ECON20003 Quantitative Methods Welfare of the Citizens of Northland

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ECON20003 Quantitative Methods 2
Second Semester, 2017
Assignment 1
Due date and time:  Monday 21 August, 4:00PM
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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)