The Humongous Book of Statistics Problems: Translated for People Who Don't Speak Math (Humongous Book Of...)

562 Pages·2009·12.95 MB·English

by  W. Michael Kelley, Robert A. Donnelly

A member of Penguin Group (USA) Inc.
A member of Penguin Group (USA) Inc.
ALPHA BOOKS
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Copyright © 2009 by W. Michael Kelley
All rights reserved. No part of this book shall be reproduced, stored in a retrieval system, or
transmitted by any means, electronic, mechanical, photocopying, recording, or otherwise,
without written permission from the publisher. No patent liability is assumed with respect to
the use of the information contained herein. Although every precaution has been taken in
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contained herein. For information, address Alpha Books, 800 East 96th Street, Indianapolis,
IN 46240.
ISBN: 1-101-15010-6
Library of Congress Catalog Card Number: 2006926601
Note: This publication contains the opinions and ideas of its author. It is intended to
provide helpful and informative material on the subject matter covered. It is sold with the
understanding that the author and publisher are not engaged in rendering professional
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professional should be consulted.
The author and publisher specifically disclaim any responsibility for any liability, loss, or risk,
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and application of any of the contents of this book.
Contents
Introduction
Chapter 1: Displaying Descriptive Statistics HjbbVg^o^c\YViV^ciVWaZh!X]Vgih!VcY\gVe]h 1
Frequency Distributions .......H..]..d.l..^.c..\..n..d.j..g..Y..V...i.V...^.c..V...i..V..W..aZ................................................ 2
Histograms ......H..].d..l..^.c.\...n.d..j..g..[..g.Z.f..j..Z..c.X..n...Y..^.h.i.g..^W..j..i..^d..c..^.c..V....X.]..V..g..i....................................... 5
Bar Charts .........................H..]..d.l...^c..\..n..d.j..g..X..V..i..Z..\.d..g.^X..V..a..Y..V..i..V...^.c..V...X..]..V..g.i............................ 8
Pie Charts ........H..].d..l..^.c.\...n.d..j..g..X..V..i.Z..\..d.g.^.X..V..a.Y...V..i.V...^.c..V...X..^.g.X..a.Z............................................. 14
Line Charts ........................H..]..d.l..^.c.\...n..d.j..g..Y..V..i..V...d.k..Z.g...i.^.b..Z...^.c..V...X..]..V..g.i............................. 19
Scatter Charts ......H..]..d.l...^c..\..g..Z.a.V..i..^d..c.h..]..^e..h..W.Z..i..l..Z..Z..c..i..l..d..k..V..g.^.V..W..aZ..h..^.c..V....X.]..V..g..i.Y..................... 21
Chapter 2: Calculating Descriptive Statistics: Measures ;o^fc YC^ce\ntir]aZl XTZendency V i 25
Mean ...............................................I..]..Z...V..k.Z..g.V..\..Z..................................................... 26
Median ...............................G..^.\..].i...h.b..V...X.`...^.c..i..].Z...b...^Y...Y..aZ............................................... 30
Midrange ........................=..V..a[..l..V..n...W.Z..i..l..Z..Z..c..i..].Z...Z..c.Y...e.d.^.c..i.h........................................... 32
Mode ...................;..^.c.Y..^.c..\..i..].Z...b...d.h.i...[.g.Z..f..j..Z..c.i..k..V..a.j..Z..................................................... 33
Percentile ...................................D..c..V...h..X.V...aZ...[..g.d.b....&..i..d..&..%.%............................................ 36
Weighted Mean ...................................6..k..Z.g..V..\.^.c..\..j..h.^.c.\...Y..^.[.[..Z..g.Z..c.i...l..Z..^\..]..i.h...................... 42
Mean of a Frequency Distribution ...............6..k..Z..g.V..\.^.c..\..Y..^.h.X..g.Z..i..Z..Y...V..i.V.............................. 45
ChapMteera 3n: oCf al cGurloautpinedg FDreqsucernipcyt iDvies tSritbautitisotnic s..:. .M..Z8.e.V.ai.as.X.uZ.j.r.agV.e.is.. ^c.co.\.f. .iV.].ia.Z].r.Z.ib.a.YZt..iV^.ho.cg.n.d. .[..\..g.d..j..e.Z..YZ..Y.Y.V.V.i.i.V...... 4571
Range ...........................................=..d.l...l..^.Y..Z...^.h..n..d.j..g..Y..V..i..V..4......................................... 52
Interquartile Range ..........;..^c..Y..^.c.\...i.]..Z...b..^.Y..Y..a.Z...*..%..e.Z..g.X..Z..c..i..d.[...i.]..Z...Y..V..i..V............................ 54
Outliers ....................................H..Z..e.V..g..V..i.^.c.\...i.]..Z...\..d.d.Y....Y..V..i.V...[..g.d..b...i.]..Z...W..V..Y..................... 58
Visualizing Distributions .....7..d..m.".V..c..Y..".l..]..^h.`..Z..g..e.a.d..i.h..V..c..Y...Y..^.h.i..g.^.W.j..i..^d..c..Y...^V..\..g.V..b...h................. 62
Stem-and-Leaf Plot ...................................I..].Z.I..b]..Zd..h.Ói..dX.l.d.b.Z.g.bd..ed.dc.l..lZ..Vg..nd.h.[.i.Y.d..Vb..iZ.V.V..h.j..g.Z...Y..^.h.e.Z..g.h.^.d.c.... 66
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Variance and Standard Deviation ofof ra G PrXopuupleiad^t iDoYna^h te.a. ....d......[...g...........Z..c.X..n....Y..................... 871
Chebyshev’s Theorem ..................E..j..i.i..^c..\..i..]..Z..h..i.V..c..Y..V..g.Y...Y..Z..k..^.V..i.^.d.c...i.d...l..d.g.`....................... 85
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Table of Contents
Chapter 4: Introduction to Probability L]ViVgZi]ZX]VcXZh4 89
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Types of Probability .................................................................................................. 90
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Addition Rules for Probability .................................................................................... 98
Conditional Probability ..............E..g.d.W..V..W..^.a^.i..^Z..h..i..]..V..i..Y..Z..e.Z..c..Y...d.c...d.i..]..Z.g...Z.k..Z..c.i..h...................106
