QUANTITATIVE TECHNIQUES FOR BUSINESS DECISIONS Master of commerce Semester I Paper II Study Material 2015 Admission onwards UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION CALICUT UNIVERSITY P.O., THENJIPALAM, MALAPPURAM-673635 QUANTITATIVE TECHNIQUES FOR BUSINESS DECISIONS Master of commerce Semester I Paper II Study Material 2015 Admission onwards UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION CALICUT UNIVERSITY P.O., THENJIPALAM, MALAPPURAM-673635 2022 QUANTITATIVE TECHNIQUES FOR BUSINESS DECISIONS Master of commerce Semester I Paper II Study Material 2015 Admission onwards UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION CALICUT UNIVERSITY P.O., THENJIPALAM, MALAPPURAM-673635 School of Distance Education Quantitative Techniques for Business Decisions Page 2 UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION Master of commerce Study Material 2015 Admission onwards Semester I Paper II QUANTITATIVE TECHNIQUES FOR BUSINESS DECISIONS Prepared by Dr. Yakoob . c. Reader and Research Guide, SS COLLEGE, AREACODE. Type settings and Lay out : Computer Section, SDE © Reserved School of Distance Education Quantitative Techniques for Business Decisions Page 3 TABLE OF CONTENT No. Topic Page No. 1 QUANTITATIVE TECHNIQUES - CONCEPTS 5 2 INFERENTIAL ANALYSIS- POINT ESTIMATION 13 3 INTERVAL ESTIMATION 19 4 SAMPLING & SAMPLE SIZE 23 5 TESTS OF SIGNIFICANCE - CONEPTS 27 6 PARAMETRIC TESTS – MEANS & PROPORTIONS 32 7 TESTS FOR VARIANCE & PAIRED OBSERVATIONS 45 8 ANALYSIS OF VARIANCE 51 9 NON P[ARAMETRIC TESTS - CONCEPTS 59 10 CHI-SQUARE TESTS 65 11 SIGN AND SIGNED RANK TESTS 73 12 RANK SUM & OTHER NON PAREMETRIC TESTS 84 13 STATISTICAL QUALITY CONTROL - CONCEPTS 93 14 CONTROL CHART FOR VARIABLES 100 15 CONTROL CHART FOR ATTRIBUTES 107 16 TOTAL QUALITY MANAGEMENT 116 17 CORRELATION ANALYSIS 122 18 RANL, PARTIAL & MULTIPLE CORRELATION 131 19 REGRESSION ANALYSIS 137 20 SOFTWARES FOR QUANTITATIVE ANALYSIS 147 21 APPENDIX 160 School of Distance Education Quantitative Techniques for Business Decisions Page 4 School of Distance Education Quantitative Techniques for Business Decisions Page 5 UNIT 1 QUANTITATIVE TECHNIQUES FOR MANAGERIAL DECISIONS Introduction Decision making is the most complex, but essential human activity. Several tools have been developed for facilitating decision making – whether in ordinary course of life or business. Good decisions are always applauded. Decisions determine the destiny of individuals or organizations. Decisions can be based on both qualitative aspects and quantitative data. Certain situations warrant the introduction of elements of quantities which support judgment and intuition. Many of the decision circumstances of business organizations necessitate planning and evaluation of alternatives. Thus emerged the subject of quantitative techniques. Business is becoming more and more complex and requires effective management to succeed. Managing complexity requires many professional skills including quantitative analysis. Business environment is being globalized, competitors are increasing, demand is getting diverse, and employees becoming more mobile and demanding. As a consequence, effective decision making is more crucial than ever before. On the other hand, managers have more access to larger and more detailed data base that are potential sources of information. However, to achieve this potential, it is required that managers know how to convert data into information. This is one of the reasons why quantitative techniques are being more and more focused. Definitions Since Quantitative technique is a practical methodological technique, there is no precise definition for the term. Quantitative techniques are defined as “those statistical techniques which lead to numerical analysis of variables, affecting a decision situation, and evaluation of alternative strategies to attain objectives of organizations.” Quantitative techniques involves “ transformation of a qualitative description of a decision situation, into quantitative format, identifying of variables, setting out alternative solutions and supplementing decision making, by replacing judgment and intuition.” Quantitative techniques may be described as those techniques “which provide decision maker, with a systematic and powerful tool of analysis, based on quantitative and numeric data relating to alternative option.” Thus quantitative techniques are a set of techniques involving numerical formulation of a decision situation and analysis of variables, so as to arrive at alternative solutions, leading to optimal decision. Meaning and Nature Quantitative techniques comprise those statistical and programming techniques which are helpful in managerial decision making. These techniques involve use of numbers, symbols and other mathematical expressions to express problems in quantitative terms. They serve as a useful supplement to human judgment and intuition. They prove a systematic means of analysis and choice for attaining predetermined objectives of an organization. Quantitative techniques involve use of scientific methods of experimentation, observation