# Practice of Statistics for Business and Economics

## Fourth EditionDavid S Moore; George P. McCabe; Layth C. Alwan; Bruce A. Craig

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*Practice of Statistics for Business and Economics* gives you the practical tools you need to make data-informed, real-world business decisions.

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Learn More## Table of Contents

To Instructors: About This Book

SaplingPlus for Statistics

To Students: What Is Statistics?

Index of Cases

Index of Data Tables

Beyond the Basics Index

About the Authors

**CHAPTER 1 Examining Distributions**

Introduction **1.1 Data SECTION 1.1 SUMMARY SECTION 1.1 EXERCISES1.2 Displaying Distributions with Graphs**

Categorical variables: bar graphs and pie charts

Quantitative variables: histograms

**CASE 1.1 Treasury Bills**

Quantitative variables: stemplots

Interpreting histograms and stemplots

Timeplots

**SECTION 1.2 SUMMARY**

SECTION 1.2 EXERCISES

1.3 Describing Distributions with Numbers

CASE 1.2 Time to Start a Business

SECTION 1.2 EXERCISES

1.3 Describing Distributions with Numbers

CASE 1.2 Time to Start a Business

Measuring center: the mean

Measuring center: the median

Comparing the mean and the median

Measuring spread: the quartiles

The five-number summary and boxplots

The 1.5 × IQR rule for outliers

Measuring spread: the standard deviation

Choosing measures of center and spread

**BEYOND THE BASICS: Risk and return**

SECTION 1.3 SUMMARY

SECTION 1.3 EXERCISES

1.4 Density Curves and the Normal Distributions

SECTION 1.3 SUMMARY

SECTION 1.3 EXERCISES

1.4 Density Curves and the Normal Distributions

Density curves

The median and mean of a density curve

Normal distributions

The 68–95–99.7 rule

The standard Normal distribution

Normal distribution calculations

Using the standard Normal table

Inverse Normal calculations

Assessing the Normality of data

**BEYOND THE BASICS: Density estimation**

SECTION 1.4 SUMMARY

SECTION 1.4 EXERCISES

CHAPTER 1 REVIEW EXERCISES

SECTION 1.4 SUMMARY

SECTION 1.4 EXERCISES

CHAPTER 1 REVIEW EXERCISES

**CHAPTER 2 Examining Relationships**

Introduction **2.1 Scatterplots CASE 2.1 Education Expenditures and Population: Benchmarking**

Interpreting scatterplots

The log transformation

Adding categorical variables to scatterplots

**SECTION 2.1 SUMMARY**

SECTION 2.1 EXERCISES

2.2 Correlation

SECTION 2.1 EXERCISES

2.2 Correlation

The correlation r

Facts about correlation

**SECTION 2.2 SUMMARY**

SECTION 2.2 EXERCISES

2.3 Least-Squares Regression

SECTION 2.2 EXERCISES

2.3 Least-Squares Regression

The least-squares regression line

Facts about least-squares regression

Interpretation of r^2

Residuals

The distribution of the residuals

Influential observations

**SECTION 2.3 SUMMARY**

SECTION 2.3 EXERCISES

2.4 Cautions about Correlation and Regression

SECTION 2.3 EXERCISES

2.4 Cautions about Correlation and Regression

Extrapolation

Lurking variables

Correlation does not imply causation

**BEYOND THE BASICS: Big Data**

SECTION 2.4 SUMMARY

SECTION 2.4 EXERCISES

2.5 Data Analysis for Two-Way Tables

CASE 2.2 Does the Right Music Sell the Product?

SECTION 2.4 SUMMARY

SECTION 2.4 EXERCISES

2.5 Data Analysis for Two-Way Tables

CASE 2.2 Does the Right Music Sell the Product?

