Statistics and Analysis

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:

55 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 used only for drawing, sketching or graphical work. Show the working steps in your answers.

Question 1 [18 marks in total]

(a)

In hypothesis testing, what is a Type I error and what is a Type 11 error? What is the motivation of choosing a small a (level of significance)? [3 marks] What conditions are required to be satisfied in order for a random variable to follow a binomial distribution? [3 marks] LetXbe a normally distributed variable with mean 11 and variance (32. Find the probability that the values of X are located within one standard deviation around the mean. [3 marks] Let eland

(b)

(c)

(d)

e 1 be two estimators of a population parameter, e. What is the

meaning that eland e 1 are unbiased estimators of e? Given that both estimators are unbiased and consistent, how do we further assess the quality of the two estimators? [3 marks] (e) What are the different approaches of assigning probabilities to events of a random experiment? Show the usefulness of all these approaches with examples. [3 marks] What is the main criteria or the objective that the ordinary least squares (OLS) method satisfies to approximate the linear relationship between two variables X and Y, where X is the 'cause' and Y is the 'effect' of the relationship. [3 marks]

(t)

2...