Student-friendly stats! Berenson’s clear and consistent explanations of how and why accepted statistical techniques are used and fresh, conversational writing style helps students with their comprehension of the concepts. Berenson’s real-world business focus takes students beyond the pure theory by connecting statistical concepts to functional areas of business through engaging examples. Examples of real people working in real business environments, and using statistics to tackle real business challenges bring the subject to life.

**Table of Contents**

Brief contents

Detailed contents

Preface

Acknowledgments

How to use this book

About the authors

Part 1: Presenting and Describing Information

Chapter 1: Introduction and data collection

1.1: Basic concepts of statistics

1.2: The growth of statistics and information technology

1.3: Collecting data

Identifying Sources of Data

1.4: Types of variables

Levels of Measurement and Types of Measurement Scales

Summary

Key terms

Chapter review problems

Appendix 1: Introduction to using Microsoft Windows and Excel

Chapter 2: Presenting data in tables and charts

2.1: Tables and charts for categorical data

Summary Tables

Bar Charts

Pie Charts

2.2: Organising numerical data

Ordered Arrays

Stem-and-Leaf Displays

2.3: Tables and graphs for numerical data

Frequency Distributions

Relative Frequency Distributions and Percentage Distributions

Cumulative Distributions

Histograms

Polygons

Cumulative Percentage Polygons (Ogives)

2.4: Cross-tabulations

Contingency Tables

Side-by-Side Bar Charts

2.5: Scatter diagrams and time-series plots

Scatter Diagrams

Time-series Plots

2.6: Misusing graphs and ethical issues

Ethical Concerns

Summary

Key terms

Chapter review problems

Appendix 2: Using statistical software for tables and charts

Chapter 3: Numerical descriptive measures

3.1: Measures of central tendency, variation and shape

Mean

Median

Mode

Quartiles

Geometric Mean

Range

Interquartile Range

Variance and Standard Deviation

Coefficient of Variation

Z Scores

Shape

Microsoft Excel Descriptive Statistics Output

3.2: Numerical descriptive measures for a population

Population Mean

Population Variance and Standard Deviation

The Empirical Rule

The Chebyshev Rule

3.3: Calculating numerical descriptive measures from a frequency distribution

3.4: Five-number summary and box-and-whisker plots

Five-Number Summary

Box-and-Whisker Plots

3.5: Covariance and the coefficient of correlation

Covariance

Coefficient of Correlation

3.6: Pitfalls in numerical descriptive measures and ethical issues

Ethical Issues

Summary

Key formulas

Key terms

Chapter review problems

Appendix 3: Using statistical software for descriptive statistics

End of Part 1 problems

Part 2: Measuring Uncertainty

Chapter 4: Basic probability

4.1: Basic probability concepts

Events and Sample Spaces

Contingency Tables and Venn Diagrams

Marginal Probability

Joint Probability

General Addition Rule

4.2: Conditional probability

Calculating Conditional Probabilities

Decision Trees

Statistical Independence

Multiplication Rules

Marginal Probability Using the General Multiplication Rule

4.3: Bayes’ theorem

4.4: Counting rules

4.5: Ethical issues and probability

Summary

Key formulas

Key terms

Chapter review problems

Appendix 4: Using statistical software for basic probability

Chapter 5: Some important discrete probability distributions

5.1: Probability distribution for a discrete random variable

Expected Value of a Discrete Random Variable

Variance and Standard Deviation of a Discrete Random Variable

5.2: Covariance and its application in finance

Covariance

Expected Value, Variance and Standard Deviation of the Sum of Two Random Variables

Portfolio Expected Return and Portfolio Risk

5.3: Binomial distribution

5.4: Poisson distribution

5.5: Hypergeometric distribution

5.6: (Online Topic) Using the poisson distribution to approximate the binomial distribution

