Business Statistics

Cover Preface to the Second Edition Preface Contents Chapter 1: Statistics: An Overview 1.1 Reasons for Learning Statistics 1.2 Growth and Development of Statistics 1.3 Statistical Thinking and Analysis 1.4 Statistics Defined 1.5 Types of Statistical Methods 1.6 Importance and Scope of Statistics 1.6.1 Statistics and the State 1.6.2 Statistics in Economics 1.6.3 Statistics in Business Management 1.6.4 Statistics in Physical Sciences 1.6.5 Statistics in Social Sciences 1.6.6 Statistics in Medical Sciences 1.6.7 Statistics and Computers 1.7 Limitations of Statistics 1.7.1 Statistics Does Not Study Qualitative Phenomena 1.7.2 Statistics Does Not Study Individuals 1.7.3 Statistics Can be Misused 1.8 How to Lie with Statistics Conceptual Question 1A 1.9 Need for Data 1.9.1 Types of Data 1.10 Principles of Measurement 1.11 Sources of Data 1.11.1 Primary Data Sources 1.11.2 Secondary Data Sources Conceptual Questions 1B Chapter Concepts Quiz Chapter 2: Data Classification, Tabulation and Presentation 2.1 Introduction 2.2 Classification of Data 2.2.1 Requisites of Ideal Classification 2.2.2 Basis of Classification 2.3 Organizing Data Using Data Array 2.3.1 Frequency Distribution 2.3.2 Methods of Data Classification 2.3.3 Bivariate Frequency Distribution 2.3.4 Types of Frequency Distributions Conceptual Questions 2A Self-Practice Problems 2A Hints and Answers 2.4 Tabulation of Data 2.4.1 Objectives of Tabulation 2.4.2 Parts of a Table 2.4.3 Types of Tables 2.4.4 General and Summary Tables 2.4.5 Original and Derived Tables Conceptual Questions 2B Self-Practice Problems 2 B Hints and Answers 2.5 Graphical Presentation of Data 2.5.1 Functions of a Graph 2.5.2 Advantages and Limitations of Diagrams (Graphs) 2.5.3 General Rules for Drawing Diagrams 2.6 Types of Diagrams 2.6.1 One-Dimensional Diagrams 2.6.2 Two-Dimensional Diagrams 2.6.3 Three-Dimensional Diagrams 2.6.4 Pictograms or Ideographs 2.6.5 Cartograms or Statistical Maps 2.7 Exploratory Data Analysis 2.7.1. Stem-and-Leaf Displays Conceptual Questions 2C Self-Practice Problems 2C Hints and Answers Formulae Used Chapter Concepts Quiz Review Self-Practice Problems Case Studies Chapter 3: Measures of Central Tendency 3.1 Introduction 3.2 Objectives of Averaging 3.3 Requisites of a Measure of Central Tendency 3.4 Measures of Central Tendency 3.5 Mathematical Averages 3.5.1 Arithmetic Mean of Ungrouped (or Raw) Data 3.5.2 Arithmetic Mean of Grouped (or Classified) Data 3.5.3 Some Special Types of Problems and Their Solutions 3.5.4 Advantages and Disadvantages of Arithmetic Mean 3.5.5 Weighted Arithmetic Mean Conceptual Questions 3A Self-Practice Problems 3A Hints and Answers 3.6 Geometric Mean 3.6.1 Combined Geometric Mean 3.6.2 Weighted Geometric Mean 3.6.3 Advantages, Disadvantages, and Applications of G.M. Conceptual Questions 3B Self-Practice Problems 3B Hints and Answers 3.7 Harmonic Mean 3.7.1 Advantages, Disadvantages, and Applications of H.M. 3.8 Relationship Between A.M., G.M., and H.M. Self-Practic e Problems 3C Hints and Answers 3.9 Averages of Position 3.9.1 Median 3.9.2 Advantages, Disadvantages, and Applications of Median 3.10 Partition Values—Quartiles, Deciles, and Percentiles Conceptual Questions 3C Self-Practice Problems 3D Hints and Answers 3.11 Mode 3.11.1 Graphical Method for Calculating Mode Value 3.11.2 Advantages and Disadvantages of Mode Value 3.12 Relationship Between Mean, Median, and Mode 3.13 Comparison Between Measures of Central Tendency Conceptual Questions 3D Self-Practice Problems 3E Hints and Answers Formulae Used Chapter Concepts Quiz Review Self- Practice Problems Hints and Answers Case Studies Chapter 4: Measures of Dispersion 4.1 Introduction 4.2 Significance of Measuring Dispersion (Variation) 4.2.1 Essential Requisites for a Measure of Variation 4.3 Classification of Measures of Dispersion 