The Multiplication Rule for Probability .I..l..d..d..g..b..d..g.Z...Z.k..Z..c.i..h..d.X..X..j..g.g.^.c..\..V..i...i.]..Z...h.V..b..Z...i..^b...Z...116
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Bayes’ Theorem .......................................................................................................120
Chapter 5: Counting Principles and Probability Distributions DYYhndjXVcXdjcidc 123
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Fundamental Counting Principle ..............................................................................124
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Permutations ..........................................................................................................127
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Combinations .........................................................................................................129
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Probability Distributions ..........................................................................................135
Chapter 6: Discrete Probability Distributions 7^cdb^Va!Ed^hhdc!VcY]neZg\ZdbZig^X 141
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Binomial Probability Distribution ..............................................................................142
Poisson Probability Distribution .......9..Z.i..Z..g.b..^.c..^c..\..e..g.d.W..V..W..^.a.^i..^.Z.h..d.d.ik.Z..g..h..e.Z..X..^Ò..X...^.c.i..Z.d.g.k.V..a.h........149
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The Poisson Distribution as an Approxim^ ationh to] the Binomial Distribution ...................156
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Hypergeometric Probability Distributicon ........^g^..V...........c........Z.....V.................e..Z.......Z.c.........159
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Chapter 7: Continuous Probability DistributiYons V g Éc Z 165
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Normal Pobability Distribution .................................................................................166
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The Empirical Rule ...................................c.........................................d.....................179
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Using the Normal Distribution to Approximate the Binomial Distribution .......................182
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Continuous Uniform Distribution .............................................................................186
Exponential Distribution ..........A.^.`..Z..i..]..Z..E..d.^.h.h.d..c..Y...^h.i..g.^.W..j..i.^.d.c..!.W..j..i..X..d..c.i..^c..j..d.j..h....................189
Chapter 8: Sampling and Sampling Distributions Ldg`^c\l^i]VhjWhZid[VedejaVi^dc 195
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Probability Sampling ........................................................................a.......................196
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Sampling Distribution of the Proportion .....................................................................207
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Finite Population Correction Factor for the Sampling Distribution of the Proportion ..........215
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Table of Contents
Chapter 9: Confidence Intervals Ejii^c\hVbeaZhidldg` 219
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Introduction to Confidence Intervals for the Mean .......................................................220
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Confidence Intervals for the Mean with Large Samples and Sigma Known ......................221
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Confidence Intervals for the Mean with Small Samples and Sigma Known ......................225
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Confidence Intervals for the Mean with Small Samples and Sigma Unknown ..................229
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Confidence Intervals for the Mean with Large Samples and Sigma Unknown ..................235
Confidence Intervals for the Proportion .....:..h.i..^.b..V..i.^.c..\..e..Z.g..X.Z..c..i.V..\..Z..h..[.g.d..b...V...e..d.e.j..a.V..i.^.d..c.......239
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Chapter 10: Hypothesis Testing for a Single Population 243

Introduction to Hypothesis Testing for the Mean L..]..V..i.V.V..g.Za..c..j..aa..V..c].Y...V..a.i.Z..g.c.V..i..^Zk..Z..]..n.e.d..i.]..Z.h..Z.h.4...244
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Hypothesis Testing for the Mean with n v
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Hypothesis Testing for the Mean with n < 30 and Sigma Known^ ...................j..^..............255
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Hypothesis Testing for the Mean with n < 30 and Sigma Unknown l...............................259
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Hypothesis Testing for the Mean with n > 30 and Sigma Unknown ...............................265
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Hypothesis Testing for the Proportion .........................................................................271
Chapter 11: Hypothesis Testing for Two Population8s ddbeVg^c\b=inledie]dZejh^aoV^ci\^dcbZVch 279
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Hypothesis Testing for Two Means with n < 30 and Sigma Unknown ............................289