and modification, in managerial decision making process. School of Distance Education Quantitative Techniques for Business Decisions Page 6 Features Descriptions of quantitative techniques reveal following characteristics or features. Measurement Measurement is the basis of quantitative technique. Measurement is assigning numbers to concepts and phenomena. Measurement generates necessary data. Numerical analysis Another basic feature of quantitative techniques is numerical expression of variables and analysis thereto. Even qualitative characteristics or phenomenon can be transformed to numbers and symbols using quantitative techniques. Scientific method Quantitative techniques for decision making are examples for the use of scientific methods of management. It offers a systematic and objective experimentation, observation and evaluation of best strategies. Decision making It is a support system in decision making process. It provides decision makers with appropriate tools of evaluation and presentation. Options Quantitative techniques should evaluate and reveal alternative strategies or options. There is no scope for decision where there is a single option. Improvement Quantitative techniques should replace personal judgment and intuition. It should lead to improved and quality decisions. Functions of quantitative techniques Quantitative Techniques are those methods in which details of a problem or situation are expressed in numerical terms, so as to support decision making. Accordingly, following are the functions of Quantitative techniques Quantification Critical factors affecting a decision situation is transformed into quantitative or numerical form. It is easy to comprehend, understand and delegate an issue in numerical form. Analysis Quantitative techniques enable scientific and systematic study of any issue. It probes deep into the factors influencing the problem and helps to express the situation in a comprehensive form. Decision making Quantitative techniques facilitate the process of decision making. It sets out all possible alternatives and enables a feasibility study of each so that the optimal alternative can be chosen Deployment of resources Quantitative techniques, if properly applied, leads to optimal allocation of available limited resources. It avoids wastages and less efficient usage of resources, and leads to conservation of resources. School of Distance Education Quantitative Techniques for Business Decisions Page 7 Sequencing Certain projects may involve several complex activities , to be performed in a sequential order. Quantitative techniques aids in determining optimal sequence of performing a set of jobs, so as to minimize total process time. Optimize service In service sector, quantitative techniques is the only option for addressing questions like waiting time, service time, traffic intensity, idle time etc. Role of quantitative techniques in decision making Quantitative techniques have been increasingly used in decision making relating to solution of complex problems of business and industry. Quantitative techniques are now recognized as an effective tool for solving managerial problems. Its role is vital due to following reasons, Better control Management of bigger organizations find it much costlier to provide continuous executive supervision over routine decisions. A Quantitative techniques approach directs the executives to devote their attention to more pressing matters. For example quantitative techniques approach deals with production scheduling and inventory control. Better coordination Sometimes quantitative techniques have been very useful in maintaining the orderly situation out of chaos. For example, quantitative techniques based planning model becomes a vehicle for coordinating possibilities of marketing decisions with the limitations imposed on manufacturing capabilities. Better system Quantitative techniques study is also initiated to analyze a particular problem of decision making such as establishing a new warehouse. Later quantitative techniques approach can be further developed into a system to be employed repeatedly. Consequently the cost of undertaking the first application may improve the profits. Better decisions Quantitative techniques models frequently yield actions that do improve an intuitive decision making. Sometimes a situation may be so complicated that the human mind can never hope to assimilate all the important factors without the help of quantitative techniques and computer analysis. Quantitative and qualitative approaches Decision making is the process of selecting optimal alternative from among several alternatives, subject to states of nature. While analyzing a situation for such a selection, two approaches can be adopted – quantitative approach and qualitative approach Quantitative approach This approach involves generation and analysis of data in numerical form. Data obtained a s per quantitative approach can be subjected to rigorous quantitative analysis in a formal fashion. This will reveal almost all inherent characteristics of the variable under study. School of Distance Education