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Chapter 1: Introduction.
1.1 What is Statistics.
1.2 Types of Statistics.
Case Study 1-1. Collegians Charge On.
1.3 Population vs. Sample.
Case Study 1-2. Most Do Not Know Their Mail Carrier.
Case Study 1-3. Yes, Looks Can Kill Your Chance for a Job.
1.4 Basic Terms.
1.5 Types of Variables.
1.6 Cross-Section vs. Time-Series Data.
1.7 Sources of Data.
1.8 Summation Notation.
*Uses & Misuses.
*Glossary.
*Supplementary Exercises.
*Self Review Test.
*Mini Project.
Chapter 2: Organizing Data.
2.1 Raw Data.
2.2 Organizing and Graphing Qualitative Data.
Case Study 2-1. If You Are Productive, It Must Be Tuesday.
Case Study 2-2. Favorite Donut Flavors.
2.3 Organizing and Graphing Quantitative Data.
Case Study 2-3. Graduates in Debt.
2.4 Shapes of Histograms.
Case Study 2-4. using Truncated Axes.
2.5 Cumulative Frequency Distributions.
2.6 Stem-and-Leaf Displays.
Chapter 3: Numerical Descriptive Measures.
3.1 Measures of Central Tendency for Ungrouped Data.
Case Study 3-1. Lifespan of $1 Bill: 18 Months.
Case Study 3-2. Education and Earnings.
3.2 Measures of Dispersion for Ungrouped Data.
3.3 Mean, Variance, and Standard Deviation for Grouped Data.
Case Study 3-3. Here Comes the SD.
3.4 Use of Standard Deviation.
3.5 Measures of Position.
3.6 Box-and-Whisper Plot.
Chapter 4: Probability.
4.1 Experiment, Outcomes & Sample Space.
4.2 Calculating Probability.
4.3 Counting Rule.
4.4 Marginal & Conditional Probabilities.
Case Study 4-1. Facing a Crowd Isn't Easy.
4.5 Mutually Exclusive Events.
4.6 Independent vs. Dependent Events.
4.7 Complementary Events.
4.8 Intersection of Events & the Multiplication Rule.
Case Study 4-2. Baseball Players Have "Slumps" and "Streaks".
4.9 Union of Events and the Addition Rule.
Chapter 5: Discrete Random Variables & Their Probability Distributions.
5.1 Random Variables.
5.2 Probability Distribution of a Discrete Random Variable.
5.3 Mean of a Discrete Random Variable.
5.4 Standard Deviation of a Discrete Random Variable.
Case Study 5-1. Aces High Instant Lottery Game.
5.5 Factorials and Combinations.
Case Study 5-2. Playing Lotto.
5.6 The Binomial Probability Distribution.
5.7 The Hypergeometric Probability Distribution.
5.8 The Poisson Probability Distribution.
Case Study 5-3. Ask Mr. Statistics.
Chapter 6: Continuous Random Variables and the Normal Distribution.
6.1 Continuous Probability Distribution.
Case Study 6-1. Distribution of Time Taken to Run a Road Race.
6.2 The Normal Distribution.
6.3 The Standard Normal Distribution.
6.4 Standardizing a Normal Distriution.
6.5 Applications of the Normal Distribution.
6.6 Determining the z and x Values When an Area Under the Normal Distribution Curve is Known.
6.7 The Normal Approximation to the Binomial Distribution.
Chapter 7: Sampling Distributions.
7.1 Population and Sampling Distributions.
7.2 Sampling and Non-Sampling Errors.
7.3 Mean and Standard Deviation of x.
7.4 Shape of the Sampling Distribution x.
7.5 Applications of the Sampling Distribution of x.
7.6 Population and Sample Proportions.
7.7 Mean, Standard Deviation, and Shape of the Sampling Distribution of p.
Case Study 7-1. Calling the Vote for Congress.
Chapter 8: Estimation of the Mean and Proportion.
8.1 Estimation: An Introduction.
8.2 Point and Interval Estimates.
8.3 Interval Estimation of a Population Mean: Large Samples.
Case Study 8-1. Where Your Energy Dollar Goes.
8.4 Interval Estimation of a Population Proportion: Small Samples.
Case Study 8-2. Cardiac Demands of Heavy Snow Shoveling.
8.5 Interval Estimation of a Population Proportion: Large Samples.
Case Study 8-3. What Is Causing Job Stress?
8.6 Determining the Sample Size for the Estimation of Mean.
8.7 Determining the Sample Size for the Estimation of Proportion.
Chapter 9: Hypothesis Tests About the Mean and Proportion.
