# Statistics for Engineering and the Sciences

## Preview

## Book Description

*Prepare Your Students for Statistical Work in the Real World*

**Statistics for Engineering and the Sciences, Sixth Edition** is designed for a two-semester introductory course on statistics for students majoring in engineering or any of the physical sciences. This popular text continues to teach students the basic concepts of data description and statistical inference as well as the statistical methods necessary for real-world applications. Students will understand how to collect and analyze data and think critically about the results.

**New to the Sixth Edition**

- Many new and updated exercises based on contemporary engineering and scientific-related studies and real data
- More statistical software printouts and corresponding instructions for use that reflect the latest versions of the SAS, SPSS, and MINITAB software
- Introduction of the case studies at the beginning of each chapter
- Streamlined material on all basic sampling concepts, such as random sampling and sample survey designs, which gives students an earlier introduction to key sampling issues
- New examples on comparing matched pairs versus independent samples, selecting the sample size for a designed experiment, and analyzing a two-factor experiment with quantitative factors
- New section on using regression residuals to check the assumptions required in a simple linear regression analysis

The first several chapters of the book identify the objectives of statistics, explain how to describe data, and present the basic concepts of probability. The text then introduces the two methods for making inferences about population parameters: estimation with confidence intervals and hypothesis testing. The remaining chapters extend these concepts to cover other topics useful in analyzing engineering and scientific data, including the analysis of categorical data, regression analysis, model building, analysis of variance for designed experiments, nonparametric statistics, statistical quality control, and product and system reliability.

## Table of Contents

**Introduction **

*STATISTICS IN ACTION*DDT Contamination of Fish in the Tennessee River

Statistics: The Science of Data

Fundamental Elements of Statistics

Types of Data

Collecting Data: Sampling

The Role of Statistics in Critical Thinking

A Guide to Statistical Methods Presented in This Text

*STATISTICS IN ACTION REVISITED*DDT Contamination of Fish in the Tennessee River—Identifying the Data Collection Method, Population, Sample, and Types of Data

**Descriptive Statistics **

*STATISTICS IN ACTION*Characteristics of Contaminated Fish in the Tennessee River, Alabama

Graphical and Numerical Methods for Describing Qualitative Data

Graphical Methods for Describing Quantitative Data

Numerical Methods for Describing Quantitative Data

Measures of Central Tendency

Measures of Variation

Measures of Relative Standing

Methods for Detecting Outliers

Distorting the Truth with Descriptive Statistics

*STATISTICS IN ACTION REVISITED*Characteristics of Contaminated Fish in the Tennessee River, Alabama

**Probability **

*STATISTICS IN ACTION*Assessing Predictors of Software Defects in NASA Spacecraft

Instrument Code

The Role of Probability in Statistics

Events, Sample Spaces, and Probability

Compound Events

Complementary Events

Conditional Probability

Probability Rules for Unions and Intersections

Bayes’ Rule (Optional)

Some Counting Rules

Probability and Statistics: An Example

*STATISTICS IN ACTION REVISITED*Assessing Predictors of Software Defects in NASA Spacecraft Instrument Code

**Discrete Random Variables **

*STATISTICS IN ACTION*The Reliability of a "One-Shot" Device

Discrete Random Variables

The Probability Distribution for a Discrete Random Variable

Expected Values for Random Variables

Some Useful Expectation Theorems

Bernoulli Trials

The Binomial Probability Distribution

The Multinomial Probability Distribution

The Negative Binomial and the Geometric Probability Distributions

The Hypergeometric Probability Distribution

The Poisson Probability Distribution

Moments and Moment Generating Functions (

*Optional*)

*STATISTICS IN ACTION REVISITED*The Reliability of a "One-Shot" Device

**Continuous Random Variables **

*STATISTICS IN ACTION*Super Weapons Development—Optimizing the Hit Ratio

Continuous Random Variables

The Density Function for a Continuous Random Variable

Expected Values for Continuous Random Variables

The Uniform Probability Distribution

The Normal Probability Distribution

Descriptive Methods for Assessing Normality

Gamma-Type Probability Distributions

The Weibull Probability Distribution

Beta-Type Probability Distributions

Moments and Moment Generating Functions (

*Optional*)

*STATISTICS IN ACTION REVISTED*Super Weapons Development—Optimizing the Hit Ratio

**Bivariate Probability Distributions and Sampling Distributions **

*STATISTICS IN ACTION*Availability of an Up/Down Maintained System

Bivariate Probability Distributions for Discrete Random Variables

Bivariate Probability Distributions for Continuous Random Variables

The Expected Value of Functions of Two Random Variables

Independence

The Covariance and Correlation of Two Random Variables

Probability Distributions and Expected Values of Functions of Random Variables (

*Optional*)

