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Introduction to Probability and Statistics 14th Edition.pdf
Cover
Title Page
Copyright
Contents
Introduction: What is Statistics?
The Population and the Sample
Descriptive and Inferential Statistics
Achieving the Objective of Inferential Statistics: The Necessary Steps
Keys for Successful Learning
1 DESCRIBING DATA WITH GRAPHS
1.1 Variables and Data
1.2 Types of Variables
1.3 Graphs for Categorical Data
Exercises
1.4 Graphs for Quantitative Data
Pie Charts and Bar Charts
Line Charts
Dotplots
Stem and Leaf Plots
Interpreting Graphs with a Critical Eye
1.5 Relative Frequency Histograms
Exercises
Chapter Review
Technology Today
Supplementary Exercises
CASE STUDY: How Is Your Blood Pressure?
2 DESCRIBING DATA WITH NUMERICAL MEASURES
2.1 Describing a Set of Data with Numerical Measures
2.2 Measures of Center
Exercises
2.3 Measures of Variability
Exercises
2.4 On the Practical Significance of the Standard Deviation
2.5 A Check on the Calculation of s
Exercises
2.6 Measures of Relative Standing
2.7 The Five-Number Summary and the Box Plot
Exercises
Chapter Review
Technology Today
Supplementary Exercises
CASE STUDY: The Boys of Summer
3 DESCRIBING BIVARIATE DATA
3.1 Bivariate Data
3.2 Graphs for Categorical Variables
Exercises
3.3 Scatterplots for Two Quantitative Variables
3.4 Numerical Measures for Quantitative Bivariate Data
Exercises
Chapter Review
Technology Today
Supplementary Exercises
CASE STUDY: Are Your Dishes Really Clean?
4 PROBABILITY AND PROBABILITY DISTRIBUTIONS
4.1 The Role of Probability in Statistics
4.2 Events and the Sample Space
4.3 Calculating Probabilities Using Simple Events
Exercises
4.4 Useful Counting Rules (Optional)
Exercises
4.5 Event Relations and Probability Rules
Calculating Probabilities for Unions and Complements
4.6 Independence, Conditional Probability, and the Multiplication Rule
Exercises
4.7 Bayes’ Rule (Optional)
Exercises
4.8 Discrete Random Variables and Their Probability Distributions
Random Variables
Probability Distributions
The Mean and Standard Deviation for a Discrete Random Variable
Exercises
Chapter Review
Technology Today
Supplementary Exercises
CASE STUDY: Probability and Decision Making in the Congo
5 SEVERAL USEFUL DISCRETE DISTRIBUTIONS
5.1 Introduction
5.2 The Binomial Probability Distribution
Exercises
5.3 The Poisson Probability Distribution
Exercises
5.4 The Hypergeometric Probability Distribution
Exercises
Chapter Review
Technology Today
Supplementary Exercises
CASE STUDY: A Mystery: Cancers Near a Reactor
6 THE NORMAL PROBABILITY DISTRIBUTION
6.1 Probability Distributions for Continuous Random Variables
6.2 The Normal Probability Distribution
6.3 Tabulated Areas of the Normal Probability Distribution
The Standard Normal Random Variable
Calculating Probabilities for a General Normal Random Variable
Exercises
6.4 The Normal Approximation to the Binomial Probability Distribution (Optional)
Exercises
Chapter Review
Technology Today
Supplementary Exercises
CASE STUDY: “Are You Going to Curve the Grades?”
