University of Punjab PU Lahore M.A / M.SC. Economics Part 1 Past Paper of Statistics for Economics Annual Examination 2010

1. a) Differentiate between the following:

(i) Biased and Unbiased Error

(ii) Time Series and Cross Sectional Data

(iii) Parameter and Statistic

(iv) Quantitative and Qualitative Data

(v) Bar Chart and Pie Chart

b) State the advantages and disadvantages of Mean. Median and Mode.

c) Consider a sample with data values of 10. 20, 12, 17 and 16, Prove that AM > GM > HM, where AM = Arithmetic Mean, GM = Geometric Mean and HM = Harmonic Mean

2. a) Differentiate between Mean Deviation and Standard Deviation.

b) Differentiate between Absolute and Relative Measures of dispersion.

c) The mean marks of 40 Economics Students in a University is 44 while when we calculate the relative measure of variability, it was 18.2. Calculate Standard Deviation and Variance for these 40 students. What is the unit of measurements of these Measures of Dispersion?

d) The national average for the verbal portion of the College Board’s Scholastic Aptitude Test (SAT) is 507. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a Bell Shaped Distribution and the Empirical Rule for the verbal test scores.

(i) What percentage of the students have a SAT verbal score greater than 607?

(ii) What percentage of the students have a SAT verbal score between 307 and 607?

(iii) What percentage of the students have a SAT verbal score between 407 and 507?

3. a) The commercial division of a real estate firm conducted a study in Lahore to determine the extent of the relationship between annual gross rents (Rs. 1,000s) and the selling price (Rs. 1,000s) for apartment buildings. Data were collected on several properties sold and information is as following of Excel output:

(i) Complete ANOVA table

(ii) How many apartment buildings were in the sample?

(iii) Write the Estimated Regression Equation and interpret the regression coefficient.

(iv) Use the F test to determine whether the selling price is related to annual gross rents, α = 0.05.

b) How can you differentiate between Multiple and Partial Correlation Coefficients?

c) Make a clear note on Interpolation and Extrapolation.

4. a) What a Standard Error of Estimate? Explain it.

b) What are different assumptions of a Linear Regression Model?

c) From a large group of students, 10 students were taken as a sample. Their final marks in Economics (X), Statistics (Y) and Mathematics (Z) gave the relationship as following:

rYZ = 0.2354, rXY 0.96250 and rXZ = 0.0360

(i) Compute Correlation Matrix.

(ii) Detect and interpret Multi-collinearity between the variables.

(iii) Compute Partial and Multiple Correlation Coefficients.

5 a) State the difference between the following:

(i) Sampling and Non-Sampling Error

(ii) Permutation and Combination Formula

(iii) Discrete and Continuous Random Variable

(iv) Probability and Non Probability Sampling

(v) Population and Sample

b) Gasoline prices reached record high level in 16 cities dung 2009. Two of the affected cities were Lahore andKarachi. The Pakistan Automobile Association reported a sample mean price of Rs. 2.04 per gallon in Lahore and a sample mean price of Rs. 1.72 per gallon in Karachi. Use a sample size of 40 for the Lahore data and a sample size of 35 for the Karachi data. Assume that prior studies indicating a population standard deviation of 0.10 in Lahore and 0.08 in Karachi arc reasonable.

(i) What is a point estimate of the difference between the population mean prices per gallon in Lahore and Karachi?

(ii) At 95% confidence, what is the margin of error?

(iii) What is the 95% confidence interval estimate of the difference between the population mean prices per gallon in the two cities?

6. a) Explain the different steps in constructing Price Index Numbers.

b) Write a short note on CPI versus GDP Deflator. Where we use CPI and where we recommend GDP Deflator.

c) The take-home pay of Ahmed Bilal and the CPI for 2003 and 2009 are:

(i) What was Ahmed Bilal’s real income in 2003?

(ii) What was Ahmed Bilal’s real income in 2009?

(iii) Interpret your findings.

7. Write a short note on any three of the following.

(i) Properties of Normal Distribution

(ii) Non-Linear Regression Models

(iii) Four Factors of a Time Series

(iv) Box Plot and Detailed Box Plot