Assignment 2 QM2 PDF

Preview

Summary

The 2nd assignment for qm2...

Description

1

ECON20003 – QUANTITATIVE METHODS 2 Second Semester, 2019 Assignment 2 Due date and time: Friday 20 September, 4:00PM Please read the following instructions carefully before starting working 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 4:00 PM on Friday 20 September. Any assignment not submitted by this due date and time will be given a mark of zero.



Students can work on the assignment in groups of two (not in groups of three, four etc.). Students should form their own groups, but both members of an assignment pair must be enrolled in the same tutorial class. 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. No credit will be given for group assignments where members of the group do not come from the same tutorial class, or where there are more than two students in a group. Individuals may work alone and submit their own assignment answers, if they wish to do so.



Please note that the assignment submission process has two stages: 1. Registering your assignment group, and 2. Submitting the assignment online via the LMS. To register your group (only necessary for pairs), go to the link that will be placed on the LMS (under Assignment Group Registration) and follow the instructions. The deadline for registering your group is 5:00 PM on Friday 13 September. Students making an individual submission do not have to register: single--member groups will be created automatically after group registration has closed. If a pair fails to register their group before the deadline for group registration, both students will need to make an individual submission. A separate link will be given to submit your assignment on Friday 13 September.



Relevant EViews printouts must be pasted in the assignment and then the whole assignment must be converted into PDF before submitting online via

ECON20003

Semester 2, 2019

Assignment 2

2

the LMS. Students should preview their assignment after uploading on the LMS to ensure they have uploaded the correct/complete assignment, and the 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. 

Please make sure to include a cover page with student IDs and the names of both group members.

Assignment Tasks and Questions Exercise 1

(40 marks = 15 + 15 +10)

In an effort to reduce absenteeism, an electronics company initiated a program under which employees could participate in a monthly lottery, provided that they had perfect attendance and punctuality during the month. A 100AUD cash prize was awarded to the winner of each monthly lottery. Approximately 80 employees participated in the program. In order to assess the impact of the program, comparisons were made between sick leave expenditures (AUD) for eight randomly selected months before and six randomly selected months after the system was instituted. The expenditures are recorded and shown in the table below.

Before

After

903

746

812

775

1012

596

855

767

826

469

814

670

755 690 (a)

Based on these data, can we conclude at the 5% significance level that the mean monthly sick leave expenditure is lower after the institution of the program? Perform the appropriate parametric test with EViews, assuming that the underlying requirements are satisfied. Do not forget to specify the null and

ECON20003

Semester 2, 2019

Assignment 2

3

alternative hypotheses, to identify the observed test statistic value, to make a statistical decision, and to draw an appropriate conclusion. (b)

The parametric test in part (a) assumes that the sampled populations are at least approximately normally distributed. Since, due to the small sample sizes, this assumption cannot be verified this time, perform an appropriate non-parametric test at the 5% significance level. Do the calculations manually. Specify the null and alternative hypotheses, show the details of your calculations, define the decision rule, make a statistical decision, and draw an appropriate conclusion. Have you arrived at the same conclusion than in part (a)?

(c)

Perform the test used in part (b) with EViews. Can you base your decision on the Probability value reported by EViews? Using only your EViews printout, show that your manual calculations in (b) were indeed correct.

Exercise 2

(30 marks: 10 + 16 + 4)

A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces its helmets transmit to wearers when subjected to an external force. The manufacturer has designed the helmets so that the mean force transmitted by the helmets to the workers is 400 kg (or less) with a standard deviation to be less than 20 kg. Tests were run on a random sample of 40 helmets, and the sample mean and sample standard deviation were found to be 412.5 kg and 24.25 kg, respectively. (a) Estimate the population variance of the force transmitted by the helmets with 95% confidence. Show the details of your calculations. (b) Do the data provide sufficient evidence, at the α = 0.05 level, to conclude that the population standard deviation of the force transmitted by the helmets exceeds 20 kg? Specify the null and alternative hypotheses, show your calculations, make and explain your statistical decision, and draw an appropriate conclusion. (c) What assumption did you have to make to validate the statistical procedures in parts (a) and (b)?

ECON20003

Semester 2, 2019

Assignment 2

4

Exercise 3

(30 marks: 16 + 14)

A consumer testing service compared the effectiveness of four different brands of drain cleaner. The experiment consisted of using each product on 50 different clogged sinks and measuring the amount of time that elapsed until each drain became unclogged. The recorded times were measured in minutes and saved in the a2e3.xlsx spreadsheet. (a) Which techniques should be considered to determine whether the four brands of drain cleaner differ in terms of their effectiveness? What are the required conditions of these techniques? Are they satisfied this time? Explain your answer and support it with as much statistics as possible. (b) Based on your answer in part (a), which technique appears to be the most appropriate this time? Perform it with EViews. Can you conclude at the 5% significance level that differences exist between the average speeds at which the four brands of drain cleaners unclog the sinks? Do not forget to specify the null and alternative hypotheses, to identify the test statistic, to make and explain your statistical decision, and to draw an appropriate conclusion.

ECON20003

Semester 2, 2019

Assignment 2...