4.4 Distance Measures 4.4.1 Range 4.4.2 Interquartile Range or Deviation Conceptual Questions 4A Self-Practice Proble ms 4A Hints and Answers 4.5 Average Deviation Measures 4.5.1 Mean Absolute Deviation 4.5.2 Variance and Standard Deviation 4.5.3 Mathematical Properties of Standard Deviation 4.5.4 Chebyshev’s Theorem 4.5.5 Coefficient of Variation Conceptual Questions 4B Self-Practice Problems 4B Hints and Answers Formulae Used Chapter Concepts Quiz Review Self-Practice Problems Hints and Answers Case Studies Chapter 5: Skewness, Moments, and Kurtosis 5.1 Introduction 5.2 Measures of Skewness 5.2.1 Relative Measures of Skewness Conceptual Questions 5A Self-Practice Problems 5A Hints and Answers 5.3 Moments 5.3.1 Moments about Mean 5.3.2 Moments about Arbitrary Point 5.3.3 Moments about Zero or Origin 5.3.4 Relationship Between Central Moments and Moments about any Arbitrary Point 5.3.5 Moments in Standard Units 5.3.6 Sheppard’s Corrections for Moments 5.4 Kurtosis 5.4.1 Measures of Kurtosis Conceptual Questions 5B Self-Practice Problems 5B Hints and Answers Formulae Used Review Self-Practice Problems Hints and Answers Chapter 6: Fundamentals of Probability 6.1 Introduction 6.2 Concepts of Probability 6.2.1 Random Experiment 6.2.2 Sample Space 6.2.3 Event Types 6.3 Definition of Probability 6.3.1 Classical Approach 6.3.2 Relative Frequency Approach 6.3.3 Subjective Approach 6.3.4 Fundamental Rules of Probability 6.3.5 Glossary of Probability Terms 6.4 Counting Rules for Determining the Number of Outcomes 6.4.1 Multistep Experiments 6.4.2 Combinations 6.4.3 Permutations Conceptual Questions 6A Self-Practice Problems 6A Hints and Answers 6.5 Rules of Probability and Algebra of Events 6.5.1 Rules of Addition 6.5.2 Rules of Multiplication 6.6 Probability Tree Diagram Self-Practice Problems 6B Hints and Answers 6.7 Bayes’ Theorem Self-Practice Problems 6C Hints and Answers Formulae Used Chapter Concepts Quiz Review Self-Practice Problems Hints and Answers Case Studies Chapter 7: Probability Distributions 7.1 Introduction 7.2 Probability Distribution Function (pdf ) 7.3 Cumulative Probability Distribution Function (cdf ) 7.4 Expected Value and Variance of a Random Variable 7.4.1 Expected Value 7.4.2 Variance and Standard Deviation 7.4.3 Properties of Expected Value and Variance Conceptual Questions 7A Self-Practice Problems 7A Hints and Answers 7.5 Discrete Probability Distibutions 7.5.1 Binomial Probability Distribution Conceptual Questions 7B Self-Practice Problems 7B Hints and Answers 7.5.2 Poisson Probability Distribution 7.5.3 Negative Binomial Probability Distribution 7.5.4 Multinomial Probability Distribution 7.5.5 Hypergeometric Probability Distribution Conceptual Questions 7C Self-Practice Problems 7C Hints and Answers 7.6 Continuous Probability Distributions 7.6.1 Normal Probability Distribution Function 7.6.2 Approximation of Binomial and Poisson Distributions to Normal Distribution 7.6.3 Uniform (Rectangular) Distribution 7.6.4 Exponential Probability Distribution 7.6.5 Gamma (or Erlang) Distribution 7.6.6 Beta Distribution Conceptual Questions 7D Self-Practice Problems 7D Hints and Answers Formulae Used Chapter Concepts Quiz Review Self-Practice Problems Hints and Answers Chapter 8: Sampling and Sampling Distributions 8.1 Introduction 8.2 Reasons of Sample Survey 8.3 Types of Bias During Sample Survey 8.3.1 Sampling and Non-Sampling Errors 8.4 Population Parameters and Sample Statistics 8.5 Principles of Sampling 8.5.1 Principle of Statistical Regularity 8.5.2 Principle of Inertia of Large Numbers 8.6 Sampling Methods 8.6.1 Probability Sampling Methods 8.6.2 Non-Random Sampling Methods 8.6.3 Choice of Sampling Methods 8.7 Sampling Distributions 8.7.1 Standard Error of Statistic 8.7.2 Distinction between Population, Sample Distributions, and Sampling Distributions Conceptual