7 SAMPLING DISTRIBUTIONS
7.1 Introduction
7.2 Sampling Plans and Experimental Designs
Exercises
7.3 Statistics and Sampling Distributions
7.4 The Central Limit Theorem
7.5 The Sampling Distribution of the Sample Mean
Standard Error
Exercises
7.6 The Sampling Distribution of the Sample Proportion
Exercises
7.7 A Sampling Application: Statistical Process Control (Optional)
A Control Chart for the Process Mean: The x Chart
A Control Chart for the Proportion Defective: The p Chart
Exercises
Chapter Review
Technology Today
Supplementary Exercises
CASE STUDY: Sampling the Roulette at Monte Carlo
8 LARGE-SAMPLE ESTIMATION
8.1 Where We’ve Been
8.2 Where We’re Going—Statistical Inference
8.3 Types of Estimators
8.4 Point Estimation
Exercises
8.5 Interval Estimation
Constructing a Confidence Interval
Large-Sample Confidence Interval for a Population Mean μ
Interpreting the Confidence Interval
Large-Sample Confidence Interval for a Population Proportion p
Exercises
8.6 Estimating the Difference between Two Population Means
Exercises
8.7 Estimating the Difference between Two Binomial Proportions
Exercises
8.8 One-Sided Confidence Bounds
8.9 Choosing the Sample Size
Exercises
Chapter Review
Supplementary Exercises
CASE STUDY: How Reliable Is That Poll? CBS News: How and Where America Eats
9 LARGE-SAMPLE TESTS OF HYPOTHESES
9.1 Testing Hypotheses about Population Parameters
9.2 A Statistical Test of Hypothesis
9.3 A Large-Sample Test about a Population Mean
The Essentials of the Test
Calculating the p-Value
Two Types of Errors
The Power of a Statistical Test
Exercises
9.4 A Large-Sample Test of Hypothesis for the Difference between Two Population Means
Hypothesis Testing and Confidence Intervals
Exercises
9.5 A Large-Sample Test of Hypothesis for a Binomial Proportion
Statistical Significance and Practical Importance
Exercises
9.6 A Large-Sample Test of Hypothesis for the Difference between Two Binomial Proportions
Exercises
9.7 Some Comments on Testing Hypotheses
Chapter Review
Supplementary Exercises
CASE STUDY: An Aspirin a Day . . . ?
10 INFERENCE FROM SMALL SAMPLES
10.1 Introduction
10.2 Student’s t Distribution
Assumptions behind Student’s t Distribution
10.3 Small-Sample Inferences Concerning a Population Mean
Exercises
10.4 Small-Sample Inferences for the Difference between Two Population Means: Independent Random Samples
Exercises
10.5 Small-Sample Inferences for the Difference between Two Means: A Paired-Difference Test
Exercises
10.6 Inferences Concerning a Population Variance
Exercises
10.7 Comparing Two Population Variances
Exercises
10.8 Revisiting the Small-Sample Assumptions
Chapter Review
Technology Today
Supplementary Exercises
CASE STUDY: School Accountability Study—How Is Your School Doing?
11 THE ANALYSIS OF VARIANCE
11.1 The Design of an Experiment
11.2 What Is an Analysis of Variance?
11.3 The Assumptions for an Analysis of Variance
11.4 The Completely Randomized Design: A One-Way Classification
11.5 The Analysis of Variance for a Completely Randomized Design
Partitioning the Total Variation in an Experiment
Testing the Equality of the Treatment Means
Estimating Differences in the Treatment Means
Exercises
11.6 Ranking Population Means
Exercises
11.7 The Randomized Block Design: A Two-Way Classification
11.8 The Analysis of Variance for a Randomized Block Design
Partitioning the Total Variation in the Experiment
Testing the Equality of the Treatment and Block Means
Identifying Differences in the Treatment and Block Means
Some Cautionary Comments on Blocking
Exercises
11.9 The a × b Factorial Experiment: A Two-Way Classification
11.10 The Analysis of Variance for an a × b Factorial Experiment
Exercises
11.11 Revisiting the Analysis of Variance Assumptions
Residual Plots
11.12 A Brief Summary
Chapter Review
Technology Today
Supplementary Exercises
CASE STUDY: How to Save Money on Groceries!
12 LINEAR REGRESSION AND CORRELATION
12.1 Introduction
12.2 A Simple Linear Probabilistic Model
12.3 The Method of Least Squares
12.4 An Analysis of Variance for Linear Regression
Exercises
12.5 Testing the Usefulness of the Linear Regression Model
Inferences Concerning β, the Slope of the Line of Means
The Analysis of Variance F-Test
Measuring the Strength of the Relationship: The Coefficient of Determination
Interpreting the Results of a Significant Regression
Exercises
12.6 Diagnostic Tools for Checking the Regression Assumptions
Dependent Error Terms
Residual Plots
Exercises
12.7 Estimation and Prediction Using the Fitted Line
Exercises
12.8 Correlation Analysis
Exercises
Chapter Review
Technology Today
Supplementary Exercises
CASE STUDY: Is Your Car “Made in the U.S.A.”?