Quantitative Techniques for Business Decisions Page 8 Quantitative approach may further be subdivided into inferential, experimental and simulation approaches. The purpose of inferential approach is to form a data base to infer characteristics or relationships of variables. Required data would be usually obtained through field survey. Experimental approach is characterized by much greater control over the study environment, and in this case variables are manipulated to observe their effect on other variables. Simulation approach involves the construction of an artificial environment or model within which relevant information and data can be generated. This permits an observation of dynamic behavior of the system or sub system under modeled conditions. The term simulation, in the context of business, means building of a model, that represents the structure of a dynamic process or operation. Qualitative approach Qualitative approach is concerned with subjective assessment of attitudes, opinions and behavior. Decision making in such situations is a function of decision maker’s insight and impressions. Such an approach generates results either in non-quantitative form or in a form which cannot be subjected to rigorous quantitative analysis. For example, opinion that a person may be good or bad Basically, the techniques of focus group interviews, projective techniques and depth interviews use qualitative approach for decision making. Generally there are four non quantitative techniques of decision making Intuition – decision making on intuition is characterized by inner feelings of the decision maker. It is purely subjective Facts –It follows the rule that decision should be based on facts, and not on feelings. Experiences – Experience is the most valuable asset, if used logically. Decisions should be based on precedence. Opinion – in decision making, expert opinions can be relied on. In fact, this is widely used by all levels of managers. However, even qualitative approach may be transformed into quantitative form, in practical studies. This is achieved through measurement and scaling. Measurement is assigning numbers or values to concepts or phenomena. Scaling refers to placing a concept or characteristic on the appropriate position of a measured scale. For example, Marital status of a person may be : (single)1 , (married)2, (divorced)3 (widowed)4. Here qualitative or non quantitative data is logically converted into quantitative data. Significance of quantitative decisions Quantitative Techniques have proved useful in tackling managerial decision problems relating to business and industrial operations. Quantitative decisions are considered significant on the following grounds. School of Distance Education Quantitative Techniques for Business Decisions Page 9 Simplifies decision making Quantitative techniques simplify the decision making process. Decision theory enables a manager to select the best course of action. Decision tree technique refines executive judgment in systematic analysis of the problem, these techniques permit scientific decision making under conditions of risk and uncertainty. Decision problems such as manpower planning ,demand forecasting, selection suppliers, production capacities, and capital requirements planning can be more effective tackled using quantitative techniques. Scientific analysis It provides a basis for precise analysis of the cause and effect relationship. They make it possible to measure the risks inherent, in business by providing an analytical and objective approach. These techniques reduce the need for intuition and objective approach. In this way quantitative techniques enable managers to use logical thinking in the analysis of organizational problems, Allocation of resources They are very helpful in the optimum deployment of resources. For example, Programme Evaluation and Review Techniques enable a manager to determine the earliest and the latest times for each of the events and activities involved in a project. The probability of completing the project by a specified date can be determined. Timely completion of the project helps to avoid time and cost overruns. Similarly, linear programming technique is very useful in optimal allocation of scarce resources, production scheduling and in deciding optimal assignments. Profit maximization Quantitative techniques are invaluable in assessing the relative profitability of alternative choices and identifying the most profitable course of action. What should be the relative mix of different products, which site to choose for location out of alternative sites, which arrangement of orders in terms of time and quantity, will give maximum profits. Such question can be answered with the help of quantitative techniques. Cost minimization Quantitative techniques are helpful in tackling cost minimization problems. For example waiting line theory enables a manager to minimize waiting and servicing costs. Their techniques help business managers in taking a correct decision through analysis of feasibility of adding facilities. Forecasting Quantitative techniques are useful in