Sampling Distributions

Approximating a Sampling Distribution by Monte Carlo Simulation

The Sampling Distributions of Means and Sums

Normal Approximation to the Binomial Distribution

Sampling Distributions Related to the Normal Distribution

*STATISTICS IN ACTION REVISITED*Availability of an Up/Down Maintained System

**Estimation Using Confidence Intervals **

*STATISTICS IN ACTION*Bursting Strength of PET Beverage Bottles

Point Estimators and their Properties

Finding Point Estimators: Classical Methods of Estimation

Finding Interval Estimators: The Pivotal Method

Estimation of a Population Mean

Estimation of the Difference between Two Population Means: Independent Samples

Estimation of the Difference between Two Population Means: Matched Pairs

Estimation of a Population Proportion

Estimation of the Difference between Two Population Proportions

Estimation of a Population Variance

Estimation of the Ratio of Two Population Variances

Choosing the Sample Size

Alternative Interval Estimation Methods: Bootstrapping and Bayesian Methods (

*Optional*)

*STATISTICS IN ACTION REVISITED*Bursting Strength of PET Beverage Bottles

**Tests of Hypotheses **

*STATISTICS IN ACTION*Comparing Methods for Dissolving Drug Tablets—Dissolution Method Equivalence Testing

The Relationship between Statistical Tests of Hypotheses and Confidence Intervals

Elements and Properties of a Statistical Test

Finding Statistical Tests: Classical Methods

Choosing the Null and Alternative Hypotheses

The Observed Significance Level for a Test

Testing a Population Mean

Testing the Difference between Two Population Means: Independent Samples

Testing the Difference between Two Population Means: Matched Pairs

Testing a Population Proportion

Testing the Difference between Two Population Proportions

Testing a Population Variance

Testing the Ratio of Two Population Variances

Alternative Testing Procedures: Bootstrapping and Bayesian Methods (

*Optional*)

*STATISTICS IN ACTION REVISITED*Comparing Methods for Dissolving Drug Tablets—Dissolution Method Equivalence Testing

**Categorical Data Analysis **

*STATISTICS IN ACTION*The Case of the Ghoulish Transplant Tissue—Who Is Responsible for Paying Damages?

Categorical Data and Multinomial Probabilities

Estimating Category Probabilities in a One-Way Table

Testing Category Probabilities in a One-Way Table

Inferences about Category Probabilities in a Two-Way (Contingency) Table

Contingency Tables with Fixed Marginal Totals

Exact Tests for Independence in a Contingency Table Analysis (

*Optional*)

*STATISTICS IN ACTION REVISITED*The Case of the Ghoulish Transplant Tissue

**Simple Linear Regression **

*STATISTICS IN ACTION*Can Dowsers Really Detect Water?

Regression Models

Model Assumptions

Estimating

*β*

_{0}and

*β*

_{1}: The Method of Least Squares

Properties of the Least-Squares Estimators

An Estimator of

*σ*

^{2}

Assessing the Utility of the Model: Making Inferences about the Slope

The Coefficients of Correlation and Determination

Using the Model for Estimation and Prediction

Checking the Assumptions: Residual Analysis

A Complete Example

A Summary of the Steps to Follow in Simple Linear Regression

*STATISTICS IN ACTION REVISITED*Can Dowsers Really Detect Water?

**Multiple Regression Analysis **

*STATISTICS IN ACTION*Bid-Rigging in the Highway Construction Industry

General Form of a Multiple Regression Model

Model Assumptions

Fitting the Model: The Method of Least Squares

Computations Using Matrix Algebra: Estimating and Making Inferences about the Individual Parameters

Assessing Overall Model Adequacy

A Confidence Interval for and a Prediction Interval for a Future Value of

*y*

A First-Order Model with Quantitative Predictors

An Interaction Model with Quantitative Predictors

A Quadratic (Second-Order) Model with a Quantitative Predictor

Regression Residuals and Outliers

Some Pitfalls: Estimability, Multicollinearity, and Extrapolation

A Summary of the Steps to Follow in a Multiple Regression Analysis

*STATISTICS IN ACTION REVISITED*Building a Model for Road Construction Costs in a Sealed Bid Market

**Model Building **

*STATISTICS IN ACTION*Deregulation of the Intrastate Trucking Industry

Introduction: Why Model Building Is Important

The Two Types of Independent Variables: Quantitative and Qualitative

Models with a Single Quantitative Independent Variable

Models with Two or More Quantitative Independent Variables

Coding Quantitative Independent Variables (

*Optional*)