13 MULTIPLE REGRESSION ANALYSIS
13.1 Introduction
13.2 The Multiple Regression Model
13.3 A Multiple Regression Analysis
The Method of Least Squares
The Analysis of Variance for Multiple Regression
Testing the Usefulness of the Regression Model
Interpreting the Results of a Significant Regression
Checking the Regression Assumptions
Using the Regression Model for Estimation and Prediction
13.4 A Polynomial Regression Model
Exercises
13.5 Using Quantitative and Qualitative Predictor Variables in a Regression Model
Exercises
13.6 Testing Sets of Regression Coefficients
13.7 Interpreting Residual Plots
13.8 Stepwise Regression Analysis
13.9 Misinterpreting a Regression Analysis
Causality
Multicollinearity
13.10 Steps to Follow When Building a Multiple Regression Model
Chapter Review
Technology Today
Supplementary Exercises
CASE STUDY: “Made in the U.S.A.”—Another Look
14 ANALYSIS OF CATEGORICAL DATA
14.1 A Description of the Experiment
14.2 Pearson’s Chi-Square Statistic
14.3 Testing Specified Cell Probabilities: The Goodness-of-Fit Test
Exercises
14.4 Contingency Tables: A Two-Way Classification
The Chi-Square Test of Independence
Exercises
14.5 Comparing Several Multinomial Populations: A Two-Way Classification with Fixed Row or Column Totals
Exercises
14.6 The Equivalence of Statistical Tests
14.7 Other Applications of the Chi-Square Test
Chapter Review
Technology Today
Supplementary Exercises
CASE STUDY: Who is the Primary Breadwinner in Your Family?
15 NONPARAMETRIC STATISTICS
15.1 Introduction
15.2 The Wilcoxon Rank Sum Test: Independent Random Samples
Normal Approximation for the Wilcoxon Rank Sum Test
Exercises
15.3 The Sign Test for a Paired Experiment
Normal Approximation for the Sign Test
Exercises
15.4 A Comparison of Statistical Tests
15.5 The Wilcoxon Signed-Rank Test for a Paired Experiment
Normal Approximation for the Wilcoxon Signed-Rank Test
Exercises
15.6 The Kruskal–Wallis H-Test for Completely Randomized Designs
Exercises
15.7 The Friedman F[sub(r)]-Test for Randomized Block Designs
Exercises
15.8 Rank Correlation Coefficient
Exercises
15.9 Summary
Chapter Review
Technology Today
Supplementary Exercises
CASE STUDY: How’s Your Cholesterol Level?
APPENDIX I
Table 1 Cumulative Binomial Probabilities
Table 2 Cumulative Poisson Probabilities
Table 3 Areas under the Normal Curve
Table 4 Critical Values of t
Table 5 Critical Values of Chi-Square
Table 6 Percentage Points of the F Distribution
Table 7 Critical Values of T for the Wilcoxon Rank Sum Test, n[sub(1)] ≤ n[sub(2)]
Table 8 Critical Values of T for the Wilcoxon Signed-Rank Test, n = 5(1)50
Table 9 Critical Values of Spearman’s Rank Correlation Coefficient for a One-Tailed Test
Table 10 Random Numbers
Table 11 Percentage Points of the Studentized Range, q.[sub(05)](k, df)
DATA SOURCES
ANSWERS TO SELECTED EXERCISES
INDEX
This is an electronic version of the print textbook. Due to electronic rights restrictions,
some third party content may be suppressed. Editorial review has deemed that any suppressed
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Introduction to
Probability and Statistics
14th
E D I T I O N
William Mendenhall, III
Robert J. Beaver
University of California, Riverside, Emeritus
Barbara M. Beaver
University of California, Riverside, Emeritus
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
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Introduction to Probability and
Statistics, Fourteenth Edition
Mendenhall/Beaver/Beaver
Editor in Chief: Michelle Julet
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1 2 3 4 5 6 7 15 14 13 12 11
Preface
Every time you pick up a newspaper or a magazine, watch TV, or surf the Internet, you
encounter statistics. Every time you fill out a questionnaire, register at an online website,
or pass your grocery rewards card through an electronic scanner, your personal infor-
mation becomes part of a database containing your personal statistical information. You
cannot avoid the fact that in this information age, data collection and analysis are an
integral part of our day-to-day activities. In order to be an educated consumer and citi-
zen, you need to understand how statistics are used and misused in our daily lives.
THE SECRET TO OUR SUCCESS
The first college course in introductory statistics that we ever took used Introduction to
Probability and Statistics by William Mendenhall. Since that time, this text—currently
in the fourteenth edition—has helped several generations of students understand what
statistics is all about and how it can be used as a tool in their particular area of applica-
tion. The secret to the success of Introduction to Probability and Statistics is its ability
to blend the old with the new. With each revision we try to build on the strong points
of previous editions, while always looking for new ways to motivate, encourage, and
interest students using new technological tools.