Marginal distributions

Conditional distributions

Mosaic plots and software output

Simpson’s paradox

**SECTION 2.5 SUMMARY**

SECTION 2.5 EXERCISES

CHAPTER 2 REVIEW EXERCISES

SECTION 2.5 EXERCISES

CHAPTER 2 REVIEW EXERCISES

**CHAPTER 3 Producing Data**

Introduction **3.1 Sources of Data**

Anecdotal data

Available data

Sample surveys and experiments

Other sources and uses of data **SECTION 3.1 SUMMARY SECTION 3.1 EXERCISES 3.2 Designing Samples**

Simple random samples

Stratified samples

Multistage samples

Cautions about sample surveys

**BEYOND THE BASICS: Capture-recapture sampling**

SECTION 3.2 SUMMARY

SECTION 3.2 EXERCISES

3.3 Designing Experiments

SECTION 3.2 SUMMARY

SECTION 3.2 EXERCISES

3.3 Designing Experiments

Comparative experiments

Randomized comparative experiments

Completely randomized designs

How to randomize

The logic of randomized comparative experiments

Cautions about experimentation

Matched pairs designs

Block designs

**SECTION 3.3 SUMMARY**

SECTION 3.3 EXERCISES

3.4 Data Ethics

SECTION 3.3 EXERCISES

3.4 Data Ethics

Institutional review boards

Informed consent

Confidentiality

Clinical trials

Behavioral and social science experiments

**SECTION 3.4 SUMMARY**

SECTION 3.4 EXERCISES

CHAPTER 3 REVIEW EXERCISES

SECTION 3.4 EXERCISES

CHAPTER 3 REVIEW EXERCISES

**CHAPTER 4 Probability: The Study of Randomness**

Introduction **4.1 Randomness**

The language of probability

Thinking about randomness and probability **SECTION 4.1 SUMMARY SECTION 4.1 EXERCISES 4.2 Probability Models**

Sample spaces

Probability rules

Assigning probabilities: Finite number of outcomes

**CASE 4.1 Uncovering Fraud by Digital Analysis**

Assigning probabilities: Equally likely outcomes

Independence and the multiplication rule

Applying the probability rules

**SECTION 4.2 SUMMARY**

SECTION 4.2 EXERCISES

4.3 General Probability Rules

SECTION 4.2 EXERCISES

4.3 General Probability Rules

General addition rules

Two-way table of counts to probabilities

Conditional probability

General multiplication rule

Tree diagrams

Bayes’ rule

Independence again

**SECTION 4.3 SUMMARY**

SECTION 4.3 EXERCISES

CHAPTER 4 REVIEW EXERCISES

SECTION 4.3 EXERCISES

CHAPTER 4 REVIEW EXERCISES

**CHAPTER 5 Random Variables and Probability Distributions**

Introduction **5.1 Random Variables**

Discrete random variables **CASE 5.1 Tracking Perishable Demand**

Continuous random variables **SECTION 5.1 SUMMARY SECTION 5.1 EXERCISES 5.2 Means and Variances of Random Variables**