Summary

Key formulas

Key terms

Chapter review problems

Appendix 5: Using statistical software for discrete probability distributions

Chapter 6: The normal distribution and other continuous distributions

6.1: Continuous probability distributions

6.2: The normal distribution

6.3: Evaluating normality

Evaluating the Properties

Constructing a Normal Probability Plot

6.4: The uniform distribution

6.5: The exponential distribution

6.6: The normal approximation to the binomial distribution

Need for a Continuity Correction

Approximating the Binomial Distribution

Calculating a Probability Approximation for an Individual Value

Summary

Key formulas

Key terms

Chapter review problems

Appendix 6: Using statistical software for continuous probability distributions

Chapter 7: Sampling distributions

7.1: Sampling distributions

7.2: Sampling distribution of the mean

The Unbiased Property of the Sample Mean

Standard Error of the Mean

Sampling from Normally Distributed Populations

Sampling from Non-normally Distributed Populations – The Central Limit Theorem

7.3: Sampling distribution of the proportion

7.4: Types of survey sampling methods

Simple Random Sample

Systematic Sample

Stratified Sample

Cluster Sample

7.5: Evaluating survey worthiness

Survey Errors

Ethical Issues

Summary

Key formulas

Key terms

Chapter review problems

Appendix 7: Using statistical software for sampling distributions

End of Part 2 problems

Part 3: Drawing Conclusions about Populations Based only on Sample Information

Chapter 8: Confidence interval estimation

8.1: Confidence interval estimation for the mean (σ known)

8.2: Confidence interval estimation for the mean (σ unknown)

Student’s t Distribution

Properties of the t Distribution

The Concept of Degrees of Freedom

The Confidence Interval Statement

8.3: Confidence interval estimation for the proportion

8.4: Determining sample size

Sample Size Determination for the Mean

Sample Size Determination for the Proportion

8.5: Applications of confidence interval estimation in auditing

Estimating the Population Total Amount

Difference Estimation

One-Sided Confidence Interval Estimation of the Rate of Non-Compliance with Internal Controls

8.6: More on confidence interval estimation and ethical issues

Summary

Key formulas

Key terms

Chapter review problems

Appendix 8: Using statistical software for confidence intervals and sample size determination

Chapter 9: Fundamentals of hypothesis testing: One-sample tests

9.1: Hypothesis-testing methodology

The Null and Alternative Hypotheses

The Critical Value of the Test Statistic

Regions of Rejection and Non-Rejection

Risks in Decision Making Using Hypothesis Testing

9.2: Z test of hypothesis for the mean (σ known)

The Critical Value Approach to Hypothesis Testing

The p-Value Approach to Hypothesis Testing

A Connection between Confidence Interval Estimation and Hypothesis Testing

9.3: One-tail tests

The Critical Value Approach

The p-Value Approach

9.4: t test of hypothesis for the mean (σ unknown)

The Critical Value Approach

The p-Value Approach

Checking Assumptions

9.5: Z test of hypothesis for the proportion

The Critical Value Approach

The p-Value Approach

9.6: The power of a test

9.7: Potential hypothesis-testing pitfalls and ethical issues

Data-Collection Method – Randomisation

Informed Consent from the Human Respondents

Type of Test: Two-Tail or One-Tail

Choice of Level of Significance, 𝛂

Data Snooping

Cleansing and Discarding of Data

Reporting of Findings

Statistical Significance Versus Practical Significance

Summary

Key formulas

Key terms

Chapter review problems

Appendix 9: Using statistical software for one-sample tests of hypothesis

Chapter 10: Hypothesis testing: Two-sample tests

10.1: Comparing the means of two independent populations

Z Test for the Difference between Two Means

Pooled-Variance t Test for the Difference between Two Means

Confidence Interval Estimate for the Difference between the Means of Two Independent Populations

