝑋𝑖 𝑌𝑖 = 4227.2
∑ 𝑋𝑖2 = 4416.73
∑ 𝑌𝑖2 = 4395
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Use this info to calculate Sx2, Sy2 and Sxy. Display working.
(1.5 marks)
c) Calculate the sample correlation coefficient. Display working. Then, provide an
interpretation of the calculated correlation in terms of the relation between price and
number of units purchased.
(2 marks)
d) Calculate the slope coefficient of the sample linear regression. Then, calculate the
intercept coefficient of the sample linear regression. Display working.
(1 mark)
e) Write the estimated sample linear regression equation.
(1 mark)
f) Provide interpretations of the slope coefficient and the intercept coefficient of the
sample linear regression in terms of the relation between price and number of units
purchased.
(2.5 marks)
g) Predict the number of units purchased if price is $25. Display working. Comment on
the validity of this prediction.
(2 marks)
h) Calculate the coefficient of determination for the regression line. Provide an
interpretation of the calculated coefficient of determination in terms of the relation
between price and number of units purchased.
(2 marks)
i) Perform the relevant hypothesis test at the 5% level of significance to see if a negative
relation exists between price and number of units purchased. Display working of the
six-steps of the hypothesis test. The t test-statistic has been calculated. t calculated
= -2.35.
(3 marks)
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Problem 4 – Time spent for meeting during Covid
(6 marks)
A newspaper report stated that the hours spent by office workers in attending meetings have
increased substantially during Covid-19. A study is conducted to examine the amount of time
that office workers spend in attending meetings per week during the pandemic. The amount
of time that office workers spend in attending meetings per week during Covid is normally
distributed with a mean of 9 hours and a standard deviation of 1.5 hours.
a) What is the probability that one randomly selected office worker would spend more
than 6 hours per week for meetings? Display working.
1 mark
b) At most how much time per week (in hours) would be used by the 3% office workers
who spend the shortest amount of time for meetings? Display working.
2 marks
c) An analyst randomly selected five office workers. What is the probability that the
mean amount of time per week spent for meetings for those five workers is less than
11 hours per week? Display working.
1.5 marks
d) Further, the analyst randomly selected four other office workers. What is the
probability that the average amount of time per week spent for meetings for those
four workers is between 8 hours and 10.5 hours? Display working.
1.5 marks
—-End of Assignment—
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