The mean of a random variable

Mean and the law of large numbers

Thinking about the law of large numbers

Rules for means

**CASE 5.2 Portfolio Analysis**

The variance of a random variable

Rules for variances and standard deviations

**SECTION 5.2 SUMMARY**

SECTION 5.2 EXERCISES

5.3 Common Discrete Distributions

SECTION 5.2 EXERCISES

5.3 Common Discrete Distributions

Binomial distributions

The binomial distributions for sample counts

The binomial distributions for statistical sampling

**CASE 5.3 Inspecting a Supplier’s Products**

Finding binomial probabilities

Binomial formula

Binomial mean and standard deviation

Assessing the binomial assumptions with data

Poisson distributions

The Poisson setting

The Poisson model

Poisson approximation of the binomial

Assessing the Poisson assumptions with data

**SECTION 5.3 SUMMARY**

SECTION 5.3 EXERCISES

5.4 Common Continuous Distributions

SECTION 5.3 EXERCISES

5.4 Common Continuous Distributions

Uniform distributions

Revisiting Normal distributions

Normal approximation for binomial distribution

The continuity correction

Normal approximation for Poisson distribution

Exponential distributions

**SECTION 5.4 SUMMARY**

SECTION 5.4 EXERCISES

CHAPTER 5 REVIEW EXERCISES

SECTION 5.4 EXERCISES

CHAPTER 5 REVIEW EXERCISES

**CHAPTER 6 Sampling Distributions**

Introduction **6.1 Toward Statistical Inference**

Sampling variability

Sampling distributions

Bias and variability in estimation

Sampling from large populations

Why randomize? **SECTION 6.1 SUMMARY SECTION 6.1 EXERCISES 6.2 The Sampling Distribution of the Sample Mean**

The mean and standard deviation of x

The central limit theorem

How large is large enough?

Two more facts

**SECTION 6.2 SUMMARY**

SECTION 6.2 EXERCISES

SECTION 6.2 EXERCISES

6.3 The Sampling Distribution of the Sample Proportion

Sample proportion mean and standard deviation

Normal approximation for proportions

**SECTION 6.3 SUMMARY**

SECTION 6.3 EXERCISES

CHAPTER 6 REVIEW EXERCISES

SECTION 6.3 EXERCISES

CHAPTER 6 REVIEW EXERCISES

**CHAPTER 7 Introduction to Inference**

Introduction

Overview of inference **7.1 Estimating with Confidence**

Statistical confidence

Confidence intervals

Confidence interval for a population mean **CASE 7.1 Bankruptcy Attorney Fees**

How confidence intervals behave

Some cautions **SECTION 7.1 SUMMARY SECTION 7.1 EXERCISES 7.2 Tests of Significance**

The reasoning of significance tests

**CASE 7.2 Fill the Bottles**

Step 1: Stating the hypotheses

Step 2: Calculating the value of a test statistic

Step 3: Finding the P-value

Step 4: Stating a conclusion

Summary of the z test for one population mean

Two-sided significance tests and confidence intervals

Assessing significance with P-values versus critical values

**SECTION 7.2 SUMMARY**

SECTION 7.2 EXERCISES

7.3 Use and Abuse of Tests

SECTION 7.2 EXERCISES

7.3 Use and Abuse of Tests

Choosing a level of significance

Statistical significance does not imply practical significance

Statistical inference is not valid for all sets of data

Beware of searching for significance

**SECTION 7.3 SUMMARY**

SECTION 7.3 EXERCISES

7.4 Prediction Intervals

SECTION 7.3 EXERCISES

Concept of random deviations

Prediction of a single observation

**SECTION 7.4 SUMMARY**

SECTION 7.4 EXERCISES

CHAPTER 7 REVIEW EXERCISES

SECTION 7.4 EXERCISES

CHAPTER 7 REVIEW EXERCISES

**CHAPTER 8 Inference for Means**

Introduction **8.1 Inference for the Mean of a Population t distributions**

The one-sample t confidence interval **CASE 8.1 Battery Life of a Smartphone**

The one-sample t test

Using software

Matched pairs t procedures

Robustness of the one-sample t procedures

Inference for non-Normal populations **BEYOND THE BASICS: The bootstrap SECTION 8.1 SUMMARY SECTION 8.1 EXERCISES 8.2 Comparing Two Means**

The two-sample t statistic

The two-sample t confidence interval

The two-sample t significance test

Robustness of the two-sample procedures

Inference for small samples

The pooled two-sample t procedures

**CASE 8.2 Active Versus Failed Retail Companies**

SECTION 8.2 SUMMARY

SECTION 8.2 EXERCISES

8.3 Additional Topics on Inference

SECTION 8.2 SUMMARY

SECTION 8.2 EXERCISES

8.3 Additional Topics on Inference

Sample size for confidence intervals

Power of a significance test

Inference as a decision

**SECTION 8.3 SUMMARY**

SECTION 8.3 EXERCISES

CHAPTER 8 REVIEW EXERCISES

SECTION 8.3 EXERCISES

CHAPTER 8 REVIEW EXERCISES

**CHAPTER 9 One-Way Analysis of Variance**

Introduction **9.1 One-Way Analysis of Variance**

The ANOVA setting

Comparing means

Revisiting the pooled two-sample t statistic

An overview of ANOVA **CASE 9.1 Tip of the Hat and Wag of the Finger? **The ANOVA model