Questions 8A 8.8 Sampling Distribution of Sample Mean 8.8.1 Sampling Distribution of Mean When Population has Non-Normal Distribution 8.8.2 Sampling Distribution of Mean When Population has Normal Distribution 8.8.3 Sampling Distribution of Difference Between Two Sample Means Self-Practice Problems 8A Hints and Answers 8.9 Sampling Distribution of Sample Proportion 8.9.1 Sampling Distribution of the Difference of Two Proportions Self Practice Problems 8B Hints and Answers Formulae Used Chapter Concepts Quiz Review Self-Practice Problems Hints and Answers Chapter 9: Estimation and Confidence Intervals 9.1 Introduction 9.2 Point Estimation 9.2.1 Properties of a Point Estimator 9.2.2 Drawback of Point Estimates 9.3 Confidence Interval Estimation 9.4 Interval Estimation of Population Mean (s Known) 9.4.1 Interval Estimation for Difference of Two Means 9.5 Interval Estimation of Population Mean (s Unknown) Self-Practice Problems 9A Hints and Answers 9.6 Interval Estimation for Population Proportion Self-Practice Problems 9B Hints and Answers 9.7 Estimating Sample Size 9.7.1 Sample Size for Estimating Population Mean 9.7.2 Sample Size for Estimating Population Proportion 9.7.4 Sample Size Determination for Finite Population Conceptual Questions 9A Self-Practice Problems 9C Hints and Answers Formulae Used Chapter Concepts Quiz Review Self-Practice Problems Hints and Answers Chapter 10: Hypothesis Testing 10.1 Introduction 10.2 Hypothesis and Hypothesis Testing 10.2.1 Formats of Hypothesis 10.3 The Rationale for Hypothesis Testing 10.4 General Procedure for Hypothesis Testing 10.5 Direction of The Hypothesis Test 10.6 Errors in Hypothesis Testing 10.6.1 Power of a Statistical Test Conceptual Questions 10A 10.7 Hypothesis Testing for Population Parameters with Largesamples 10.7.1 Hypothesis Testing for Single Population Mean 10.7.2 Relationship between Interval Estimation and Hypothesis Testing 10.7.3 p – Value Approach to Test Hypothesis of Single Population Mean 10.7.4 Hypothesis Testing for Difference between Two Population Means Self-Practice Problems 10A Hints and Answers 10.8 Hypothesis Testing for Single Population Proportion 10.8.1 Hypothesis Testing for Difference Between Two Population Proportions 10.9 Hypothesis Testing for a Binomial Proportion Self-Practice Problems 10B Hints and Answers 10.10 Hypothesis Testing for Population Mean with Small Samples 10.10.1 Properties of Student’s T-Distribution 10.10.2 Hypothesis Testing for Single Population Mean 10.10.3 Hypothesis Testing for Difference of Two Population Means (Independent Samples) 10.10.4 Hypothesis Testing for Difference of Two Population Means (Dependent Samples) Self-Practice Problems 10C Hints and Answers 10.11 Hypothesis Testing Based on F-Distribution 10.11.1 Properties of F-distribution 10.11.2 Comparing Two Population Variances Self-Practice Problems 10D Hints and Answers Formulae Used Chapter Concepts Quiz Review-Self Practice Problems Hints and Answers Chapter 11: Chi-Square and Other Non-Parametric Tests 11.1 Introduction 11.2 Advantages and Limitations of Non-Parametric Methods 11.3 The Chi-Square Distribution 11.3.1 Properties of χ2 Distribution 11.3.2 Conditions for the Applications of χ2 Test 11.4 The Chi-Square Test-Statistic 11.4.1 Grouping of Small Frequencies 11.5 Applications of Χ2 Test 11.5.1 Contingency Table Analysis : Chi-Square Test of Independence Self-Practice Problems 11A Hints and Answers 11.5.2 Chi-Square Test for Goodness-of-Fit 11.5.3 Yate’s Correction for Continuity Self-Practice Problems 11B Hints and Answers 11.5.4 χ2 Test for Population Variance 11.5.5 Coefficient of Contingency 11.5.6 Chi-Square Test of Homogeneity Conceptual Questions 11A 11.6 The Sign Test for Paired Data 11.7 Runs Test for Randomness 11.8 Mann-Whitney U-Test 11.9 Wilcoxon Matched Pairs Test 11.10 Kruskal-Wallis Test