HALLMARK FEATURES OF THE
FOURTEENTH EDITION
The fourteenth edition retains the traditional outline for the coverage of descriptive and
inferential statistics. This revision maintains the straightforward presentation of the
thirteenth edition. In this spirit, we have continued to simplify and clarify the language
and to make the language and style more readable and “user friendly”—without sacri-
ficing the statistical integrity of the presentation. Great effort has been taken to explain
not only how to apply statistical procedures, but also to explain
how to meaningfully describe real sets of data
•
• what the results of statistical tests mean in terms of their practical applications
•
• what to do when statistical assumptions have been violated
how to evaluate the validity of the assumptions behind statistical tests
iv ❍
PREFACE
Exercises
In the tradition of all previous editions, the variety and number of real applications in
the exercise sets is a major strength of this edition. We have revised the exercise sets to
provide new and interesting real-world situations and real data sets, many of which are
drawn from current periodicals and journals. The fourteenth edition contains over 1300
problems, many of which are new to this edition. A set of classic exercises compiled
from previous editions is available on the website (http://www.cengage. com/statistics/
mendenhall). Exercises are graduated in level of difficulty; some, involving only basic
techniques, can be solved by almost all students, while others, involving practical
applications and interpretation of results, will challenge students to use more sophisti-
cated statistical reasoning and understanding.
Organization and Coverage
We believe that Chapters 1 through 10—with the possible exception of Chapter 3—
should be covered in the order presented. The remaining chapters can be covered in any
order. The analysis of variance chapter precedes the regression chapter, so that the
instructor can present the analysis of variance as part of a regression analysis. Thus, the
most effective presentation would order these three chapters as well.
Chapters 1–3 present descriptive data analysis for both one and two variables, us-
ing both MINITAB and Microsoft Excel® graphics. Chapter 4 includes a full presenta-
tion of probability and probability distributions. Three optional sections—Counting
Rules, the Total Law of Probability, and Bayes’ Rule—are placed into the general
flow of text, and instructors will have the option of complete or partial coverage. The
sections that present event relations, independence, conditional probability, and the
Multiplication Rule have been rewritten in an attempt to clarify concepts that often
are difficult for students to grasp. As in the thirteenth edition, the chapters on analy-
sis of variance and linear regression include both calculational formulas and computer
printouts in the basic text presentation. These chapters can be used with equal ease
by instructors who wish to use the “hands-on” computational approach to linear re-
gression and ANOVA and by those who choose to focus on the interpretation of com-
puter-generated statistical printouts.
One important feature in the hypothesis testing chapters involves the emphasis on
p-values and their use in judging statistical significance. With the advent of computer-
generated p-values, these probabilities have become essential components in report-
ing the results of a statistical analysis. As such, the observed value of the test statistic
and its p-value are presented together at the outset of our discussion of statistical hy-
pothesis testing as equivalent tools for decision-making. Statistical significance is de-
fined in terms of preassigned values of a, and the p-value approach is presented as
an alternative to the critical value approach for testing a statistical hypothesis. Ex-
amples are presented using both the p-value and critical value approaches to hypoth-
esis testing. Discussion of the practical interpretation of statistical results, along with
the difference between statistical significance and practical significance, is emphasized
in the practical examples in the text.
Special Features of the Fourteenth Edition
• NEED TO KNOW. . .: A special feature of this edition are highlighted sections
called “NEED TO KNOW. . .” and identified by this icon.
These
sections provide information consisting of definitions, procedures or step-by-step
PREFACE
v
hints on problem solving for specific questions such as “NEED TO KNOW… How
to Construct a Relative Frequency Histogram?” or “NEED TO KNOW… How to
Decide Which Test to Use?”
• Applets: Easy access to the Internet has made it possible for students to visualize
statistical concepts using an interactive webtool called an applet. Applets written
by Gary McClelland, author of Seeing StatisticsTM, are found on the CourseMate
Website that accompanies the text. Following each applet, appropriate
exercises are available that provide visual reinforcement of the concepts pre-
sented in the text. Applets allow the user to perform a statistical experiment, to
interact with a statistical graph, to change its form, or to access an interactive
“statistical table.”
• Graphical and numerical data description includes both traditional and EDA
methods, using computer graphics generated by MINITAB 16 for Windows and
MS Excel.
❍
vi
PREFACE
• All examples and exercises in the text contain printouts based on MINITAB 16
and consistent with earlier versions of MINITAB or MS Excel. Printouts are pro-
vided for some exercises, while other exercises require the student to obtain so-
lutions without using a computer.
