Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: THEend8_
ECON20003 Semester 1, 2023
Assignment 1
ECON20003 – QUANTITATIVE METHODS 2
First Semester, 2023
Assignment 1
Due date and time: Monday 27 March, 10:00AM
Please read the following instructions carefully before starting to work on the
assignment.
• There is a total of 43 marks for this assignment. It is worth 5% of the final
grade for QM2.
• This assignment must be submitted online via the LMS by 10:00AM on
Monday 27 March. Any assignment not submitted by this due date and time
will be given a mark of zero.
• Students may work alone and submit their own assignment answers, if they
wish to do so, or they can work on the assignment in pairs. In the latter case,
each assignment pair must submit only one set of assignment answers and
both students of the pair will receive the same mark for their assignment.
You are not required to be in the same tutorial to form a pair. It is not
allowed to form assignment groups of more than two students.
• Please note that the assignment submission process has two stages:
1. Registering your assignment group (only if you work in a pair), and
2. Submitting the assignment online via the LMS.
Students who intend to work on the assignment in pairs must register their
groups. To do so, click the “People” link and then the Groups tab in the
Canvas course navigation menu. The group names (set by default) are A1 1,
A1 2, A1 3 etc. Every assignment pair MUST register as one of these created
groups for submitting the assignment and not create a new group. The
deadline for registering your group is 5:00PM on Friday 17 March. If a pair
fails to register their group before the deadline for group registration, both
students will need to make an individual, i.e., sufficiently different,
submission.
Students making an individual submission do not need to register.
• Answer the assignment questions using Microsoft Word. Make sure to
include a cover page in the document with the student ID, the name, and the
tutorial group of each group member.
• If a task involves some manual calculations, use a calculator (not R, Excel,
or any other software), the relevant statistical table(s), and show the major
steps, including the formulas in the document. If a task involves using R /
RStudio, paste your relevant scripts, screenshots, and printouts (graphs,
output tables etc.) in the document.
2
ECON20003 Semester 1, 2023
Assignment 1
• Convert the whole Microsoft Word file to PDF before submitting it online via
the LMS.
• Do not forget to preview your assignment after uploading on the LMS to
ensure that you have indeed uploaded the correct and complete assignment,
and that its formatting is in order as in their original document. Submissions
that are late because of formatting issues or because a version is
incomplete, will not be accepted.
Assignment Tasks and Questions
Exercise 1 (4 marks = 1 + 1 + 1 + 1)
A large population is not normally distributed with a mean and a variance of 4 and 16,
respectively. Consider the sampling distribution of the sample mean based on simple
random samples of size 100. Answer the following questions by performing all required
calculations manually.
(a) (1 mark)
What can you tell about the shape of this sampling distribution? Explain why this is
the case.
(b) (1 mark)
What are the mean and the standard deviation of this sampling distribution?
(c) (1 mark)
What is the probability that the mean of a single sample is at most 5.5?
(d) (1 mark)
What proportion of the sample means are between 3 and 5?
3
ECON20003 Semester 1, 2023
Assignment 1
Exercise 2 (23 marks = 3 + 6 + 2 + 6 + 6)
An online retailer is looking to improve its delivery time to customers. The company
believes that by using a new shipping method, it can reduce the mean delivery time
below 5 business days. The company takes a random sample of 50 deliveries using
the new shipping method. These observations are available in the a1e2.xlsx Excel file.
(a) (3 marks)
Launch RStudio, create a new RStudio project and script, and name both of these
as a1e2. Import the data set from the a1e2 Excel data file to RStudio and save it
as well as a1e2.RData. Attach the data to your RStudio project. Take a screenshot
of your RStudio window and paste it into your assignment.
Perform the following tasks with RStudio / R.
(b) (6 marks)
Obtain the smallest observation, the largest observation, the range, the 1st quartile,
the median, the 3rd quartile, the mean, the standard deviation, and the coefficient
of variation for delivery_time. What do these statistics tell you about the number of
business days it took to delivery items using the new shipping method? Provide a
precise interpretation of each of these statistics.
(c) (2 marks)
Construct a 95% confidence interval for the population mean number of days to
delivery using the new shipping method. Interpret your confidence interval.
4
ECON20003 Semester 1, 2023
Assignment 1
(d) (6 marks)
Perform an appropriate test at the 5% significance level on the sample data to see
whether the new shipping method is a success. Specify meaningful null and
alternative hypotheses, calculate the observed test statistic, make a statistical
decision based on the p-value, and draw an appropriate conclusion (following the 6
steps of hypothesis testing mentioned in lectures).
(e) (6 marks)
What conditions are required to validate the confidence interval and the test in
parts (c) and (d)? Are they likely satisfied? Use as much evidence as you can to
support your answers.
Exercise 3 (16 marks = 2 + 6 + 8)
A coffee shop owner wants to determine if the median customer satisfaction score for
their coffee is higher than the industry median of 80 on a scale of 1 to 100. The owner
randomly selects 100 customers and asks them to rate the coffee on this satisfaction
scale. These scores are available in the a1e3.xlsx Excel file. Perform all required
calculations and tasks with RStudio / R.
(a) (2 marks)
Granted that the required conditions are satisfied, which tests can be used to
answer the research question? Explain your answer.
(b) (6 marks)
Perform the tests you nominated in part (a) at the 1% significance level. For each
test specify the null and alternative hypotheses, the observed test statistic, make
a statistical decision based on the p-value, and draw an appropriate conclusion
(following the 6 steps of hypothesis testing mentioned in lectures).
(c) (8 marks)
What conditions are required to validate the tests you performed in part (b)? Are
they likely satisfied this time? Which test do you think is the best this time? Explain
your answers and provide as much evidence as you can.