Self-Practice Problems 11C Hints and Answers Formulae Used Chapter Concepts Quiz Review Self-Practice Problems Hints and Answers Chapter 12: Analysis of Variance 12.1 Introduction 12.2 Analysis of Variance Approach 12.3 Testing Equality of Population (Treatment) Means :One-Way Classification 12.3.1 Steps for Testing Null Hypothesis 12.4 Inferences About Population (Treatment) Means Self-Practice Problems 12A Hints and Answers 12.5 Testing Equality of Poputation (Treatment) Means: Two-Way Classification Conceptual Questions 12A Self-Practice Problems 12B Hints and Answers Formulae Used Chapter Concepts Quiz Review Self-Practice Problems Hints and Answers Case Studies Chapter 13: Correlation Analysis 13.1 Introduction 13.2 Significance of Measuring Correlation 13.3 Correlation and Causation 13.4 Types of Correlations 13.4.1 Positive and Negative Correlation 13.4.2 Linear and Non-Linear Correlation 13.4.3 Simple, Partial, and Multiple Correlation 13.5 Methods of Correlation Analysis 13.5.1 Scatter Diagram Method 13.5.2 Karl Pearson’s Correlation Coefficient 13.5.3 Probable Error and Standard Error of Coefficient of Correlation 13.5.4 The Coefficient of Determination Self-Practice Problems 13A Hints and Answers 13.5.5 Spearman’s Rank Correlation Coefficient 13.5.6 Method of Least-Squares 13.5.7 Auto-Correlation Coefficient Self-Practice Problems 13B Hints and Answers 13.6 Hypothesis Testing for Correlation Coefficient 13.6.1 Hypothesis Testing about Population Correlation Coefficient (Small Sample) 13.6.2 Hypothesis Testing about Population Correlation Coefficient (Large Sample) 13.6.3 Hypothesis Testing about the Difference between Two Independent13.6.3 Correlation Coefficients Conceptual Questions 13A Self-Practice Problems 13C Hints and Answers Formulae Used Chapter Concepts Quiz Review-Self Practice Problems Hints and Answers Chapter 14: Regression Analysis 14.1 Intruduction 14.2 Advantages of Regression Analysis 14.3 Types of Regression Models 14.3.1 Simple and Multiple Regression Models 14.3.2 Linear and Nonlinear Regression Models 14.4 Estimation : The Method of Least Squares 14.5 Assumptions for a Simple Linear Regression Model 14.6 Parameters of Simple Linear Regression Model 14.6.1 Regression Coefficients 14.7 Methods to Determine Regression Coefficients 14.7.1 Least Squares Normal Equations 14.7.2 Deviations Method 14.7.3 Regression Coefficients for Grouped Sample Data Self-Practice Problems 14A Hints and Answers 14.8 Standard Error of Estimate and Prediction Intervals 14.8.1 Coefficient of Determination: Partitioning of Total Variation Conceptual Questions 14A Formulae Used Chapter Concepts Quiz Review Self-Practice Problems Hints and Answers Case Studies Chapter 15: Partial and Multiple Correlation and Regression Analysis 16.1 Introduction Chapter 16: Forecasting and Time Series Analysis 16.1 Introduction 16.2 Types of Forecasts 16.3 Timing of Forecasts 16.4 Forecasting Methods 16.4.1 Quantitative Forecasting Methods 16.4.2 Qualitative Forecasting Methods 16.5 Steps of Forecasting 16.6 Time Series Analysis 16.6.1 Objectives of Time Series Analysis 16.6.2 Time Series Patterns 16.6.3 Components of a Time Series 16.7 Time Series Decomposition Models 16.7.1 Multiplicative Model 16.7.2 Additive Model Conceptual Questions 16A 16.8 Quantitative Forecasting Methods 16.8.1 Freehand Method 16.8.2 Smoothing Methods 16.8.3 Exponential Smoothing Method Self-Practice Problems 16A Hints and Answers 16.9 Trend Projection Methods 16.9.1 Linear Trend Model 16.9.2 Quadratic Trend Model 16.9.3 Exponential Trend Model 16.9.4 Changing the Origin and Scale of Equations Self-Practice Problems 16B Hints and Answers 16.10 Measurement of Seasonal Effects 16.10.1 Seasonal Index 16.10.2 Method of Simple Averages 16.10.3 Ratio-to-Trend Method 16.10.4 Ratio-to-Moving Average Method 16.10.5 Link Relative Method 16.11 