Models with One Qualitative Independent Variable

Models with Both Quantitative and Qualitative Independent Variables

Tests for Comparing Nested Models

External Model Validation

*(Optional)*

Stepwise Regression

*STATISTICS IN ACTION REVISITED*Deregulation in the Intrastate Trucking Industry

**Principles of Experimental Design **

*STATISTICS IN ACTION*Anti-Corrosive Behavior of Epoxy Coatings Augmented with Zinc

Introduction

Experimental Design Terminology

Controlling the Information in an Experiment

Noise-Reducing Designs

Volume-Increasing Designs

Selecting the Sample Size

The Importance of Randomization

*STATISTICS IN ACTION REVISITED*Anti-Corrosive Behavior of Epoxy Coatings Augmented with Zinc

**The Analysis of Variance for Designed Experiments **

*STATISTICS IN ACTION*Pollutants at a Housing Development—A Case of Mishandling Small Samples

Introduction

The Logic behind an Analysis of Variance

One-Factor Completely Randomized Designs

Randomized Block Designs

Two-Factor Factorial Experiments

More Complex Factorial Designs (

*Optional*)

Nested Sampling Designs (

*Optional*)

Multiple Comparisons of Treatment Means

Checking ANOVA Assumptions

*STATISTICS IN ACTION REVISTED*Pollutants at a Housing Development—A Case of Mishandling Small Samples

**Nonparametric Statistics **

*STATISTICS IN ACTION*How Vulnerable Are New Hampshire Wells to Groundwater Contamination?

Introduction: Distribution-Free Tests

Testing for Location of a Single Population

Comparing Two Populations: Independent Random Samples

Comparing Two Populations: Matched-Pairs Design

Comparing Three or More Populations: Completely Randomized Design

Comparing Three or More Populations: Randomized Block Design

Nonparametric Regression

*STATISTICS IN ACTION REVISITED*How Vulnerable Are New Hampshire Wells to Groundwater Contamination?

**Statistical Process and Quality Control **

*STATISTICS IN ACTION*Testing Jet Fuel Additive for Safety

Total Quality Management

Variable Control Charts

Control Chart for Means:

*x*-Chart

Control Chart for Process Variation: R-Chart

Detecting Trends in a Control Chart: Runs Analysis

Control Chart for Percent Defectives:

*p*-Chart

Control Chart for the Number of Defects per Item:

*c*-Chart

Tolerance Limits

Capability Analysis (

*Optional*)

Acceptance Sampling for Defectives

Other Sampling Plans (

*Optional*)

Evolutionary Operations (

*Optional*)

*STATISTICS IN ACTION REVISITED*Testing Jet Fuel Additive for Safety

**Product and System Reliability **

*STATISTICS IN ACTION*Modeling the Hazard Rate of Reinforced Concrete Bridge Deck Deterioration

Introduction

Failure Time Distributions

Hazard Rates

Life Testing: Censored Sampling

Estimating the Parameters of an Exponential Failure Time Distribution

Estimating the Parameters of a Weibull Failure Time Distribution

System Reliability

*STATISTICS IN ACTION REVISITED*Modeling the Hazard Rate of Reinforced Concrete Bridge Deck Deterioration

**Appendix A: ****Matrix Algebra ****Appendix B: Useful Statistical Tables ****Appendix C: ****SAS for Windows Tutorial Appendix D: **

**MINITAB for Windows Tutorial**

Appendix E: SPSS for Windows Tutorial

Appendix E: SPSS for Windows Tutorial

## Author(s)

### Biography

**William Mendenhall** was a professor emeritus in the Statistics Department and the first chairman of the department at the University of Florida. Dr. Mendenhall published articles in top statistics journals and was a prolific author of statistics textbooks.

**Terry L. Sincich** is an associate professor in the Information Systems Decision Sciences Department at the University of South Florida, where he teaches introductory statistics at the undergraduate level and advanced statistics courses at the doctoral level. He has won numerous teaching awards, including the Kahn Teaching Award and Outstanding Teacher Award. Dr. Sincich is a member of the American Statistical Association and the Decision Sciences Institute. His research interests include applied statistical analysis and statistical modeling.

## Reviews

"A salient feature of this book is the clarity with which many statistical concepts have been presented. A very nice blend of theory and applications. It contains a wealth of illustrative examples and problem sets. All the important concepts have been highlighted; real-life data has been extensively used throughout the book. Students will find it very appealing and useful on their way to learning the basic statistical concepts and tools."

—Dharam V. Chopra, Wichita State University"I like the problems because they are all based on engineering applications of probability and statistics. I especially like the problems at the end of chapters because students have to think more to solve them. I favor problems that require calculations because engineers are problem solvers."

—Charles H. Reilly, University of Central Florida"I think this text is one of the best I have seen when it comes down to real data sets. The authors successfully included small and large real data sets from various real-world problems in engineering, mathematical sciences, and natural sciences."

—Edward J. Danial, Morgan State University