demand forecasting. They provide a scientific basis of coping with the uncertainties of future demand. Demand forecasts serve as the basis for capacity planning. Quantitative technique enables a manager to adopt the minimum risk plan. Inventory control Inventory planning techniques help in deciding when to buy and how much to buy. It enables management to arrive at appropriate balance between the costs and benefits of holding stocks. The integrated production models technique is very useful in minimizing costs of inventory, production and workforce. Statistical quality controls help us to determine whether the production process is under control or not. School of Distance Education Quantitative Techniques for Business Decisions Page 10 Applications of quantitative techniques in business operations Quantitative techniques are widely applied for solving decision problems of routine operations of business organizations. It is especially useful for business managers, economist, statisticians, administrators, technicians and others in the field of business, agriculture, industry services and defense. It has specific applications in the following functional areas of business organizations. Planning In planning, quantitative techniques are applied to determine size and location of plant, product development, factory construction, installation of equipment and machineries etc. Purchasing Quantitative techniques are applied in make or buy decisions, vendor development, vendor rating, purchasing at varying prices, standardization and variety reduction, logistics management. Manufacturing Quantitative techniques address questions like product mix, production planning, quality control, job sequencing, and optimum run sizes. Marketing Marketing problems like demand forecasting, pricing competitive strategies, optimal media planning and sales management can be solved through application appropriate quantitative techniques. Human resource management Quantitative techniques supports decision making relating to maower planning with due consideration to age, skill, wastage and recruitment , recruitment on the basis of proper aptitude, method study , work measurement, job evaluation, development of incentive plans, wage structuring and negotiating wage and incentive plan with the union. Research and Development Quantitative techniques are helpful in deciding research issues like market research, market survey, product innovation, process innovations, plant relocation, merger and acquisitions etc. Classification of quantitative techniques Quantitative techniques are a set of methods used to quantitatively formulate, analyze, integrate and decide problems or issues. They are broadly classified into three –mathematical techniques, statistical techniques and programming techniques. Mathematical techniques They are quantitative techniques in which numerical data are used along with the principles of mathematics such as integration, calculus etc. They include permutations, combinations, set theory, matrix analysis, differentials integration etc. Permutations and combinations Permutation is mathematical device of finding possible number of arrangements or groups which can be made of a certain number of items from a set of observations. They are groupings considering order of arrangements. School of Distance Education Quantitative Techniques for Business Decisions Page 11 Combinations are number of selections or subsets which can be made of a certain number of items from a set of observations, without considering order. Both combinations and permutations help in ascertaining total number of possible cases. Set theory It is a modern mathematical device which solves the various types of critical problems on the basis of sets and their operations like Union, intersection etc. Matrix Algebra Matrix is an orderly arrangement of certain given numbers or symbols in rows and columns. Matrix analysis is thus a mathematical device of finding out the results of different types of algebraic operations on the basis of relevant matrices. This is useful to find values of unknown numbers connected with a number of simultaneous equations. Differentials Differential is a mathematical process of finding out changes in the dependent variable with reference to a small change in the independent variable. It involves differential coefficients of dependent variables with or without variables. Integration It is a technique just reversing the process of differentiation. It involves the formula f(x) dx where f(x) is the function to be integrated Statistical techniques They are techniques which are used in conducting statistical inquiry concerning a certain phenomenon. They include all the statistical methods beginning from the collection of data till interpretation of those collected data. Important statistical techniques include collection of data, classification and tabulation, measures of central tendency, measures of dispersion, skewness and kurtosis, correlation, regression, interpolation and extrapolation, index numbers, time series analysis, statistical quality control, ratio analysis , probability