Measurement of Cyclical Variations—residual Method 16.12 Measurement of Irregular Variations Conceptual Questions 16B Self-Practice Problems 16C Hints and Answers Formulae Used Chapter Concepts Quiz Review Self-Practice Problems Hints and Answers Chapter 17: Index Numbers 17.1 Introduction 17.2 Index Number Defined 17.3 Types of Index Numbers 17.4 Characteristics and Uses of Index Numbers 17.4.1 Characteristics of Index Numbers 17.4.2 Uses of Index Numbers Conceptual Questions 17A 17.5 Methods for Construction of Price Indexes 17.6 Unweighted Price Indexes 17.6.1 Single Price Index 17.6.2 Aggregate Price Index 17.6.3 Average Price Relative Index Self-Practice Problems 17A Hints and Answers 17.7 Weighted Price Indexes 17.7.1 Weighted Aggregate Price Index 17.8 Quantity or Volume Indexes 17.9 Value Indexes Self-Practice Problems 17B Hints and Answers 17.10 Tests of Adequacy of Indexes 17.10.1 Time Reversal Test 17.10.2 Factor Reversal Test 17.10.3 Circular Test 17.11 Chain Indexes 17.12 Applications of Index Numbers 17.12.1 Changing the Base of an Index 17.12.2 Combining Two or More Overlapping Indexes 17.12.3 Correction (Adjustment) of Value of an Item Self-Practice Problems 17C Hints and Answers 17.13 Consumer Price Indexes 17.13.1 Uses of Consumer Price Index (CPI) Number 17.13.2 Construction of a Consumer Price Index 17.14 Problems of Index Numbers Construction Conceptual Questions Formulae Used Chapter Concepts Quiz Review Self-Practice Problems Hints and Answers Chapter 18: Statistical Qualtiy Control 18.1 Introduction 18.2 Quality and Quality Control 18.2.1 Quality Control 18.3 Cost of Quality Control 18.4 Statistical Quality Control 18.4.1 Definitions of Statistical Quality Control 18.5 Techniques of Statistical Quality Control 18.5.1 Through 100 Per Cent Inspection 18.5.2 Through Statistical Quality Control 18.6 In-Process Quality Control Techniques 18.6.1. Control Charts 18.6.2 Setting up the Control Limits 18.7 Control Charts for Variables 18.7.1 Mean or Chart 18.7.2 R - Chart : A Control Chart for Dispersion 18.7.3 Choice and Interpretation of x and R Charts Conceptual Questions 18A Self-Practice Problems 18A Hints and Answers 18.8 Control Charts for Attributes 18.8.1 C-Chart: Control Chart for Defects per Unit 18.8.2 p-Chart: Control Chart for Proportion of Defectives 18.8.3 np–Chart: Control Chart for Total Number of Defectives Self-Practice Problems Hints and Answers 18.9 Sampling Plan for Attributes and Variables 18.9.1 Acceptance Sampling 18.10 Specifying an Acceptance Sampling Plan 18.10.1 Types of Acceptance Sampling Plans 18.11 Determining Error and OC Curve 18.11.1 Producer and Consumer Risk 18.11.2 Effect of Change in Sample Size n and Acceptance Number c 18.11.3 Average Outgoing Quality (AOQ) 18.12 Advantages and Limitations of Statistical Quality Control Conceptual Questions 18B Formulae Used Chapter Concepts Quiz Review Self-Practice Problems Hints and Answers Case Studies Chapter 19: Statistical Decision Theory 19.1 Introduction 19.2 Steps in Decision Theory Approach 19.3 Types of Decision-Making Environments 19.4 Decision-Making under Uncertainty 19.4.1 Criterion of Optimism (Maximax or Minimin) 19.4.2 Criterion of Pessimism (Maximin or Minimax) 19.4.3 Equally Likely Decision (Laplace) Criterion 19.4.4 Criterion of Realism (Hurwicz Criterion) 19.4.5 Criterion of Regret Self-Practice Problems 19A Hints and Answers 19.5 Decision-Making Under Risk 19.5.1 Expected Monetary Value (EMV) 19.5.2 Expected Opportunity Loss (EOL) 19.5.3 Expected Value of Perfect Information (EVPI) 19.6 Posterior Probabilities and Bayesian Analysis Self-Practice Problems 19B Hints and Answers 19.7 Decision Tree Analysis Conceptual Questions 19A Self-Practice Problems 19C Hints and Answers Formulae Used Chapter Concepts Quiz Review Self-Practice Problems Hints and Answers Appendices Index