Elementary Statistics: A Step By Step Approach

892 Pages·2017·27.982 MB·English

by  Allan Bluman

Connect Math Hosted by ALEKS
Glossary of Symbols
Built By Today’s Educators,
a y intercept of a line F Scheffé test value
S
α Probability of a type I error GM Geometric mean
For Today’s Students
b Slope of a line H Kruskal-Wallis test value
β Probability of a type II error H Null hypothesis
0
Fewer clicks means more time for you... C Column frequency H Alternative hypothesis
1
cf Cumulative frequency HM Harmonic mean
C Number of combinations of n objects taking k Number of samples
n r
r objects at a time λ Number of occurrences for the Poisson
C.V. Critical value distribution
Change assignment
CVar Coefficient of variation s Standard deviation of the differences
dates right from the D
D Difference; decile s Standard error of estimate
home page. __ est
Teaching multiple D Mean of the differences SSB Sum of squares between groups
sections? Easily move
d.f. Degrees of freedom SS Sum of squares within groups
W
from one to another. d.f.N. Degrees of freedom, numerator sB2 Between-group variance
d.f.D. Degrees of freedom, denominator sW2 Within-group variance
E Event; expected frequency; maximum error t t test value
of estimate t Two-tailed t critical value
__ α∕2
E Complement of an event μ Population mean
e Euler’s constant ≈ 2.7183 μ Mean of the population differences
D
E(X) Expected value μ _X Mean of the sample means
f Frequency w Class width; weight
F F test value; failure r Sample correlation coefficient
F′ Critical value for the Scheffé test R Multiple correlation coefficient
...and your students. MD Median r2 Coefficient of determination
MR Midrange 𝜌 Population correlation coefficient
MS Mean square between groups r Spearman rank correlation coefficient
Online Exercises were carefully selected and B S
MS Mean square within groups (error) S Sample space; success
developed to provide a seamless transition from W
n Sample size s Sample standard deviation
textbook to technology.
N Population size s2 Sample variance
n(E) Number of ways E can occur σ Population standard deviation
n(S) Number of outcomes in the sample space σ2 Population variance
O Observed frequency σ _X Standard error of the mean
P Percentile; probability Σ Summation notation
p Probability; population proportion w Smaller sum of signed ranks, Wilcoxon
s
P ˆ Sample proportion signed-rank test
_p_ Weighted estimate of p X Data value; number of successes for a
P(BA⃒ ) Conditional probability binomial distribution
__
P(E) Probability of an event E X Sample mean
__
P( E ) Probability of the complement of E x Independent variable in regression
__
P Number of permutations of n objects taking X Grand mean
n r GM
r objects at a time X Midpoint of a class
m
π Pi ≈ 3.14 �2 Chi-square
For consistency, the guided solutions match the style and voice Q Quartile y Dependent variable in regression
of the original text as though the author is guiding the students q 1 − p; test value for Tukey test y′ Predicted y value
through the problems. qˆ 1 − pˆ z z test value or z score
_q_ 1 − _p_ z Two-tailed critical z value
α∕2
R Range; rank sum ! Factorial
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A L L A N G . B L U M A N
PROFESSOR EMERITUS
COMMUNITY COLLEGE OF ALLEGHENY COUNTY
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ELEMENTARY STATISTICS: A STEP BY STEP APPROACH, TENTH EDITION
Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2018 by McGraw-Hill
Education. All rights reserved. Printed in the United States of America. Previous editions © 2014, 2012, and
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limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.
Some ancillaries, including electronic and print components, may not be available to customers outside the
United States.
This book is printed on acid-free paper.
1 2 3 4 5 6 7 8 9 LWI 21 20 19 18 17
ISBN 978-1-259-75533-0
MHID 1-259-75533-9
ISBN 978-1-260-04200-9 (Annotated Instructor’s Edition)
MHID 1-260-04200-6
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All credits appearing on page or at the end of the book are considered to be an extension of the copyright page.
Library of Congress Cataloging-in-Publication Data
Bluman, Allan G.
Elementary statistics : a step by step approach / Allan G. Bluman,
professor emeritus, Community College of Allegheny Dounty.
Tenth edition. | New York, NY : McGraw-Hill Education, [2018] |
Includes index.
LCCN 2016028437 | ISBN 9781259755330 (alk. paper)
LCSH: Statistics—Textbooks. | Mathematical statistics—Textbooks.
LCC QA276.12 .B59 2018 | DDC 519.5—dc23 LC record available
at https://lccn.loc.gov/2016028437
The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does
not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not
guarantee the accuracy of the information presented at these sites.
mheducation.com/highered
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A B O U T T H E A U T H O R
Allan G. Bluman
Allan G. Bluman is a professor emeritus at the Community College of Allegheny County,
South Campus, near Pittsburgh, Pennsylvania. He has taught mathematics and statistics
for over 35 years. He received an Apple for the Teacher award in recognition of his bring-
ing excellence to the learning environment at South Campus. He has also taught statistics
for Penn State University at the Greater Allegheny (McKeesport) Campus and at the
Monroeville Center. He received his master’s and doctor’s degrees from the University
of Pittsburgh.
Courtesy Allan G. Bluman He is also author of Elementary Statistics: A Brief Version and coauthor of Math in
Our World. In addition, he is the author of four mathematics books in the McGraw-Hill
DeMystified Series. They are Pre-Algebra, Math Word Problems, Business Math, and
Probability.
He is married and has two sons, a granddaughter, and a grandson.
Dedication: To Betty Bluman, Earl McPeek, and Dr. G. Bradley Seager, Jr.
iii
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C O N T E N T S
Preface ix Relative Frequency Graphs 61
Distribution Shapes 63
C H A P T E R 1 2–3 Other Types of Graphs 74
Bar Graphs 75
The Nature of Pareto Charts 77