Separate-Variance t Test for the Difference between Two Means

10.2: Comparing the means of two related populations

Paired t Test

Confidence Interval Estimate for the Mean Difference

10.3: F test for the difference between two variances

Finding Lower-Tail Critical Values

10.4: Comparing two population proportions

Z Test for the Difference between Two Proportions

Confidence Interval Estimate for the Difference between Two Proportions

Summary

Key formulas

Key terms

Chapter review problems

Appendix 10: Using statistical software for two-sample tests

Chapter 11: Analysis of variance

11.1: The completely randomised design: One-way analysis of variance

F Test for Differences between More than Two Means

Multiple Comparisons: The Tukey–Kramer Procedure

ANOVA Assumptions

The Levene Test for Homogeneity of Variance

11.2: The randomised block design

Tests for the Treatment and Block Effects

Multiple Comparisons: The Tukey Procedure

11.3: The factorial design: Two-way analysis of variance

Testing for Factor and Interaction Effects

Interpreting Interaction Effects

Multiple Comparisons: The Tukey Procedure

Summary

Key formulas

Key terms

Chapter review problems

Appendix 11: Using statistical software for ANOVA

End of Part 3 problems

Part 4: Determining Cause and Making Reliable Forecasts

Chapter 12: Simple linear regression

12.1: Types of regression models

12.2: Determining the simple linear regression equation

The Least-Squares Method

Predictions in Regression Analysis: Interpolation versus Extrapolation

Calculating the Y Intercept, b0, and the Slope, b1

12.3: Measures of variation

Calculating the Sum of Squares

The Coefficient of Determination

Standard Error of the Estimate

12.4: Assumptions

12.5: Residual analysis

Evaluating the Assumptions

12.6: Measuring autocorrelation: The Durbin–Watson statistic

Residual Plots to Detect Autocorrelation

The Durbin–Watson Statistic

12.7: Inferences about the slope and correlation coefficient

t Test for the Slope

F Test for the Slope

Confidence Interval Estimate of the Slope (𝛃1)

t Test for the Correlation Coefficient

12.8: Estimation of mean values and prediction of individual values

The Confidence Interval Estimate

The Prediction Interval

12.9: Pitfalls in regression and ethical issues

Summary

Key formulas

Key terms

Chapter review problems

Appendix 12: Using statistical software for simple linear regression

Chapter 13: Introduction to multiple regression

13.1: Developing the multiple regression model

Interpreting the Regression Coefficients

Predicting the Dependent Variable, Y

13.2: R2, adjusted R2 and the overall F test

Coefficients of Multiple Determination

Test for the Significance of the Overall Multiple Regression Model

13.3: Residual analysis for the multiple regression model

13.4: Inferences concerning the population regression coefficients

Tests of Hypothesis

Confidence Interval Estimation

13.5: Testing portions of the multiple regression model

Coefficients of Partial Determination

13.6: Using dummy variables and interaction terms in regression models

Interactions

13.7: Collinearity

Summary

Key formulas

Key terms

Chapter review problems

Appendix 13: Using statistical software for multiple regression

Chapter 14: Time-series forecasting and index numbers

14.1: The importance of business forecasting

14.2: Component factors of the classical multiplicative time-series model

14.3: Smoothing the annual time series

Moving Averages

Exponential Smoothing

14.4: Least-squares trend-fitting and forecasting

Linear Trend Model

Quadratic Trend Model

Exponential Trend Model

Model Selection Using First, Second and Percentage Differences

14.5: The Holt–Winters method for trend-fitting and forecasting

14.6: Autoregressive modelling for trend-fitting and forecasting

14.7: Choosing an appropriate forecasting model

Performing a Residual Analysis

Measuring the Magnitude of the Residual Error with Squared or Absolute Differences

Principle of Parsimony

Comparison of Five Forecasting Methods

14.8: Time-series forecasting of seasonal data

Least-Squares Forecasting with Monthly or Quarterly Data

14.9: Index numbers

The Price Index

Aggregate Price Indices

Weighted Aggregate Price Indices

Some Common Price Indices

14.10: Pitfalls in time-series forecasting

Summary

Key formulas

Key terms

Chapter review problems

Appendix 14: Using statistical software for time-series forecasting and index numbers

Chapter 15: Chi-square tests

15.1: Chi-square test for the difference between two proportions (independent samples)