9.1 Hypothesis Tests: An Introduction.
9.2 Hypothesis Tests About µ for Large samples Using the p-Value Approach.
9.3 Hypothesis Tests About a Population Mean: Large Samples.
9.4 Hypothesis Tests About a Population Mean: Small Samples.
9.5 Hypothesis Tests About a Population Proportion: Large Samples
Case Study 9-1. Employees' Concerns.
Chapter 10: Estimation & Hypothesis Testing: Two Populations.
10.1 Inferences About the Difference Between Two Population Means For Large and Independent Samples.
10.2 Inferences About the Difference Between Two Populations Means for Small and Independent Samples: Equal Standard Deviations.
10.3 Inferences About the Difference Between Two Population Means for Small and Independent Samples: Unequal Standard Deviations.
10.4 Inferences About the Difference Between Two Population Means for Paired Samples.
10.5 Inferences About the Difference Between Two Population Proportions for Large and Independent Samples.
Case Study 10-1. Teenagers Butt Out of Smoking.
Chapter 11: Chi Square Tests.
11.1 The Chi Square Distribution.
11.2 A Goodeness-of-Fit Test.
Case Study 11-1. Up with "the Color Purple".
11.3 Contingency Tables.
11.4 A Test of Independence or Homogeneity.
11.5 Inferences About the Population Variance.
Chapter 12: Analysis of Variance.
12.1 The F Distribution.
12.2 One-Way Analysis of Variance.
Chapter 13: Simple Linear Regression.
13.1 Simple Linear Regression Model.
13.2 Simple Linear Regression Analysis.
13.3 Standard Deviation of Random Errors.
13.4 Coefficient of Determination.
13.5 Inferences About B.
13.6 Linear Correlation.
13.7 Regression Analysis: A Complete Example.
13.8 Using the Regression Model.
13.9 Cautions in Using Regression.
Chapter 14: Nonparametric Methods.
14.1 The Sign Test.
14.2 The Wilcoxon Signed-Rank Test for Two Dependent Samples.
14.3 The Wilcoxon Rank Sum Test for Two Independent Samples.
14.4 The Kruskal-Wallis Test.
14.5 The Spearman Rho Rank Correlation Coefficient Test.
14.6 The Runs Test for Randomness.
Appendix A: Sample Surveys, Sampling Techniques, and Design Experiments.
A.1 Sources of Data.
A.1.1 Internal Sources.
A.1.2 External Sources.
A.1.3 Surveys and Experiments.
A.2 Sample Surveys and Sampling Techniques.
A.2.1 Why Sample.
A.2.2 Random and Nonrandom Samples.
A.2.3 Sampling and Nonsampling Errors.
A.2.4 Random Sampling Techniques.
A.3 Design of Experiments.
Appendix B: Explanation of Data Sets.
Data Set I: City Data.
Data Set II: Data On States.
Data Set III: NBA Data.
Data Set IV: Population Data on Manchester Road Race.
Data Set V: Sample of 500 Observations Selected from Manchester Road Race Data.
Appendix C: Statistical Tables.
I Table of Binomial Probabilities.
II Values of e-.
III Table of Poisson Probabilities.
IV Standard Normal Distribution Table.
V The t Distribution Table.
VI Chi-Square Distribution Table.
VII The F Distribution Table.
VIII Critical Values of X for the Sign Test.
IX Critical Values of T for the Wilcoxon Signed-Rank Test.
X Critical Values of T for the Wilcoxon Rank Sum Test.
XI Critical Values for the Spearman Rho Rank Correlation Coefficient Test.
XII Critical Values for a Two-Tailed Runs Test with à = .05.
ANSWERS TO SELECTED ODD-NUMBERED EXERCISES AND SELF-REVIEW TESTS.
PHOTO CREDITS.
INDEX.
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Thomas Brooks
reviewed Introductory Statistics, Technology Version on November 11, 2014 Introductory Statistics
There are different ways to use and think about mathematical concepts and they do not all leave a historical record in a form that can be interpreted with certainty. The gap between people engaged in trade and those indulging in philosophy has been especially important, notably for the ancient Greeks, whose philosophers used geometry to think mathematically and despised the mere counting required for trade. Others have used sand or beads or counting boards or diverse tools in which the technique for even complex calculations did not necessarily entail a corresponding grasp of the theory or the concepts at work. In such cases, zero might arise and vanish repeatedly without making an impression on the way people thought about numbers. The key fact is that we do not know what they were thinking unless we can find a record.
Although we can find written number systems as old as the Sumerians, 5,000 years ago, in which we see zero at work, it is used in unexpected ways. They appear to require a form of zero to indicate "nothing in this column" - for which there is a record at Kush dated to 700BC - but it is used only in the middle and never at the end of numbers. So they cannot distinguish between 2, 20 and 200. The ancient Greeks - from the Fifth Century BC - used their letters as symbols first for numbers 1 to 9, then tens up to 90, then hundreds up to 900, but had no letter as a symbol for zero. They seem to have incorporated zero first after invading the Babylonian Empire in 331 BC. There is good evidence, which Kaplan reviews, that the Greeks in turn passed the concept to India. Kaplan spends some time debunking claims that the Indians invented zero, insisting that their valid claims are already remarkable and do not need the additional support of being exaggerated. Why deprive Zero of its much longer history?