The Time Series Graph 78
Probability and
The Pie Graph 80
Statistics 1 Dotplots 83
Stem and Leaf Plots 83
Introduction 2 Misleading Graphs 86
1–1 Descriptive and Inferential Statistics 3 Summary 100
1–2 Variables and Types of Data 6
3
1–3 Data Collection and Sampling Techniques 11 C H A P T E R
Random Sampling 12
Systematic Sampling 12 Data Description
109
Stratified Sampling 13

Cluster Sampling 14
Other Sampling Methods 14
1–4 Experimental Design 18
Observational and Experimental Studies 18 Introduction 110
Uses and Misuses of Statistics 21 3–1 Measures of Central Tendency 111
1–5 Computers and Calculators 26 The Mean 111
Summary 33 The Median 114
The Mode 116
C H A P T E R 2 The Midrange 118
The Weighted Mean 119
Frequency Distributions Distribution Shapes 121
3–2 Measures of Variation 127
and Graphs
41 Range 129
Population Variance and Standard Deviation 129
Sample Variance and Standard Deviation 132
Introduction 42 Variance and Standard Deviation for Grouped
2–1 Organizing Data 42 Data 135
Coefficient of Variation 137
Categorical Frequency Distributions 43
Range Rule of Thumb 138
Grouped Frequency Distributions 44
2–2 Histograms, Frequency Polygons, and Chebyshev’s Theorem 139
Ogives 57 The Empirical (Normal) Rule 141
The Histogram 57 Linear Transformation of Data 142
The Frequency Polygon 58 3–3 Measures of Position 148
The Ogive 59 Standard Scores 148
All examples and exercises in this textbook (unless cited) are hypothetical and are presented to enable students to achieve a basic understanding of the statistical concepts
explained. These examples and exercises should not be used in lieu of medical, psychological, or other professional advice. Neither the author nor the publisher shall be held
responsible for any misuse of the information presented in this textbook.
v
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vi Contents
Percentiles 149 Variance and Standard Deviation 267
Quartiles and Deciles 155 Expectation 269
Outliers 157 5–3 The Binomial Distribution 275
3–4 Exploratory Data Analysis 168 5–4 Other Types of Distributions 289
The Five-Number Summary and Boxplots 168 The Multinomial Distribution 289
Summary 177 The Poisson Distribution 291
The Hypergeometric Distribution 293
C H A P T E R 4 The Geometric Distribution 295
Summary 303
Probability and
6
Counting Rules C H A P T E R
185