Estimates of population parameters

Testing hypotheses in one-way ANOVA

The ANOVA table

The F test

Using software

**BEYOND THE BASICS: Testing the equality of spread**

SECTION 9.1 SUMMARY

SECTION 9.1 EXERCISES

9.2 Additional Comparisons of Group Means

Contrasts

SECTION 9.1 SUMMARY

SECTION 9.1 EXERCISES

9.2 Additional Comparisons of Group Means

**CASE 9.2 Evaluation of a New Educational Product**

Multiple comparisons

Simultaneous confidence intervals

Assessing the power of the ANOVA F test

**SECTION 9.2 SUMMARY**

SECTION 9.2 EXERCISES

CHAPTER 9 REVIEW EXERCISES

SECTION 9.2 EXERCISES

CHAPTER 9 REVIEW EXERCISES

**CHAPTER 10 Inference for Proportions**

Introduction **10.1 Inference for a Single Proportion CASE 10.1 Trends in the Workplace**

Large-sample confidence interval for a single proportion

**BEYOND THE BASICS: Plus four confidence interval for a single proportion**

Significance test for a single proportion

Choosing a sample size for a confidence interval

**CASE 10.2 Marketing Christmas Trees**

Choosing a sample size for a significance test

**SECTION 10.1 SUMMARY**

SECTION 10.1 EXERCISES

10.2 Comparing Two Proportions

SECTION 10.1 EXERCISES

10.2 Comparing Two Proportions

Large-sample confidence intervals for a difference in proportions

**CASE 10.3 Social Media in the Supply Chain**

BEYOND THE BASICS: Plus four confidence intervals for a difference in proportions

BEYOND THE BASICS: Plus four confidence intervals for a difference in proportions

Significance tests

Choosing a sample size for two sample proportions

**BEYOND THE BASICS: Relative risk**

SECTION 10.2 SUMMARY

SECTION 10.2 EXERCISES

CHAPTER 10 REVIEW EXERCISES

SECTION 10.2 SUMMARY

SECTION 10.2 EXERCISES

CHAPTER 10 REVIEW EXERCISES

**CHAPTER 11 Inference for Categorical Data**

Introduction **11.1 Inference for Two-Way Tables**

Two-way tables **CASE 11.1 Are Flexible Companies More Competitive?**

Describing relations in two-way tables

The null hypothesis: no association

Expected cell counts

The chi-square test

The chi-square test and the z test

Models for two-way tables **BEYOND THE BASICS: Meta-analysis SECTION 11.1 SUMMARY SECTION 11.1 EXERCISES 11.2 Goodness of Fit SECTION 11.2 SUMMARY SECTION 11.2 EXERCISES CHAPTER 11 REVIEW EXERCISES **

**CHAPTER 12 Inference for Regression**

Introduction **12.1 Inference about the Regression Model**

Statistical model for simple linear regression

From data analysis to inference **CASE 12.1 The Relationship between Income and Education for Entrepreneurs**

Estimating the regression parameters

Conditions for regression inference

Confidence intervals and significance tests

The word “regression”

Inference about correlation **SECTION 12.1 SUMMARY SECTION 12.1 EXERCISES 12.2 Using the Regression Line**

