2007 Institute of Chartered Financial Analysts of India (ICFAI) University Management M.B.A Quantitative Methods (MB151): January 2004 Question paper
Question Paper Quantitative Methods (MB151): January 2004 Section A : Basic Concepts (30 Marks) • This section consists of questions with serial number 1  30. • Answer all questions. • Each question carries one mark. 1. Which of the following is the binary equivalent of the decimal number 57? a. 111000 b. 101001 c. 111001 d. 100111 e. 101010. < Answer > 2. How many different numbers can be formed by using six out of the nine digits 1, 2, 3, 4, 5, 6, 7, 8, 9? a. 54 b. 84 c. 15120 d. 60480 e. 181440. < Answer > 3. The sum of the 20 terms of the series 3, 5, 7, 9, 11…. is a. 440 b. 450 c. 460 d. 470 e. 480. < Answer > 4. If a function is defined such as y = f(x) = 5 x + 4, then the inverse function can be denoted as a. (y – 5) / 4 b. (y – 4) / 5 c. 5y + 4 d. 4y + 5 e. 4x + 5. f 1(x) < Answer > 5. Which of the following is not correct about construction of bar charts? a. All bars should rise from the same base line b. The gaps between the bars should be uniform c. The bars should be arranged from the left to right d. Length of the bars should be proportional to the data represented e. Width of the bar should be proportional to the data represented. < Answer > 6. Which of the following is used to represent data in the form of pictures, where the size of the picture is proportional to the magnitude of the data? a. Bar chart b. Line chart c. Pictogram d. Pie chart e. Scatter diagram. < Answer > e. Scatter diagram. 7. Which of the following is not true about median? a. Median is not strongly affected by the extreme values b. It can be also be calculated from grouped data c. It can also be calculated for qualitative data d. It can not be computed for grouped data having openended classes e. It involves a time consuming process for raw data as the data has to be arranged. < Answer > 8. For a given data set, the values of mode and median were found to be 50.25 and 65.50 respectively; then the mean of the data set is approximately equal to a. 27.125 b. 57.875 c. 59.250 d. 73.125 e. 85.325. < Answer > 9. If the quartiles, Q1 = 52.0 and Q3 = 65.0, then the coefficient of quartile deviation is equal to a. 9.00 b. 0.11 c. 0.80 d. 1.25 e. 0.64. < Answer > 10. Which of the following is not true about mean absolute deviation? a. Mean deviation is obtained by calculating the absolute deviations of each observation from mean b. Mean deviation is a more comprehensive measure compared to range c. It is conducive to further algebraic treatment d. It cannot be computed for distributions with open end classes e. It can also be computed for grouped or continuous frequency distribution. < Answer > 11. If the b coefficient for regression equation of Y on X is 0.75, and the b coefficient for regression equation of X on Y is 1.05, then the coefficient of correlation for the given data set is a. 0.81 b. 0.83 c. 0.85 d. 0.87 e. 0.89. < Answer > 12. If the points in a scatter diagram show a very little spread and a tendency to rise from the left to the right along the horizontal axis, then we can conclude that a. There is perfectly positive correlation b. There is perfectly negative correlation c. There is no correlation d. There is high degree of positive correlation e. There is low degree of negative correlation. < Answer > 13. Which of the following is not correct about standard error of estimate? a. It measures the reliability of the estimating equation b. It is the measure of variation of the observed values around the regression line c. The smaller the value of the standard error of estimate, the farther are the observations from the regression line d. The larger the value of the standard error of estimate, the farther are the observations from the regression line e. If the value of the standard error of estimate is zero, then there is no variation of the observations from the regression line. < Answer > from the regression line. 14. The value of the coefficient of correlation between two variables can take values in the range of a. 0 and 1 b. –1 and 1 c. –1 and 0 d. 0 to 8 e. –8 to 8. < Answer > 15. The value index number measures the a. Changes in prices of a basket of commodities from one period to another b. Changes in quantities consumed of a basket of commodities over a period of time c. Change in the total monetary value of a basket of commodities over a period of time d. Change in the retail prices of various commodities e. Change in the general price level in a country. < Answer > 16. Which of the following weighted price index numbers uses only the quantity measures for the current period as