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ECON20003 Quantitative Methods 2

Second Semester, 2017

Assignment 1

Due date and time: Monday 21 August, 4:00PM

Please read the following instructions carefully before working on the assignment.

We cannot accept assignments where the instructions have not been followed.

This assignment must be submitted online via the LMS by 4:00 PM on Monday August 21.

Any assignment not submitted by this due date and time will be given a mark of zero. This

assignment is worth 5% of the final grade for QM2.

A group of two students (but no more than two students) may work together and submit

one set of assignment answers for the group. Both members of the group must be enrolled

in the same tutorial. Individuals may work alone if they wish, and submit their own

assignment answers, but I urge students to work in pairs.

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2. Submitting the assignment online via the LMS.

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are 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 16 August, after the assignment

group registration process is completed.

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the assignment. Students should form their own groups. No credit can be given for group

assignments where members of the group do not come from the same tutorial, or where

there are more than two students in a group.

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members.

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The World Bank is comparing the welfare of the citizens of Northland (NTH) with those of

Southland (STH). Of interest is their level of income, income inequality, poverty, and

happiness.

Random samples of 200 citizens of Northland and 100 citizens of Southland were taken. Data

from these samples is stored in the file assmt1.wf1. The variables in this file are:

INC_NTH Incomes of the sampled Northland citizens in thousands of dollars.

INC_STH Incomes of the sampled Southland citizens in thousands of dollars.

POV_NTH = 1 if a sampled individual in Northland is considered poor, otherwise 0.

POV_STH = 1 if a sampled individual in Southland is considered poor, otherwise 0.

HAP_NTH and HAP_STH are indicators of how happy each individual is in Northland

and Southland, respectively, according to the following scale.

Very unhappy 1

Unhappy 2

OK 3

Happy 4

Very happy 5

Wherever possible, EViews can be used to answer the following questions.

Question 1 (21 marks)

This question is concerned with using the variances of incomes from each country to compare

income inequality.

Is there evidence that the variances of income in the two countries are different? In your

answer:

(a) Specify suitable null and alternative hypotheses and define your notation.

(6 marks)

(b) Define a test statistic and specify its distribution assuming the null hypothesis is true.

(6 marks)

(c) Give the critical value(s) for a 5% significance level. (3 marks)

(d) Find the value of the test statistic. (3 marks)

(e) State your conclusion. (3 marks)

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Question 2 (16 marks)

In this question we investigate whether mean income is greater in Northland than it is in

Southland.

(a) Specify suitable null and alternative hypotheses and define your notation. (8 marks)

(b) Assuming that the variances of the incomes in Northland and Southland are the

same, find the p-value for a test designed to test the hypotheses in part (a).

(4 marks)

(c) At a 10% significance level, do you conclude that mean income in Northland is

greater than mean income in Southland? (4 marks)

Question 3 (16 marks)

In this question we investigate the degree of poverty in each of the two countries.

(a) Find estimates of the proportions of individuals who live in poverty in each of the

two countries. (4 marks)

(b) Find estimates of the variances of the sample proportions found in (a). (4 marks)

(c) Find an estimate of the variance of the difference between the two sample

proportions found in (a). (4 marks)

(d) Find an estimate of the variance of the difference between the two sample

proportions found in (a) assuming that the two population proportions of those living

in poverty in the two countries are equal. (4 marks)

Question 4 (17 marks)

In this question we investigate whether the citizens of Northland and Southland are equally

happy.

(a) What is the value of the test statistic Z for testing whether the citizens of Northland

and those of Southland are equally happy? (4 marks)

(b) The test statistic in part (a) has 3 components. Let’s call them a, b and c such that

a b Z

c

Find a, b and c. (9 marks)

(c) Would you conclude that the citizens of Northland and Southland are equally happy?

(4 marks)