Confidence and prediction intervals

**BEYOND THE BASICS: Nonlinear regression**

SECTION 12.2 SUMMARY

SECTION 12.2 EXERCISES

12.3 Some Details of Regression Inference

SECTION 12.2 SUMMARY

SECTION 12.2 EXERCISES

12.3 Some Details of Regression Inference

Standard errors

Analysis of variance for regression

**SECTION 12.3 SUMMARY**

SECTION 12.3 EXERCISES

CHAPTER 12 REVIEW EXERCISES

SECTION 12.3 EXERCISES

CHAPTER 12 REVIEW EXERCISES

**CHAPTER 13 Multiple Regression**

Introduction **13.1 Data Analysis for Multiple Regression**

Using a linear model with multiple variables**CASE 13.1 The Inclusive Development Index (IDI)**

Data for multiple regression

Preliminary data analysis for multiple regression

Estimating the multiple regression coefficients

Regression residuals

The regression standard error **SECTION 13.1 SUMMARY SECTION 13.1 EXERCISES 13.2 Inference for Multiple Regression**

Multiple linear regression model

**CASE 13.2 Predicting Movie Revenue**

Estimating the parameters of the model

Inference about the regression coefficients

Inference about prediction

ANOVA table for multiple regression

Squared multiple correlation R^2

Inference for a collection of regression coefficients

**SECTION 13.2 SUMMARY**

SECTION 13.2 EXERCISES

13.3 Multiple Regression Model Building

CASE 13.3 Prices of Homes

SECTION 13.2 EXERCISES

13.3 Multiple Regression Model Building

CASE 13.3 Prices of Homes

Models for curved relationships

Models with categorical explanatory variables

More elaborate models

Variable selection methods

**BEYOND THE BASICS: Regression trees**

SECTION 13.3 SUMMARY

SECTION 13.3 EXERCISES

CHAPTER 13 REVIEW EXERCISES

SECTION 13.3 SUMMARY

SECTION 13.3 EXERCISES

CHAPTER 13 REVIEW EXERCISES

**CHAPTER 14 Time Series Forecasting**

Introduction

Overview of Time Series Forecasting **14.1 Assessing Time Series Behavior CASE 14.1 Adidas Stock Price Returns**

Random process model

Nonrandom processes

**CASE 14.2 Amazon Sales**

Runs test

Autocorrelation function

Forecasts of a random process

**SECTION 14.1 SUMMARY**

SECTION 14.1 EXERCISES

14.2 Random Walks

SECTION 14.1 EXERCISES

14.2 Random Walks

Price changes versus returns

Deterministic and stochastic trends

**BEYOND THE BASICS: Dickey-Fuller tests**

SECTION 14.2 SUMMARY

SECTION 14.2 EXERCISES

14.3 Basic Smoothing Models

SECTION 14.2 SUMMARY

SECTION 14.2 EXERCISES

14.3 Basic Smoothing Models

Moving-average models

**CASE 14.3 Lake Michigan Water Levels**

Forecasting accuracy

Moving average and seasonal indexes

Exponential smoothing models

**SECTION 14.3 SUMMARY**

SECTION 14.3 EXERCISES

14.4 Regression-Based Forecasting Models

SECTION 14.3 EXERCISES

14.4 Regression-Based Forecasting Models

Modeling deterministic trends

Modeling seasonality

Residual checking

Modeling with lagged variables

**BEYOND THE BASICS: ARCH models**

SECTION 14.4 SUMMARY

SECTION 14.4 EXERCISES

CHAPTER 14 REVIEW EXERCISES

SECTION 14.4 SUMMARY

SECTION 14.4 EXERCISES

CHAPTER 14 REVIEW EXERCISES

**Tables T-1Answers to Odd-Numbered Exercises S-1Index I-1**

The following optional Companion Chapters can be found online at www.macmillanhighered.com/psbe5e.