weights? a. Laspeyre's price index b. Paasche price index c. Fisher's ideal price index d. Fixed weight aggregates price index e. Weighted aggregates index. < Answer > 17. A card is drawn from a pack of cards randomly. What is the probability that the card drawn is a King of Spade? a. 1/4 b. 1/13 c. 1/51 d. 17/52 e. 1/52. < Answer > 18. If A and B are nonmutually exclusive events such that P(A) = 0.25, P(B) = 0.40 and P(AB) = 0.10, then P(A or B) is equal to a. 0.06 b. 0.10 c. 0.55 d. 0.65 e. 0.80. < Answer > 19. Which of the following is true about Binomial Distribution? a. It is a continuous distribution b. The probability of the outcome of any trial varies over time c. Each trial will have more than two possible outcomes d. The outcomes of the trials are statistically independent of each other e. None of the above. < Answer > 20. A fair coin is tossed five times. If getting head is defined as success, what is the probability of getting exactly four successes in the five tosses? a. 0.25725 b. 0.15625 c. 0.31250 d. 0.10325 e. 0.03125. < Answer > e. 0.03125. 21. A market researcher wants to find out the buying behavior of the typical household during the weekends. He divides the city into various localities such that each locality represents the city population in terms of age group, gender and social status. Then he randomly selects five localities and surveys each household. Which of the following sampling techniques best describes the method used by the researcher? a. Cluster sampling b. Systematic sampling c. Stratified sampling d. Convenience sampling e. Sequential sampling. < Answer > 22. Which of the following is not a type of random sampling? a. Simple Random sampling b. Stratified sampling c. Systematic sampling d. Judgmental sampling e. Cluster sampling. < Answer > 23. A Type II error is said to be committed in a test of hypothesis when a. The null hypothesis is true but rejected b. The null hypothesis is true and accepted c. The null hypothesis is false but accepted d. The null hypothesis is false and rejected e. The alternative hypothesis is true and accepted. < Answer > 24. The manager of a cyber café says that the number of customers visiting on the weekdays follows a binomial distribution. Which of the following techniques can be used to accept this hypothesis at a given level of significance? a. Test of significance of mean b. Chi square test as a test of goodness of fit c. Test of significance of difference between two means d. Correlation analysis e. Regression analysis. < Answer > 25. Which of the following is not true about decision tree analysis? a. Decision tree is a diagrammatic representation of a decision process b. It is an excellent tool for making financial or number based decisions c. Alternative decisions and the implications of taking those decisions can be laid and evaluated d. Decision tree cannot help in assessing the risk in making decisions concerning investment e. Decision tree analysis can be used with the help of computer. < Answer > 26. If the objective function of a profit maximizing linear programming problem is parallel to an edge of the feasible region, which is in the direction of the optimal movement of the objective function, then which of the following statements is true? a. There are multiple optimal solutions to the problem b. The constraint equations have been formulated incorrectly c. There cannot be any optimal solution to the problem d. There is only one optimal solution to the problem e. The problem cannot be solved graphically. < Answer > 27. Which of the following is not a requirement of a linear programming problem? a. The problem must have a well defined single objective to achieve b. There must be alternative courses of action, one of which will achieve the objective c. The decision variables should be able to take any nonnegative value d. The objective and constraints must be linear functions of the decision variables e. The resources need not be limited in supply. < Answer > e. The resources need not be limited in supply. 