theory, sampling technique, variance analysis, theory of attributes etc. Programming techniques These techniques focus on model building, and are widely applied by decision makers relating to business operations. In programming, problem is formulated in numerical form, and a suitable model is fitted to the problem and finally a solution is derived. Prominent programming techniques include linear programming, queuing theory, inventory theory, theory of games, decision theory, network programming, simulation, replacement non linear programming, dynamic programming integer programming etc. Quantification of qualitative data In most cases, information is born in the form of qualitative description of situations. This may be quantified. Such quantification leads to following favorable out comes 1. It attracts readers’ attention to patterns in the information 2. It helps to memorize and stacking of information 3. It assists in timely retrieval of data. 4. It supports efficient decision making. School of Distance Education Quantitative Techniques for Business Decisions Page 12 Example : A carpet factory manufactures carpets of which minimum length is 15.1 mts and maximum is 16.9 mts. It produces carpets having length of 15.1 – 15.5 - 2 nos, 15.6 – 15.8 - 8 nos, 15.9 - 16.1 - 9 nos, 16.2 - 16.5 - 7 nos and 16.6 - 16.9 - 4 nos. it is convenient to present this information in the form of a frequency distribution as below: Class Frequency 15.1 - 15.5 2 15.6 - 15.8 8 15.9 - 16.1 9 16.2 - 16.5 7 16.6 - 16.9 4 Total 30 Review Questions and Exercises 1. Define Quantitative Technique. 2. Describe the various methods of classifying of Quantitative Techniques. 3. State the various Mathematical Quantitative Techniques. 4. State sources of the important Statistical techniques. 5. State various Operations Research Techniques. 6. Explain the role of Quantitative Techniques in business management 7. List out the important areas where Quantitative techniques have applications. 8. Discuss the Scope and limitations of Quantitative techniques 9. Explain the uses quantitative techniques in business EX 1.1 An employment exchange gave following information about its registered candidates. Level of education – not completed +2 = 35%, completed +2 31%, attended but not completed degree 16%, completed degree 9%, not completed PG 6% and completed PG 3%. Construct a relative frequency table and comment on the trend of registration. Ex 1.2 The administrator of a hospital provided following information on waiting time in casually department. Construct a table on the waiting and comment on this. Waiting time (minutes) 12 16 21 20 24 3 11 17 29 28 No of patients 26 4 7 14 25 1 27 15 16 5 School of Distance Education Quantitative Techniques for Business Decisions Page 13 UNIT II INFERENTIAL ANALYSIS – POINT ESTIMATE Introduction One of the main objectives of statistical studies is to draw valid conclusion about the population on the basis of samples drawn from the population. Such a process of inferring about the population is called inferential analysis. Inferential analysis is often required and applied in business management. Management is confronted with various practical problems like augmentation of production, maximization of profit, minimization of cost, introduction of innovations improvement of production methods etc. these problems lead to accomplishment of certain pre- determined objectives and goals. There has been a growing tendency to turn to quantitative techniques as a means for solving many of these managerial decision problems that arise in a business or industrial enterprise. A large number of business problems have been given quantitative representation with considerable degree of success. Inferential analysis is such a quantitative e technique widely applied for managerial decision taking. Inferential analysis Inferential analysis is a prominent quantitative technique based on probability concept to deal with uncertainty in decision making it is a set of statistical methods to assume with reasonable accuracy, population characteristics on the basis of given en sample statistics. Statistical inference can be defined as drawing inference from probabilistic sample, about unknown population parameters. Types of statistical inference Statistical inference may be focused either on examining hypotheses or on predicting probable values. Accordingly two types of statistical inferences are hypotheses testing and statistical estimation. In hypotheses testing we examine the claims made about unknown population parameter using sample statistics. These claims are made using some past experience and logic. Statistical Estimation means estimating unknown population parameters, with reasonable accuracy, using sample statistics. This unit focuses on statistical estimation. Statistical Estimation Everyone makes estimates. When we are ready to cross a road, we estimate the speed of any approaching car, the distance to the car, and our own speed. Having made these quick estimates, we decide whether to wait or to walk. Business managers also estimate for various purposes. Estimation is the