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ECON20003 – QUANTITATIVE METHODS 2

Second Semester, 2021

Assignment 2

Please read the following instructions carefully before starting to work on the assignment.

● There is a total of 100 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 September. 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. 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 A2 1, A2 2, A2 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 September. If a pair fails to register their group before the deadline for group registration, both students will need to make an individual 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. Paste your R/RStudio scripts, screenshots, and printouts (graphs, output tables etc.) in the relevant sections of the document. Convert the whole 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    (26 marks = 8 + 10 + 8)

A loan officer intends to compare the interest rate for 48-month fixed-rate auto loans and 48-month variable-rate auto loans. She selects two independent random samples of 48-month auto loans and observes the following loan rates:

These data are saved in the a2e1.xlsx file.

Using this data set perform the following tasks. Do all calculations ‘manually’, i.e., with a hand calculator without using R, Excel or any other software, showing the relevant formulas and the major steps.

a) (8 marks)

Estimate and interpret the ratio of the population variances of the interest rates for 48-month fixed-rate and variable-rate auto loans with 90% confidence.

b) (10 marks)

Carry out an appropriate hypothesis test at the 5% significance level to see whether the population variance of the fixed-rate 48-months auto loans likely exceeds the population variance of the variable-rate 48-months auto loans. Briefly discuss the steps of the test showing all relevant details.

c) (8 marks)

What conditions are required by the confidence interval estimator and the hypothesis test in parts (a) and (b)? Are they likely satisfied? Explain your answer.

Exercise 2    (42 marks = 4 + 12 + 16 + 10)

On a given Saturday evening, a local newspaper randomly selects 20 patrons from each of two restaurants and asks them to rate the quality of their meal as 5 (excellent), 4 (good), 3 (average), 2 (poor), or 1 (unsatisfactory). The following results are obtained:

These data are saved in the a2e2.xlsx file.

Suppose that we wish to know whether these data provide sufficient evidence to conclude that patrons rate the Saturday evening meal higher in Restaurant 1 than in Restaurant 2.

(a) (4 marks)

What is the variable of interest? Is it qualitative or quantitative? If it is qualitative, is it ranked or unranked? If it is quantitative, is it discrete or continuous? What is its level of measurement? Explain your answers.

(b) (12 marks)

Given your answers in part (a), which test(s) do you think the researcher should perform? Explain your choice by discussing the required conditions. Are these conditions likely satisfied this time? Provide as many supporting evidence as possible.

(c) (16 marks)

Perform the test you think is the best this time at the 1% significance level. Do the calculations ‘manually’. Briefly discuss the steps of this test showing all relevant details.

(d) (10 marks)

Repeat the test you performed in part (c) with R/RStudio. Do you get the same results as in part (c)?

Exercise 3    (32 marks = 6 + 14 + 10 + 2)

A consumer preference study involving three different bottle designs (A, B, and C) for the jumbo size of a new liquid laundry detergent was carried out in four supermarkets (1, 2, 3, and 4). These four supermarkets were supplied with the new liquid laundry detergent in all three bottle designs. The new liquid laundry detergent was priced the same, irrespectively of the supermarket and the bottle design. The table below shows the number of bottles of new liquid laundry detergent sold in a 24-hour period at each supermarket. The same data are saved in the a2e3.xlsx file.

The study aims to find out whether there are differences in mean daily sales across the bottle designs, or across the supermarkets.

(a) (6 marks)

What is the variable of interest? Is it qualitative or quantitative? If it is qualitative, is it ranked or unranked? If it is quantitative, is it discrete or continuous? What is its level of measurement? What is the experimental design? Explain your answers.

(b) (14 marks)

Are there differences between the effects of the bottle designs on mean daily sales? Are there differences between the effects of the supermarkets on mean daily sales? Answer these questions by performing appropriate parametric tests at the 5% significance level with R. State the hypotheses, report the observed test statistics, make statistical decisions, and draw the implied conclusions.

(c) (10 marks)

Suppose that you are advised that the required conditions of the parametric tests you ran in part (b) might not be fully satisfied. Answer the questions in part (b) by performing this time appropriate nonparametric tests at the 5% significance level with R. State the hypotheses, report the observed test statistics, make statistical decisions, and draw the implied conclusions.

(d) (2 marks)

Compare the tests you ran in parts (b) and (c) to each other. Do they lead to the same or different conclusions? What if the significance level is reduced to 1%? Explain your answers.