THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF ECONOMICS ECON1203IECON2292 (ARTS) QUANTITATIVE METHODS B FINAL EXAMINATION Session 1, 2008
Time allowed: Two hours. Total marks:
There are three questions in this examination. Answer all three questions. The marks assigned to questions are not of equal value. The value of each sub-section of a question is indicated in brackets. On the front of your answer book, write the number of each question you have attempted. Statistical tables and useful formulae are attached to this examination paper. Electronic calculators may be used. The examination paper may be retained by the candidate. Answers must be written in ink. Pencils may be ...view middle of the document...
Question 2 [18 marks in total]
(a) Suppose that the annual percentage change in labour cost for a randomly selected company in Australia for the year 2006 approximately follows a normal distribution. The mean and standard deviation of a random sample of changes in labour cost for 16 companies turn out to be 5% and 12%, respectively.
Assume that the population standard deviation is known to be 12%. A confidence interval for the mean change in labour cost is constructed. Its upper confidence limit is 9.935%. What is the level of confidence? [3 Marks] Assume that the population standard deviation is unknown. Find 95% confidence interval for the mean change in labour cost. [3 marks]
A financial advisor uses the variance of annual return of stocks as a measure of investment risk. The distribution of the annual return of stocks in the market is approximately normal. The observed sample variance of annual return is found to be 0.0256 for 15 stocks randomly selected from the market. i. Construct the 90% confidence interval for the population variance of annual return. [3 marks] Interpret the numerical result found in b(i). [3 marks]
In order to test whether the average content of a particular brand of detergent powder packets is 1 kilogram (kg) as advertised, a random sample of 5 packets was selected. The observed contents were weighed and found to be: 1.1, 22.214.171.124,0.9 and 1.0 kgs.
What are the null and alternative hypotheses that need to be tested? [2 marks] Conduct the test using a significance level of a = 0.05 and assume that the distribution of the packet contents is normal. [4 marks]
Question 3 [19 marks in total]
For a linear regression model Yi = Po + Pr)C; + t:i to be valid, the error t:i must satisfy certain conditions. What are these conditions? [3 marks] The following summary output (Table 1) is obtained from a regression equation estimated using Microsoft Excel. The dependent variable (Y) is the Australian Imports (in billion $) and the independent variable (X) is the Australian Gross National Expenditure (in billion $). The model is:
Quarterly data from March 1981 to December 2000 comprising 80 observations was used to estimate the regression equation. In answering the following questions, assume that the basic assumptions about linear regression models are satisfied. Table 1: Output for linear regression of imports on gross national expenditure Regression Statistics R Square Observations
0.2750 80 p-value 0.0000 0.0098
Coefficients Standard Error t Stat 13 .8575 Intercept 4.4602 0.3219 X Variable 0.2408 0.0897 2.6845 (i) (ii) (iii)
What is the interpretation ofthe parameter PI. [2 mark] Find the 90% confidence interval for PI. [2 marks] Test the null hypothesis that PI = 0.3 against the alternative that PI < 0.3 at the 1% level of significance. Write down your decision rule and conclusion. [2 marks] The R Square is...