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Hypothesis Testing for Two Means with n v 30 and Sigma Unknown ............................299
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Hypothesis Testing for Two Means with Dependent Samples ..........................................302
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Hypothesis Testing for Two Proportions ......................................................................309
Chapter 12: Chi-Square and Variance Tests IZhi^c\XViZ\dg^XVaYViV[dgkVg^Vi^dc 317
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Chi-Square Goodness-of-Fit Test .................................................................................318
Chi-Square Test for Independence ................6..g.Z...i..].Z...k..V..g.^.V..W..aZ..h..g..Z.a.V..i..Z.Y...4........................331
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Hypothesis Test for a Single Population Variance .........................................................338
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Hypothesis Test for Two Population Variances .............................................................346
Chapter 13: Analysis of Variance 8dbeVg^c\bjai^eaZbZVchl^i]i]Z;"Y^hig^Wji^dc 351
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One-Way ANOVA: Completely Randomized Design ......................................................352
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One-Way ANOVA: Randomized Block Design .............................................................371
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Chapter 14: Correlation and Simple Regression Analysis k 389
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Correlation ............................................................................................................390
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Simple Regression Analysis .......................................................................................396
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Chapter 15: Nonparametric Tests 413
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The Sign Test with a Small Sample Size ......................................................................414
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The Sign Test with a Large Sampcle Size ......................................................................418
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The Wilcoxon Rank Sum Test for Small Samples .........................................................425
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The Wilcoxon Rank Sum Test for Large Samples .........................................................428
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The Wilcoxon Signed-Rank Test ................................................................................431
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The Kruskal-Wallis Test ................8.d..g.g.Z..aV..i..^c..\..Y..V..i.V...h.Z..i.h..V..X..X..d.g.Y..^.c.\..i..d..g.V..c.`...Y..^[..[.Z..g.Z..c.X..Z.h.......436
The Spearman Rank Correlation Coefficient Test .........................................................442
Chapter 16: Forecasting EgZY^Xi^c\[jijgZkVajZhd[gVcYdbkVg^VWaZh 449
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Simple Moving Average ...........................................................................................450
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Weighted Moving Average ........................................................................................454
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Exponential Smoothing ............................................................................................458
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Exponential Smoothing with Trend Adjustment ...........................................................462
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Trend Projection and Seasonality ..............................................................................468
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Causal Forecasting ..................................................................................................477
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Chapter 17: Statistical Process Cmontrol J^ h^c\hciVinie^hZi^XhidbZVhjgZZfjVa^Zin 483
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Introduction to Statistical Process Control ...................................................................484
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Statistical Process Control for Variable Measurement ....................................................484
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Statistical Process Control for Attribute Measurement Using p-charts ..............................491
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Statistical Process Control for Attribute Measurement Using c-charts ..............................495
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Process Capability Ratio ...........................................................................................498
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Process Capability Index ..........................................................................................500
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Chapter 18: Contextualizing Statistical Concepts ;^\jg^c\djil]ZcidjhZl]Vi[dgbjaV 503
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Index 545
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