Assignment 2 PDF

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ECON20003 – QUANTITATIVE METHODS 2 First Semester, 2019 Assignment 2 Due date and time: Thursday 2 May, 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.

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This assignment must be submitted online via the LMS by 4:00 PM on Thursday 2 May. Any assignment not submitted by this due date and time will be given a mark of zero.

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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.

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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 10.00 AM on Monday 29 April. 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 (under Assignment Submission) will be added to LMS on Monday 29 April through which to submit your assignment.

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Relevant EViews printouts must be pasted in the assignment and then the whole assignment must be converted into PDF before submitting online via the LMS. Students should preview their assignment after uploading on the LMS to ensure they have uploaded the correct/complete assignment, and

ECON20003

Semester 1, 2019

Assignment 2

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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)

The following pairs of matching observations were drawn randomly from two quantitative and continuous populations measured on a ratio scale: Pair 1 2 3 4 5 6

Sample 1 9 12 13 8 7 10

Sample 2 5 10 11 9 3 9

(a) Suppose we wish to test whether the central locations of the sampled populations differ. In general, the central location of a population can be captured by its mean, the median and the mode. Which of them is the most appropriate this time for the purpose of hypothesis testing and (briefly) why? State the null and alternative hypotheses in terms of this parameter. (b) Based on the provided information, which tests can be used to test the null hypothesis in part (a)? What assumptions do we need to make to be able to rely on these tests? Explain your answer. (c) Conduct the test(s) you deemed appropriate in part (b) at the 10% significance level assuming that the required conditions are satisfied. Do all calculations manually (i.e. with a hand calculator and the appropriate probability tables) and show your working. Report your statistical decision(s) and the conclusion(s).

ECON20003

Semester 1, 2019

Assignment 2

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Exercise 2

(30 marks)

At the height of the energy shortage during the 1970s, governments were actively seeking ways to persuade consumers to reduce their energy consumption. Among other efforts undertaken, several advertising campaigns were launched. To provide input on how to design effective advertising messages, a poll was taken in which people were asked how concerned they were about shortages of petrol and electricity. There were four possible responses to the questions: 1 = Not concerned at all, 2 = Not too concerned, 3 = Somewhat concerned, and 4 = Very concerned. A poll of 150 individuals was undertaken. Their responses, labelled as petrol and electricity, are saved in the a2p2.xlsx file. (a) Identify the type and measurement scale of both variables. Explain your answer. Suppose we would like to find out whether people’s concern about a petrol shortage exceeded their concern about an electricity shortage. (b) State the null and alternative hypotheses. Denote the responses given to the questions as X1 for petrol and X2 for electricity. (c) Which test(s) can be used for these hypotheses and why? (d) Conduct the test(s) you deemed appropriate in part (c) at the 5% significance level with EViews. Based on the EViews printout, what is your statistical decision and conclusion and why?

Exercise 3

(30 marks)

A university administrator has noted that an 80% average at a high school with low standards of grading may be equivalent to a 70% average at another school with higher standards. In an effort to more equitably compare applications, a pilot study was initiated. Independent random samples of students who were admitted the previous year from four local high schools were drawn. All of the students entered the business program with averages of between 70% and 80%. Their average grades in the first year at the university were calculated and saved in the a2p3.xlsx file as S1, S2, S3 and S4.

ECON20003

Semester 1, 2019

Assignment 2

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In this question, we investigate whether there are differences in grading standards between the four high schools. (a) Set up the null and alternative hypotheses. (b) Perform the ANOVA F-test with EViews at the 5% significance level, assuming that the underlying conditions are satisfied. Based on your EViews printout decide whether or not to reject the null hypothesis and draw a conclusion. c) The ANOVA F-test has three required conditions, including normality. Suppose you are not convinced about normality. Perform the Kruskal-Wallis test with EViews at the 5% significance level. What are the null and alternative hypotheses this time? Based on your EViews printout decide whether or not to reject the null hypothesis and draw a conclusion.

ECON20003

Semester 1, 2019

Assignment 2...