Document Sample

B.A. (H) Economics I Year MOCK TEST STATISTICAL METHODS IN ECONOMICS Time : 2 Hours Maximum Marks : 38 Attempt All questions. Use of simple calculator is allowed 1. (a) For the numbers (X) : 1, 3, 4, 5 and 12, find: (i) the value v for which X v is minimized. 2 (ii) the value v for which X v is minimized. 2 (b) The first four moments about 4 are 1, 3, 43 and 146. Is the data consistent? Explain. 2 Or (a) Given that mean of a distribution is 50 and mode is 58: 2 (i) Calculate the median; (ii) What can you say about the shape of the distribution? Explain why? (b) Given that the mean of a distribution is 5, variance is 9 and the moment coefficient of skewness is –1, find the first three moments about the origin. 2 2. (a) A random variable has the following probability distribution : Value of X : 0 1 2 3 Probability : 0.1 0.3 0.4 0.2 Find (i) E(X) and (ii) Var (X) 3 (b) If the random variable X is normally distributed with mean μ and variance σ 2 , derive the mean and variance of the variable z X μ /σ . 3 (c) Prove that two mutually exclusive events with positive probabilities cannot be independent. 4 Or (a) (i) Write the axioms of probability. (ii) What is the chance that a leap year selected at random will contain 53 Sundays? 3 Bliss Point Studies 1 Amit 9811343411 9891555578 www.ecoblisspoint.com B.A. (H) Economics I Year MOCK TEST (b) The probability that a teacher will give an unannounced test during any class meeting is 1/5- If a student is absent twice, what is the probability that he will miss at least one test? 3 (c) In an examination a student passes if he secures 30% or more marks. He is placed in the first, second or third divisions accordingly as he secured 60% or more marks, between 45% and 60% marks and between 30% and 45% respectively. He gets a distinction in case he secures 80% or more marks. It is noticed from the results that 10% of the students failed whereas 5% of them obtained distinction. Calculate the percentage of students placed in the second division. (Assume marks to be normally distributed). 4 3. (a) Differentiate between Type I and Type-II errors. 2 (b) Show that sample variance is a consistent estimator but not an unbiased estimator of population variance. What would be an unbiased estimator of the population variance? 4 (c) A die is suspected of being biased. It is rolled 24 times with the following result. Conduct a significance test to see if it is biased : 4 Outcome Frequency 1 8 2 4 3 1 4 8 5 3 6 0 Or (a) An international airline analyzed the data on 200 randomly selected booking of seats according to the method used for making reservations and the class of travel. The results are presented below: Reservation Method Class of Travel Travel Agent Internet Toll-free no. Business Class 18 11 9 Economy Class 55 65 42 Test at 5% level of significance the airline’s belief that class of travel is unrelated with the method used for reservations. 4 (b) A population consists of the numbers 12, 14 and 16. (i) Enumerate all possible samples of size two which can be drawn from the population (without replacement). (ii) Show that the mean of the sampling distribution of the sample means is equal to the population mean. (iii) Calculate the variance of the sampling distribution of the sample mean and show that it is less than the population variance. 3 Bliss Point Studies 2 Amit 9811343411 9891555578 www.ecoblisspoint.com B.A. (H) Economics I Year MOCK TEST (c) (i) Distinguish between a parameter and a statistic. (ii) Derive the variance of the sampling distribution of the sample mean. Is it more than population variance? 3 4. (a) In regression analysis, the sum of squares of the deviations about the mean for the predicted scores is 80 and the sum of squares of the error is 40, what is R 2 ? Explain. 3 (b) The rank correlation of physical fitness contest involving 12 participants was calculated as 0.6. However, it was later discovered that the difference in ranks of a participant was read as 8 instead of 3. Find the correct coefficient of rank correlation. 3 (c) Given the regression line Y 2.27X 0.79, r 2 0.98, Sx 26.67, SY 17.68 , for 9 pairs of observations, calculate : (i) Standard error of the regression of Y on X; (ii) Standard error of the regression coefficient b y x ; (iii) 95% confidence interval for the population regression coefficient βyx . 4 Or (a) The equations of two regression lines between two variables are expressed as 2X – 3Y = 0 and 4Y – 5X – 8 = 0 (i) Identify which of the two can be called regression of Y on X and X on Y. (ii) Find the means of the variables. (iii) Determine rXY . 3 (b) The following results were obtained from a random sample of 50 observations from a bivariate distribution: sx = 3.65, sy= 7.3 and rxy=0.6, where sx and sy are sample standard deviations and rxy is sample correlation coefficient between X and Y. Calculate: (i) The regression coefficient byx; (ii) The standard error of the regression coefficient of Y on X (SEb). (iii) Test the hypothesis: β y x 0 . 4 Bliss Point Studies 3 Amit 9811343411 9891555578 www.ecoblisspoint.com B.A. (H) Economics I Year MOCK TEST (c) What do you mean by the standard error of estimate of the linear regression of Y on X? If two variables are perfectly correlated, find the standard error of estimating Y from X. 3 5. (a) Show that in general, the Laspeyre’s Price Index is greater than the Paasche’s Index. When would this not be so? 3 (b) Show that Laspeyre’s Price Index can be written as a weighted average of price relatives. What are the weights? 1 Or (a) During a certain period the consumer price index increased from 110 to 200 and the salary of a worker also increased from Rs. 3500 to Rs. 5000. What is the real gain, if any, to the worker? 1 (b) A fresh graduate is offered jobs by a recruiting company in cities A and B. He is offered monthly salary of Rs. 20000 in A and Rs. 18000 in B. Given that the consumer price index is 180 in A and 150 in B. (i) Which job offer should he accept? (ii) How much should be the minimum salary at which he would accept the other job offer? 3 ***** Bliss Point Studies 4 Amit 9811343411 9891555578 www.ecoblisspoint.com

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 32 |

posted: | 9/23/2011 |

language: | English |

pages: | 4 |

OTHER DOCS BY stariya

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.