ECON20003 Semester 2, 2022 Assignment 2 ECON20003 – QUANTITATIVE METHODS 2 Second Semester, 2022 Assignment 2 Due date and time: Monday 19 September, 10:00AM 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 19 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 9 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 2 ECON20003 Semester 2, 2022 Assignment 2 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 = 10 + 10 + 6) The management of a large fleet of vehicles is concerned about vehicle downtime, i.e., about the number of days a vehicle is unavailable due to some repair after an accident, and decided to experiment with a new bumper that might reduce the damage in low-speed collisions. In order to see whether this new bumper is indeed effective, she took a random sample of the company’s cars and had the new bumper installed on them for a trial period of two months. At the end of the trial period, accident data showed that the cars with the new bumper had 12 repair incidents, while during the same period another random sample of cars equipped with the original bumper had 9 repair incidents. Vehicle downtime due to these repair incidents are shown in the following table. New Original 9 7 2 5 5 7 12 4 5 18 4 4 7 8 5 14 11 13 3 7 1 In this table New and Original denote vehicle downtime in number of days per repair incident for cars with the new bumper and with the original bumper, respectively. 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. 3 ECON20003 Semester 2, 2022 Assignment 2 (a) (10 marks) Do these data provide sufficient information to indicate at the 5% significance level that the new bumper reduces the variance of vehicle downtime Briefly discuss the steps of the test you perform showing all relevant details. (b) (10 marks) Do these data provide sufficient information to indicate at the 5% significance level that the new bumper reduces mean vehicle downtime Briefly discuss the steps of the test you perform showing all relevant details. (c) (6 marks) What are the requirements of the hypothesis tests you performed in parts (a) and (b) Are the requirements about the experimental design, the variable of interest and the measurement scale met Explain your answers. Exercise 2 (38 marks = 12 + 14 + 12) To make children’s toys safer and more difficult to change, toy packaging has become cumbersome for parents to remove in many cases. Accordingly, the director of marketing at Toys4Tots, a large toy manufacturer, wants to evaluate the effectiveness of a new packaging design that engineers claim will reduce customer complaints. Customer satisfaction surveys were sent to 250 randomly selected parents who registered toys packaged under the old design and 250 randomly selected parents who registered toys packaged under the new design. Of these, 85 parents expressed dissatisfaction with packaging of the old design, and 70 parents expressed dissatisfaction with packaging of the new design. Suppose that the director charges you to test whether the new packaging design can be indeed expected to reduce customer complaints. (a) (12 marks) Perform the appropriate test with R at the 5% significance level. State the hypotheses, report the observed test statistic, make a statistical decision, and draw the implied conclusion. 4 ECON20003 Semester 2, 2022 Assignment 2 (b) (14 marks) Suppose now that you have access neither to R nor to a computer, so you can only perform the test by manual calculations. Briefly discuss the steps and show all relevant details of your calculations. Is your observed test statistic the same as the one reported by R in part (a) Do you arrive at the same decision and conclusion as in part (a) (c) (12 marks) What conditions are required by the tests you performed in parts (a) and (b) Are they satisfied this time Provide as many supporting evidence as possible. Exercise 3 (36 marks = 10 + 14 + 4 + 8) Ten patients suffering from arthritis take part in an experiment to evaluate the relative effectiveness of three pain-relieving drugs. The following table shows how they ranked the three drugs in order of effectiveness (1: least effective, 3: most effective). Drug Patient X Y Z A 1 2 3 B 1 2 3 C 1 2 3 D 1 3 2 E 1 2 3 F 1 3 2 G 2 1 3 H 1 3 2 I 2 1 3 J 1 3 2 This data is also saved in the a2e3.xlsx file. (a) (10 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. 5 ECON20003 Semester 2, 2022 Assignment 2 (b) (14 marks) Do these data provide sufficient evidence to indicate at the 1% significance level that the three drugs are not equally preferred State the hypotheses, perform the appropriate test with R, report the observed test statistic, make a statistical decision, and draw the implied conclusion. (c) (4 marks) Calculate the test statistic manually for the test you performed with R in part (b). Does your test statistic match the one reported by R (d) (8 marks) What are the requirements of the test you performed in parts (b) and (c) Are they satisfied this time, or you have to assume that they are met Provide as many supporting evidence as possible.