15.2: Chi-square test for differences between more than two proportions

The Marascuilo Procedure

15.3: Chi-square test of independence

15.4: Chi-square goodness-of-fit tests

Chi-Square Goodness-of-Fit Test for a Poisson Distribution

Chi-Square Goodness-of-Fit Test for a Normal Distribution

15.5: Chi-square test for a variance or standard deviation

Summary

Key formulas

Key terms

Chapter review problems

Appendix 15: Using statistical software for chi-square tests

End of Part 4 problems

Part 5: Further Topics in Stats

Chapter 16: Multiple regression model building

16.1: Quadratic regression model

Finding the Regression Coefficients and Predicting Y

Testing for the Significance of the Quadratic Model

Testing the Quadratic Effect

The Coefficient of Multiple Determination

16.2: Using transformations in regression models

The Square-Root Transformation

The Log Transformation

16.3: Influence analysis

The Hat Matrix Elements hi

The Studentised Deleted Residuals ti

Cook’s Distance Statistic Di

Overview

16.4: Model building

The Stepwise Regression Approach to Model Building

The Best-Subsets Approach to Model Building

Model Validation

16.5: Pitfalls in multiple regression and ethical issues

Pitfalls in Multiple Regression

Ethical Considerations

Summary

Key formulas

Key terms

Chapter review problems

Appendix 16: Software for multiple regression model building

Chapter 17: Decision making

17.1: Payoff tables and decision trees

17.2: Criteria for decision making

Expected Monetary Value

Expected Opportunity Loss

Return-to-Risk Ratio

17.3: Decision making with sample information

17.4: Utility

Summary

Key formulas

Key terms

Chapter review problems

Appendix 17: Using statistical software for decision making

Chapter 18: Statistical applications in quality and productivity management

18.1: Total quality management

18.2: Six sigma management

The DMAIC Model

18.3: The theory of control charts

18.4: Control chart for the proportion – the p chart

18.5: The red bead experiment: Understanding process variability

18.6: Control chart for an area of opportunity – the c chart

18.7: Control charts for the range and the mean

The R Chart

The X Chart

18.8: Process capability

Customer Satisfaction and Specification Limits

Capability Indices

CPL, CPU and Cpk

Summary

Key formulas

Key terms

Chapter review problems

Appendix 18: Using statistical software for statistical applications in quality management

Chapter 19: Further non-parametric tests

19.1: McNemar test for the difference between two proportions (related samples)

19.2: Wilcoxon rank sum test: Non-parametric analysis for two independent populations

19.3: Wilcoxon signed ranks test: Non-parametric analysis for two related populations

19.4: Kruskal–Wallis rank test: Non-parametric analysis for the one-way ANOVA

19.5: Friedman rank test: Non-parametric analysis for the randomised block design

Summary

Key formulas

Key terms

Chapter review problems

Appendix 19: Using statistical software for non-parametric tests

End of Part 5 problems

Appendices

A: Review of arithmetic, algebra and logarithms

A.1: Rules for Arithmetic Operations

A.2: Rules for Algebra: Exponents and Square Roots

A.3: Rules for Logarithms

B: Summation notation

C: Statistical symbols and Greek alphabet

C.1: Statistical Symbols

C.2: Greek Alphabet

D: Phstat2 user’s guide

D.1: Sampling Distributions Simulation

D.2: Confidence Interval Estimate for the Mean, Sigma known

D.3: Confidence Interval Estimate for the Mean, Sigma unknown

D.4: Confidence Interval Estimate for the Proportion

D.5: Sample Size Determination for the Mean

D.6: Sample Size Determination for the Proportion

D.7: Confidence Interval Estimate for the Population Total

D.8: Confidence Interval Estimate for the Total Difference

D.9: Z Test for the Mean, Sigma Known

D.10: t Test for the Mean, Sigma Unknown

D.11: Z Test for the Proportion

D.12: Z Test for Differences in two Means

D.13: Pooled-Variance t Test for Differences in two Means (Summarised and Unsummarised Data)

D.14: t Test for Difference in two means (Unsummarised Data)

D.15: F Test for Differences in two Variances

D.16: Z Test for the Differences in two Proportions

D.17: Tukey–Kramer Procedure

D.18: Levene’s Test

D.19: Simple Linear Regression

D.20: Multiple Regression

D.21: Chi-Square Test for Differences in two Proportions

D.22: Chi-Square Test

D.23: Opportunity Loss

D.24: Expected Opportunity Loss

D.25: Expected Monetary Value

E: Tables

E.1: Table of random numbers

E.2: The cumulative standardised normal distribution

E.3: Critical values of t

E.4: Critical values of χ2

E.5: Critical values of F

E.6: Table of binomial probabilities

E.7: Table of Poisson probabilities

E.8: Lower and upper critical values T1 of Wilcoxon rank sum test

E.9: Lower and upper critical values W of Wilcoxon signed ranks test

E.10: Critical values of the Studentised range Q

E.11: Critical values dL and dU of the Durbin–Watson statistic D

E.12: Selected critical values of F for Cook’s Di statistic

E.13: Control chart factors

E.14: The standardised normal distribution

F: Using Microsoft Excel with this text

F.1: Configuring Microsoft Excel

F.2: Using the Data Analysis Tools

F.3: Enhancing the Appearance of Worksheets

F.4: Mac Users and Statistical Programs

Glossary

Index

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