28. Consider the following formulation of a linear programming problem: Maximize Z = 12x1 +15x2 Subject to : x1 = 15 x2 = 10 x1 +x2 = 20 Which of the following is correct about the above problem? a. The problem has infeasible solutions b. The problem has multiple optimal solutions c. The problem has no constraint d. The problem has unbounded solution e. The problem has a unique optimal solution. < Answer > 29. What is the reason that the value of chisquare statistic can never be negative? a. The difference between the observed and expected frequencies is always positive b. The differences between the observed and expected frequencies is always squared c. The difference between the observed and expected frequencies is divided by expected frequency d. The observed frequency can never be negative e. The expected frequency can never be negative. < Answer > 30. Which of the following is true with regard to a given coefficient of correlation and its corresponding coefficient of determination? a. The coefficient of determination is always greater than or equal to zero b. The coefficient of determination is always negative c. The coefficient of determination is always zero d. The coefficient of determination always has the same sign as the coefficient of correlation e. The magnitude of the coefficient of determination is always greater than the coefficient of correlation. < Answer > END OF SECTION A Section B : Problems (50 Marks) • This section consists of questions with serial number 1 – 5. • Answer all questions. • Marks are indicated against each question. • Detailed workings should form part of your answer. • Do not spend more than 110  120 minutes on Section B. 1. The administrator of Nizam's Hospital studied the number of days stayed at the hospital by all the patients during the last month. The number of all the patients who stayed at the hospital during the last month is 200. The management wants to understand the pattern of stay and have a measure of central tendency and dispersion for this. It is assumed that the patients stayed for a whole number of days. The data collected are: You are required to calculate a. The mean b. The median and c. The standard deviation. Stay in hospital (days) 13 46 79 1012 1315 1618 Frequency 18 90 44 21 18 9 (3 + 4 + 5 = 12 marks) < Answer > 2. Pradeep Khanna, a second year MBA student, is doing a study of companies going public for the first time. He is curious to see whether or not there is a significant relationship between the sizes of the offering (in crores of rupees) and the price per share after the issue. The data are given below: You are required to calculate the coefficient of correlation for the above data set and comment what conclusion Pradeep should draw from the sample. (9 marks) < Answer > 3. A fruit merchant in the Fruit Market of the city is worried about the rising prices of the fruits and its effect on the quantity consumed by the consumers. He wants to understand this effect by finding a suitable index. The following table produces the prices and quantities of some fruits in the year 1996 and 2002: You are required to find out Fisher's price index number for the year 2002, taking 1996 as the base year. (6 marks) < Answer > 4. The Mumbai Cricket Club, a professional club for the cricketers, has the player who led the league in batting average for many years. Over the past ten years, Amod Kambali has achieved a mean batting average of 54.50 runs with a standard deviation of 5.5 runs. This year Amod played 25 matches and achieved an average of 48.80 runs only. Amod is negotiating his contract with the club for the next year, and the salary he will be able to obtain is highly dependent upon his ability to convince the team's owner that his batting average this year was not significantly worse than in the previous years. The selection committee of the club is willing to use a 0.01 significance level. You are required to find out whether Amod's salary will be cut next year. (8 marks) < Answer > 5. A farmer has 1,000 acres of land on which he can grow gram, sunflower or soyabeans. Each acre of gram costs Rs. 100 for preparation, requires 7 mandays of work and yields a profit of Rs. 30. An acre of sunflower costs Rs. 120 to prepare, requires 10 mandays of work and yields a profit of Rs. 40. Each acre of soyabean costs Rs. 70 to prepare, requires 8 mandays of work and yields a profit of Rs. 20. If the farmer has Rs. 1,00,000 for preparation and can count on 8,000 mandays of work, how many acres should he allocate to each crop to maximize profits? You are required to formulate this problem as a linear programming problem and find the optimal solution using simplex method. (15 marks) < Answer > END OF SECTION B Section C : Applied Theory (20 Marks) • This section consists of questions with serial number 6  8. • Answer all questions. • Marks are indicated against each question. sted Answers Quantitative Methods (MB151): January 2004 • Do not spend more than 25 30 minutes on Section C. 6. Briefly explain the model construction phase of operations research. (8 marks) < Answer > 7. Briefly explain the cluster sampling technique. (6 marks) < Answer > 8. Briefly explain the classical approach to probability theory and the limitations of classical definition of probability. (6 marks
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