Kaplan says very early on that "we count by giving different number names to different sized heaps of things." In places this is as much a history of 1 as a history of zero, discussing the different ways people group stuff into units. The Sumerians used units, tens and sixties for example. Archimides named vast large numbers by working with myriads and myriad -myriads, which could be of the first order or the second order. Until 1971, England worked with units of 12 pennies to one shilling, twenty shillings to one pound. We still have sixty seconds to a minute, sixty minutes to an hour, twenty four hours to a day, seven days to a week and so on .. Kaplan devotes a chapter also to Mayan number systems, with a range of cyclical calendars all seeking to defer the end of time. They took their obsession with counting to extremes.
Kaplan argues that up to this point in the history of numbers, the principle remained valid that there was a correspondence between numbers and things, such that there would be no consideration given to the notion that zero / nothing / void / empty was a thing in need of a name in the way other numbers were. But Indian mathematics achieved a "paradigm shift" which focused on how numbers behaved instead of what numbers were. Such behaviour took place in equations, where the solution (the number which made the equation balance) was as likely to be zero as any other number. The names of numbers were contracted to written symbols, including symbols for operations (plus, minus, equals, squared), which could be used yet often not visualised (what would x squared look like?). Indeed, for the first time it became reasonable to deal with negative numbers as well as positive ones. Numbers no longer named or described objects but became objects themselves to which adjectives could be attached: positive, negative, natural, rational, real. "The change in mathematics we've been following, where the names for numbers narrow down to signs of them and the numbers themselves are subordinated to the laws they obey, began when someone first counted and evolved through the ongoing project of deriving these laws from as thrifty a set of axioms as mathematicians could manage."
It was through Islam and the Arabic language that Indian mathematics was transmitted to China, Russia and Western Europe, the latter by 970 AD. Kaplan gives credit for this but does not suggest that the Arabs transformed Indian maths in any fundamental way. Perhaps this impression arises through the specific focus of this book on Zero. In any case, Europeans struggled with many aspects of the new approach to mathematics. For all the crushing difficulty of using existing methods, there were a lot of new concepts to absorb in Arabic (or "Saracen") methods, and for counting itself Europeans could make good use of the abacus to meet their practical needs. Kaplan suggests that the major breakthrough for Zero was after 1340, when Pacioli introduced the novelty of double entry book-keeping, in which Zero held the essential balance between credits and debits, positive and negative.
Yet it was not in counting that Zero had its crucial impact. It remained the case that counting with an abacus was much faster and more efficient that using the quill to apply the Saracen techniques. Kaplan writes: "Wordless manipulation will carry you with dash and glory to the outermost edges of arithmetic - but it will leave you stranded once you cross the border into algebra and all the lands of mathematics that lie beyond. There thought travels by signs laced into a language that can speak even about itself…. This language came into its own when zero entered it as the sign for an operation: the operation of changing a digit's value by shifting its place."
Kaplan proceeds in the remainder of his book to explore diverse ways in which the role of zero has been significant in the development of mathematical ideas. This is not material to read with a passive attitude - it requires effort and patience from the reader. His explanations unfold very logically to give insights into the power - but also the confusing nature - of this surprising number.
The book does not demand a knowledge of difficult mathematics but it sadly does demand a willingness to read difficult prose that is sometimes too dense and to wade through his laboured humour and philosophising in places where that just confuses things. The result for me was that I literally nodded off to sleep on occasion. In the end, I also found it necessary to speed read through the book for a second time, just to clarify what it was about. It made more sense in retrospect than it had done at the time of first reading. Maybe that suggests that the book had a great idea which called for more editing before it was released into the wild. It could have been a lot better. A heavy read and a struggle but all the same, interesting stuff and filled with unexpected gems.
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Add Introductory Statistics, Technology Version, Get the Tools You Need to Succeed in Statistics! Mann's Introductory Statistics Using Technology, Fifth Edition is Accompanied by a powerful array of study tools that will give you an extra advantage in your statistics class. Student Solutions Manua, Introductory Statistics, Technology Version to the inventory that you are selling on WonderClubX
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Add Introductory Statistics, Technology Version, Get the Tools You Need to Succeed in Statistics! Mann's Introductory Statistics Using Technology, Fifth Edition is Accompanied by a powerful array of study tools that will give you an extra advantage in your statistics class. Student Solutions Manua, Introductory Statistics, Technology Version to your collection on WonderClub |