process of assessing characteristics of a phenomenon, on the basis of intuition, experience, statistics and other available information When estimation is exclusively based on statistical methods, it is statistical estimation. Statistical estimation is a useful quantitative technique. School of Distance Education Quantitative Techniques for Business Decisions Page 14 Significance of estimation in managerial decision making Decision making is the most important and complex task of management. Estimation is inherent to decision making. Thus, in decision making process, estimation plays a significant role, in the following ways. 1. Long term - the outcome of estimation will affect organizational effectiveness, for a long time. Therefore estimates will be critical in the long run. 2. Accuracy - estimates are made basing on past experience and realistic projections in to the future. This will ensure reasonable accuracy in estimates. 3. Goal oriented - estimates are made , revolving around the objectives and goals of the organization. Goal orientation of estimates will improve decision making process. 4. Guidance - estimates are realistic projections into the future. They serve as milestones and guidance towards the attainment of vision and mission of organization. 5. scientific outlook - estimates and follow up will create a systematic and scientific environment within the organization. It will eliminate rule of thumb and intuition in managerial decisions. 6. Relationship - management will have to take decisions in situations of uncertainty and risk. Statistical estimates in such situations will rationalize decisions. Types of estimates Estimates mean rationally assessed values of populations on the basis of sample statistics. Such estimates may be specific single point values or range values. Accordingly there are two types of estimates - point estimate and interval estimate. Point estimate When the estimated value is a single specific value of the population, it is called point estimate. In point estimate we determine a value which may be taken as an estimate of the population parameter. Sample mean is popular point estimate of the population mean. Arithmetic mean is generally used to express the characteristics of a phenomenon. For example, when a football fan says “the average age of Kerala Blasters team is 26”, it is point estimate. Other popular point estimates are population proportion, standard deviation and variance. Properties of good estimator Estimation enables prediction, with reasonable accuracy, of unknown value on the basis of known value. Such accuracy depends on following qualities. Unbiasedness while taking sample for population estimate, it must be done in an unbiased manner. Each item should be given equal opportunity of being taken as sample. Consistency Sample value should approach population value, when sample size is increased. This property is consistency. So sample size should be sufficiently large. Efficiency Variation between population estimate and sample value should be the least. When the variation is more, it leads to inefficiency. Ease Process of estimation should be simple . It should be understood and done with less calculation. School of Distance Education Quantitative Techniques for Business Decisions Page 15 Merits of point estimation Point estimates are valuable tools in analyzing complex decision problems. Following are their merits 1. It provides a single value as the estimate of population parameter. It is easy and simple to understand and calculate. 2. It gives an exact value for the parameter under investigation. There is no confusion as to which value to be selected. 3. It is considered unbiased and consistent, if the sample size is sufficiently large. It became more reliable with large samples. Demerits of point estimate. 1. It does not consider uncertainty of estimation. A point estimate cannot ensure whether population parameter will come equal to sample statistics or not . 2. It does not consider the concept of standard error, which will purify estimation process. Standard error will rectify fluctuations in sample data. 3. Lack of confidence level will eliminate the confidence of the estimator in assessing unknown population values on the basis of known sample value. Steps - point estimation  Consider the given sample data – sample size and given sample statistic  Obtain sample mean, variance, standard deviation or proportion as the case may be by dividing sum of quantities by number of elements within a sample.  Apply the sample statistic over population  Treat sample statistic as population parameter. Ex . 2.1 An auditorium is considering its seating capacity. Following are the attendance in 9 days (in 000s). Find point estimates of mean, and variance of daily attendance of people for the coming days. Attendance (000s) 8.8 14.0 21.3 7.9 12.5 20.6 16.3 14.1 13.0 Ans X X - x ( x = 14.3) x-x² 8.8 -5.5 30.25 14.0 -0.3 0.09 21.3 7.0 49.00 7.9 -6.4 40.96 12.5 -0.8 0.64 20.6 6.3 41.58 16.3 2.0 4.00 14.1 -0.2 0.04 13.0 -1.3 1.69 Total 128.5 168.25 Estimated population mean = 14.3 Estimated population variance = 168.25