Business Statistics: Problems and Solutions

599 Pages·2010·5.353 MB·English

by  J. K. Sharma

BUSINESS STATISTICS
Problems and Solutions
J. K. Sharma
Formerly Professor
Faculty of Management Studies
University of Delhi, Delhi
Delhi • Chennai • Chandigarh
Assistant Acquisitions Editor: Dhiraj Pandey
Associate Production Editor: Ruchi Sachdev
Composition: Sara Assignments
Printer:

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Preface xi
About the Author x iii
CHAPTER 1 DATA CLASSIFICATION, TABULATION, AND PRESENTATION 1–42
1.1 Classification of Data 1
1.2 Organizing Data Using Data Array 2
Self-Practice Problems 1A 15
Hints and Answers 16
1.3 Tabulation of Data 17
Self-Practice Problems 1B 23
Hints and Answers 24
1.4 Graphical Presentation of Data 25
1.5 Types of Diagrams 26
1.6 Exploratory Data Analysis 39
Self-Practice Problems 1C 41
Hints and Answers 42
CHAPTER 2 MEASURES OF CENTRAL TENDENCY 43–77
2.1 Introduction 43
2.2 Measures of Central Tendency 43
2.3 Mathematical Averages 43
Self-Practice Problems 2A 58
Hints and Answers 59
2.4 Geometric Mean 59
Self-Practice Problems 2B 62
Hints and Answers 63
2.5 Harmonic Mean 64
2.6 Averages of Position 65
Self-Practice Problems 2C 71
Hints and Answers 72
2.7 Mode 72
2.8 Relationship Between Mean, Median, and Mode 74
Self-Practice Problems 2D 75
Hints and Answers 77
CHAPTER 3 MEASURES OF DISPERSION 78–100
3.1 Introduction 78
iv CONTENTS
3.2 Classification of Measures of Dispersion 78
3.3 Distance Measures 79
Self-Practice Problems 3A 81
Hints and Answers 82
3.4 Average Deviation Measures 83
Self-Practice Problems 3B 97
Hints and Answers 99
CHAPTER 4 SKEWNESS, MOMENTS, AND KURTOSIS 101–130
4.1 Introduction 101
4.2 Measures of Skewness 101
Self-Practice Problems 4A 107
Hints and Answers 108
4.3 Moments 110
4.4 Kurtosis 114
4.5 Miscellaneous Solved Examples 118
Self-Practice Problems 4B 129
Hints and Answers 130
CHAPTER 5 FUNDAMENTALS OF PROBABILITY 131–169
5.1 Introduction 131
5.2 Event Types 131
5.3 Definition of Probability 132
5.4 Fundamental Rules of Probability 133
5.5 Counting Rules for Determining the Number of Outcomes 133
Self-Practice Problems 5A 135
Hints and Answers 135
5.6 Rules of Probability and Algebra of Events 136
Self-Practice Problems 5B 146
Hints and Answers 148
5.7 Bayes’ Theorem 150
Self-Practice Problems 5C 168
Hints and Answers 169
CHAPTER 6 PROBABILITY DISTRIBUTIONS 170–203
6.1 Introduction 170
6.2 Probability Distribution Function 170
6.3 Cumulative Probability Distribution Function 171
6.4 Expected Value and Variance of a Random Variable 172
Self-Practice Problems 6A 176
Hints and Answers 177
6.5 Discrete Probability Distributions 177
Self-Practice Problems 6B 181
Hints and Answers 182
CONTENTS v
6.6 Poisson Probability Distribution 183
Self-Practice Problems 6C 188
Hints and Answers 189
6.7 Continuous Probability Distributions 191
6.8 Miscellaneous Solved Examples 196
Self-Practice Problems 6D 201
Hints and Answers 202
CHAPTER 7 SAMPLING AND SAMPLING DISTRIBUTIONS 204–223
7.1 Population Parameters and Sample Statistics 204
7.2 Sampling Methods 204
7.3 Sampling Distributions 206
7.4 Sampling Distribution of Sample Mean 207
Self-Practice Problems 7A 213
Hints and Answers 213
7.5 Sampling Distribution of Sample Proportion 215
7.6 Miscellaneous Solved Examples 217
Self-Practice Problems 7B 222
Hints and Answers 222
CHAPTER 8 ESTIMATION AND CONFIDENCE INTERVALS 224–234
8.1 Introduction 224
8.2 Interval Estimation of Population Mean (σ Known) 224
8.3 Interval Estimation of Population Mean (σ Unknown) 226
Self-Practice Problems 8A 228
Hints and Answers 228
8.4 Interval Estimation for Population Proportion 229
Self-Practice Problems 8B 230
Hints and Answers 231
8.5 Estimating Sample Size 231
Self-Practice Problems 8C 233
Hints and Answers 234
CHAPTER 9 HYPOTHESIS TESTING 235–279
9.1 Hypothesis and Hypothesis Testing 235
9.2 Hypothesis Testing for Population Parameters with Large Samples 237
Self-Practice Problems 9A 243
Hints and Answers 243
9.3 Hypothesis Testing for Single Population Proportion 245
9.4 Hypothesis Testing for a Binomial Proportion 248
Self-Practice Problems 9B 249
Hints and Answers 250
9.5 Hypothesis Testing for Population Mean with Small Samples 251
Self-Practice Problems 9C 260
Hints and Answers 261
vi CONTENTS
9.6 Hypothesis Testing Based on F-Distribution 263
9.7 Miscellaneous Solved Examples 265
Self-Practice Problems 9D 278
Hints and Answers 278