The Normal
Introduction 186 Distribution 311
4–1 Sample Spaces and Probability 186
Basic Concepts 186
Classical Probability 189
Introduction 312
Complementary Events 192
6–1 Normal Distributions 312
Empirical Probability 194
The Standard Normal Distribution 315
Law of Large Numbers 196
Finding Areas Under the Standard Normal
Subjective Probability 196 Distribution Curve 316
Probability and Risk Taking 196 A Normal Distribution Curve as a Probability
4–2 The Addition Rules for Probability 201 Distribution Curve 318
4–3 The Multiplication Rules and Conditional 6–2 Applications of the Normal Distribution 328
Probability 213
Finding Data Values Given Specific
The Multiplication Rules 213 Probabilities 332
Conditional Probability 217 Determining Normality 334
Probabilities for “At Least” 220 6–3 The Central Limit Theorem 344
4–4 Counting Rules 226 Distribution of Sample Means 344
The Fundamental Counting Rule 227 Finite Population Correction Factor (Optional) 350
Factorial Notation 229 6–4 The Normal Approximation to the Binomial
Distribution 354
Permutations 229
Summary 361
Combinations 232
4–5 Probability and Counting Rules 242
Summary 246 7
C H A P T E R
5
C H A P T E R Confidence Intervals
and Sample Size
Discrete Probability 369
Distributions
257
Introduction 370
7–1 Confidence Intervals for the Mean When σ Is
Introduction 258 Known 370
5–1 Probability Distributions 258 Confidence Intervals 371
5–2 Mean, Variance, Standard Deviation, and Sample Size 377
Expectation 265 7–2 Confidence Intervals for the Mean When σ Is
Mean 265 Unknown 383
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Contents vii
7–3 Confidence Intervals and Sample Size for 9–5 Testing the Difference Between Two
Proportions 390 Variances 528
Confidence Intervals 391 Summary 539
Sample Size for Proportions 393
7–4 Confidence Intervals for Variances and C H A P T E R 10
Standard Deviations 398
Summary 406
Correlation and
C H A P T E R 8 Regression 547
Hypothesis
Introduction 548
Testing
413
10–1 Scatter Plots and Correlation 548
Correlation 552
10–2 Regression 563
Introduction 414
Line of Best Fit 564
8–1 Steps in Hypothesis Testing—Traditional
Determination of the Regression Line
Method 414
Equation 565
8–2 z Test for a Mean 426 10–3 Coefficient of Determination and Standard
P-Value Method for Hypothesis Testing 430 Error of the Estimate 580
8–3 t Test for a Mean 442 Types of Variation for the Regression Model 580
8–4 z Test for a Proportion 453 Residual Plots 582
8–5 𝛘2 Test for a Variance or Standard Coefficient of Determination 583
Deviation 461
Standard Error of the Estimate 584
8–6 Additional Topics Regarding Hypothesis
Prediction Interval 587
Testing 474
10–4 Multiple Regression (Optional) 590
Confidence Intervals and Hypothesis Testing 474
The Multiple Regression Equation 591
Type II Error and the Power of a Test 476
Testing the Significance of R 593
Summary 479
Adjusted R2 594
Summary 599
9
C H A P T E R
11
C H A P T E R
Testing the
Difference Between Other Chi-Square
Two Means, Two Tests
607
Proportions, and
Two Variances
487
Introduction 608
11–1 Test for Goodness of Fit 608
Introduction 488
Test of Normality (Optional) 614
9–1 Testing the Difference Between Two Means:
Using the z Test 488 11–2 Tests Using Contingency Tables 622
9–2 T esting the Difference Between Two Means Test for Independence 622
of Independent Samples: Using the t Test 499 Test for Homogeneity of Proportions 628
9–3 Testing the Difference Between Two Means: Summary 638
Dependent Samples 507
9–4 Testing the Difference Between
Proportions 519
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viii Contents
12 14
C H A P T E R C H A P T E R
Analysis of Sampling and
Variance Simulation
645 737
Introduction 646 Introduction 738
12–1 One-Way Analysis of Variance 646 14–1 Common Sampling Techniques 738
12–2 The Scheffé Test and the Tukey Test 658 Random Sampling 739
Scheffé Test 658 Systematic Sampling 742
Tukey Test 659 Stratified Sampling 744
12–3 Two-Way Analysis of Variance 662 Cluster Sampling 746
Summary 676 Other Types of Sampling Techniques 746
14–2 Surveys and Questionnaire Design 753
C H A P T E R 13 14–3 Simulation Techniques and the Monte Carlo
Method 756
The Monte Carlo Method 756
Nonparametric
Summary 762
Statistics
685
A P P E N D I C E S
Introduction 686 A Tables 769
13–1 Advantages and Disadvantages B Data Bank 794
of Nonparametric Methods 686
Advantages 686 C Glossary 801
Disadvantages 686 D Selected Answers SA–1
Ranking 687
13–2 The Sign Test 689
Single-Sample Sign Test 689
Paired-Sample Sign Test 691
13–3 The Wilcoxon Rank Sum Test 698
13–4 The Wilcoxon Signed-Rank Test 703 Index I–1
13–5 The Kruskal-Wallis Test 708
13–6 The Spearman Rank Correlation Coefficient ADDITIONAL TOPICS ONLINE
and the Runs Test 715
(www.mhhe.com/bluman)
Rank Correlation Coefficient 715
Algebra Review
The Runs Test 718
Summary 729
Writing the Research Report
Bayes’ Theorem
Alternate Approach to the Standard
Normal Distribution
Bibliography
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