**CHAPTER 15 Statistics for Quality: Control and Capability**

Introduction

Quality overview

Systematic approach to process improvement

Process improvement toolkit **15.1 Statistical Process Control SECTION 15.1 SUMMARY SECTION 15.1 EXERCISES 15.2 Variable Control Charts**

x and R charts

**CASE 15.1 Turnaround Time for Lab Results**

CASE 15.2 O-Ring Diameters

x and s charts

CASE 15.2 O-Ring Diameters

Assumptions underlying subgroup charts

Charts for individual observations

**SECTION 15.2 SUMMARY**

SECTION 15.2 EXERCISES

15.3 Process Capability Indices

SECTION 15.3 SUMMARY

SECTION 15.3 EXERCISES

15.4 Attribute Control Charts

SECTION 15.2 EXERCISES

15.3 Process Capability Indices

SECTION 15.3 SUMMARY

SECTION 15.3 EXERCISES

15.4 Attribute Control Charts

Control charts for sample proportions

**CASE 15.3 Reducing Absenteeism**

Control charts for counts per unit of measure

**SECTION 15.4 SUMMARY**

SECTION 15.4 EXERCISES

CHAPTER 15 REVIEW EXERCISES

SECTION 15.4 EXERCISES

CHAPTER 15 REVIEW EXERCISES

**CHAPTER 16 Two-Way Analysis of Variance **Introduction

**16.1 The Two-Way ANOVA Model**

Advantages of two-way ANOVA

The two-way ANOVA model

Main effects and interactions

**SECTION 16.1 SUMMARY**

SECTION 16.1 EXERCISES

16.2 Inference for Two-Way ANOVA

SECTION 16.1 EXERCISES

16.2 Inference for Two-Way ANOVA

The ANOVA table for two-way ANOVA

Carrying out a two-way ANOVA

**CASE 16.1 Discounts and Expected Prices**

CASE 16.2 Expected Prices, Continued

SECTION 16.2 SUMMARY

SECTION 16.2 EXERCISES

CHAPTER 16 REVIEW EXERCISES

CASE 16.2 Expected Prices, Continued

SECTION 16.2 SUMMARY

SECTION 16.2 EXERCISES

CHAPTER 16 REVIEW EXERCISES

**CHAPTER 17 Nonparametric Tests **Introduction

**17.1 The Wilcoxon Rank Sum Test**

CASE 17.1 Price Discrimination?

CASE 17.1 Price Discrimination?

The rank transformation

The Wilcoxon rank sum test

The Normal approximation

What hypotheses do the Wilcoxon test?

Ties

**CASE 17.2 Consumer Perceptions of Food Safety**

Rank versus t tests

**SECTION 17.1 SUMMARY**

SECTION 17.1 EXERCISES

17.2 The Wilcoxon Signed Rank Test

SECTION 17.1 EXERCISES

17.2 The Wilcoxon Signed Rank Test

The Normal approximation

Ties

**SECTION 17.2 SUMMARY**

SECTION 17.2 EXERCISES

17.3 The Kruskal-Wallis Test

SECTION 17.2 EXERCISES

17.3 The Kruskal-Wallis Test

Hypotheses and assumptions

The Kruskal-Wallis test

**SECTION 17.3 SUMMARY**

SECTION 17.3 EXERCISES

CHAPTER 17 REVIEW EXERCISES

SECTION 17.3 EXERCISES

CHAPTER 17 REVIEW EXERCISES

**CHAPTER 18 Logistic Regression**

Introduction **18.1 The Logistic Regression Model CASE 18.1 Clothing Color and Tipping **Binomial distributions and odds

Model for logistic regression

Fitting and interpreting the logistic regression model

**SECTION 18.1 SUMMARY**

SECTION 18.1 EXERCISES

18.2 Inference for Logistic Regression

SECTION 18.1 EXERCISES

18.2 Inference for Logistic Regression

Examples of logistic regression analyses

**SECTION 18.2 SUMMARY**

SECTION 18.2 EXERCISES

18.3 Multiple Logistic Regression

SECTION 18.3 SUMMARY

SECTION 18.3 EXERCISES

CHAPTER 18 REVIEW EXERCISES

SECTION 18.2 EXERCISES

18.3 Multiple Logistic Regression

SECTION 18.3 SUMMARY

SECTION 18.3 EXERCISES

CHAPTER 18 REVIEW EXERCISES