CHAPTER 10 CHI-SQUARE AND OTHER NON-PARAMETRIC TEST 280–318
10.1 Introduction 280
10.2 The Chi-Square Distribution 280
10.3 Applications of χ2 Test 281
Self-Practice Problems 10A 285
Hints and Answers 286
10.4 Chi-square Test for Goodness-of-Fit 287
Self-Practice Problems 10B 292
Hints and Answers 292
10.5 χ2-Test for Population Variance 293
10.6 The Sign Test for Paired Data 297
10.7 Runs Test for Randomness 298
10.8 Mann-Whitney U-Test 300
10.9 Wilcoxon Matched Pairs Test 302
10.10Kruskal-Wallis Test 304
10.11Miscellaneous Solved Examples 306
Self-Practice Problems 10C 316
Hints and Answers 317
CHAPTER 11 ANALYSIS OF VARIANCE 319–337
11.1 Introduction 319
11.2 Testing Equality of Population (Treatment) Means: One-Way Classification 319
11.3 Inferences About Population (Treatment) Means 326
Self-Practice Problems 11A 326
Hints and Answers 327
11.4 Testing Equality of Population (Treatment) Means: Two-Way Classification 328
Self-Practice Problems 11B 334
Hints and Answers 335
CHAPTER 12 CORRELATION ANALYSIS 338–370
12.1 Introduction 338
12.2 Types of Correlations 338
Self-Practice Problems 12A 347
Hints and Answers 348
12.3 Spearman’s Rank Correlation Coefficient 348
Self-Practice Problems 12B 356
Hints and Answers 357
12.4 Hypothesis Testing for Correlation Coefficient 357
CONTENTS vii
12.5 Miscellaneous Solved Examples 361
Self-Practice Problems 12C 369
Hints and Answers 369
CHAPTER 13 REGRESSION ANALYSIS 371–395
13.1 Introduction 371
13.2 Methods to Determine Regression Coefficients 372
13.3 Standard Error of Estimate and Prediction Intervals 382
Self-Practice Problems 13A 391
Hints and Answers 393
CHAPTER 14 PARTIAL AND MULTIPLE CORRELATION, AND REGRESSION ANALYSIS 396–413
14.1 Introduction 396
14.2 Assumptions in Multiple Linear Regression 396
14.3 Estimating Parameters of Multiple Regression Model 396
Self-Practice Problems 14A 402
Hints and Answers 403
14.4 Standard Error of Estimate for Multiple Regression 404
14.5 Coefficient of Multiple Determination 405
14.6 Multiple Correlation Analysis 405
14.7 Partial Correlation Analysis 406
14.8 Miscellaneous Solved Examples 410
Self-Practice Problems 14B 416
Hints and Answers 416
CHAPTER 15 FORECASTING AND TIME SERIES ANALYSIS 418–455
15.1 Introduction 418
15.2 Time Series Analysis 418
15.3 Time Series Decomposition Models 419
15.4 Quantitative Forecasting Methods 419
Self-Practice Problems 15A 427
Hints and Answers 429
15.5 Trend Projection Methods 431
Self-Practice Problems 15B 436
Hints and Answers 437
15.6 Measurement of Seasonal Effects 438
Self-Practice Problems 15C 454
Hints and Answers 454
CHAPTER 16 INDEX NUMBERS 456–491
16.1 Introduction 456
16.2 Types of Index Numbers 456
16.3 Unweighted Price Indexes 457
Self-Practice Problems 16A 459
Hints and Answers 460
16.4 Weighted Price Indexes 462
viii CONTENTS
16.5 Quantity or Volume Indexes 467
16.6 Value Indexes 470
Self-Practice Problems 16B 470
Hints and Answers 471
16.7 Tests of Adequacy of Indexes 473
16.8 Chain Indexes 474
Self-Practice Problems 16C 481
Hints and Answers 482
16.9 Consumer Price Indexes 484
16.10Miscellaneous Solved Examples 487
CHAPTER 17 STATISTICAL QUALITY CONTROL 492–520
17.1 Quality and Quality Control 492
17.2 Costs of Quality Control 492
17.3 Statistical Quality Control 493
17.4 Techniques of Statistical Quality Control 493
17.5 In-Process Quality Control Techniques 493
17.6 Control Charts for Variables 495
Self-Practice Problems 17A 501
Hints and Answers 501
17.7 Control Charts for Attributes 502
17.8 Specifying an Acceptance Sampling Plan 505
17.9 Determining Error and OC Curve 507
17.10Miscellaneous Solved Examples 510
Self-Practice Problems 17B 519
Hints and Answers 519
CHAPTER 18 STATISTICAL DECISION THEORY 521–552
18.1 Introduction 521
18.2 Decision-Making Under Uncertainty 522
Self-Practice Problems 18A 526
Hints and Answers 527
18.3 Decision-Making Under Risk 527
18.4 Posterior Probabilities and Bayesian Analysis 538
Self-Practice Problems 18B 543
Hints and Answers 543
18.5 Decision Tree Analysis 544
Self-Practice Problems 18C 551
Hints and Answers 552
CHAPTER 19 INTERPOLATION AND EXTRAPOLATION 553–571
19.1 Introduction 553
19.2 Methods of Interpolation 553
19.3 Inverse Interpolation 563
19.4 Extrapolation 564
Self-Practice Problems 19A 570
CONTENTS ix
CHAPTER 20 ASSOCIATIONS OF ATTRIBUTES 572–585
20.1 Consistency of Data 572
20.2 Association and Disassociation 572
20.3 Methods of Studying Association 573
Self-Practice Problems 585