1.47 Presidential Vetoes Here is a list of the
44 presidents of the United States along with
EX0147
the number of regular vetoes used by each:5
Washington
J. Adams
Jefferson
Madison
Monroe
J. Q. Adams
Jackson
Van Buren
W. H. Harrison
Tyler
Polk
Taylor
Fillmore
Pierce
Buchanan
Lincoln
A. Johnson
Grant
Hayes
Garfield
Arthur
Cleveland
Source: The World Almanac and Book of Facts 2011
B. Harrison
Cleveland
McKinley
T. Roosevelt
Taft
Wilson
Harding
Coolidge
Hoover
F. D. Roosevelt
Truman
Eisenhower
Kennedy
L. Johnson
Nixon
Ford
Carter
Reagan
G. H. W. Bush
Clinton
G. W. Bush
Obama
19
42
6
42
30
33
5
20
21
372
180
73
12
16
26
48
13
39
29
36
11
1
2
0
0
5
1
0
5
0
0
6
2
0
0
9
4
2
21
45
12
0
4
304
Use an appropriate graph to describe the number of
vetoes cast by the 44 presidents. Write a summary
paragraph describing this set of data.
1.48 Windy Cities Are some cities more
windy than others? Does Chicago deserve to be
EX0148
121.3
120.2
121.4
122.2
123.0
123.2
122.0
121.3
122.4
121.0
125.0
122.1
121.1
122.2
122.2
122.1
120.3
122.1
123.2
122.4
121.4
121.1
122.0
120.1
121.1
123.0
122.0
121.4
120.0
119.2† 124.0
122.2
122.1
122.2
123.3
122.1
(1950) 121.3 122.3
121.4
(1960) 122.2 124.0
122.2
(1970) 123.2 123.1
125.0
(1980) 122.0 122.0
(1990) 122.0 123.0
123.2
(2000) 121.0 119.97 121.13 121.19 124.06 122.75 121.36 122.17 121.86 122.66
(2010) 124.4
†Record time set by Secretariat in 1973.
Source: www.kentuckyderby.com
a. Do you think there will be a trend in the winning
times over the years? Draw a line chart to verify
your answer.
b. Describe the distribution of winning times using an
appropriate graph. Comment on the shape of the
distribution and look for any unusual observations.
1.50 Gulf Oil Spill Cleanup On April 20,
2010, the United States experienced a major
EX0150
environmental disaster when a Deepwater Horizon
drilling rig exploded in the Gulf of Mexico. The
number of personnel and equipment used in the Gulf
oil spill cleanup, beginning May 2, 2010 (Day 13)
through June 9, 2010 (Day 51) is given in the
following table.13
Number of personnel (1000s)
Federal Gulf fishing areas closed
Booms laid (miles)
Dispersants used (1000 gallons)
Day 13 Day 26 Day 39 Day 51
24.0
32%
909
1143
20.0
25%
644
870
17.5
8%
315
500
3.0
3%
46
156
The Role of Computers in the
Fourteenth Edition—TECHNOLOGY TODAY
Computers are now a common tool for college students in all disciplines. Most students
are accomplished users of word processors, spreadsheets, and databases, and they have no
trouble navigating through software packages in the Windows environment. We believe,
however, that advances in computer technology should not turn statistical analyses into a
“black box.” Rather, we choose to use the computational shortcuts and interactive visual
tools that modern technology provides to give us more time to emphasize statistical rea-
soning as well as the understanding and interpretation of statistical results.
In this edition, students will be able to use computers for both standard statistical
analyses and as a tool for reinforcing and visualizing statistical concepts. Both MS Excel
and MINITAB 16 (consistent with earlier versions of MINITAB) are used exclusively
as the computer packages for statistical analysis. However, we have chosen to isolate
the instructions for generating computer output into individual sections called Tech-
nology Today at the end of each chapter. Each discussion uses numerical examples to
guide the student through the MS Excel commands and option necessary for the pro-
cedures presented in that chapter, and then present the equivalent steps and commands
needed to produce the same or similar results using MINITAB. We have included screen
captures from both MS Excel and MINITAB 16, so that the student can actually work
through these sections as “mini-labs.”
If you do not need “hands-on” knowledge of MINITAB or MS Excel, or if you are
using another software package, you may choose to skip these sections and simply
use the printouts as guides for the basic understanding of computer printouts.
❍
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