Applied statistical methods

300 Pages·2013·7.204 MB·English

by  Bakir, Saad Taha;Shayib, Mohammed A

Applied Statistics
Mohammed A. Shayib
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Mohammed A. Shayib
Applied Statistics
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Applied Statistics
1st edition
© 2013 Mohammed A. Shayib & bookboon.com
ISBN 978-87-403-0493-0
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Applied Statistics Contents
Contents
Preface 8

1 Descriptive Statistics 10
Outline 10
1.1 Introduction 10
1.2 Descriptive Statistics 13
1.3 Frequency Distributions 14
1.4 Graphical Presentation 18
1.5 Summation Notation 28
1.6 Numerical Methods for Summarizing Quantitative Data 31
1.7 Some Properties of the Numerical Measures of Quantitative Data 41
1.8 Other Measures for Quantitative Data 43
1.9 Methods of Counting 47
1.10 Description of Grouped Data 50
CHAPTER 1 EXERCISES 55
TECHNOLOGY STEP-BY-STEP 62
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Applied Statistics Contents
2 R andom Variables and Probability Distributions 67
Outline 67
2.1 Introduction 67
2.2 Probability 69
2.3 Operations and Probability calculation on Events 72
2.4 Random Variables 78
2.5 Expected Value and Variance of a Random Variable 79
2.6 Some Discrete Probability Distributions 84
2.7 Normal Distribution 94
CHAPTER 2 EXERCISES 107
TECHNOLOGY STEP-BY-STEP 111
3 Estimation 117
Outline 117
3.1 Sampling 118
3.2 Point Estimation 122
3.3 Interval Estimation 127
3.4 Confidence Interval about One Parameter 128
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Applied Statistics Contents
3.5 Sample Size Determination 133
3.6 Confidence Interval about two Parameters 136
CHAPTER 3 EXERCISES 149
RANDOM NUMBERS TABLE 156
TECHNOLOGY STEP-BY-STEP 156
4 Testing of Statistical Hypotheses 162
Outline 162
4.1 Introduction 163
4.2 Fundamental Concepts 163
4.3 Methods in Testing a Statistical Hypothesis 167
4.4 Hypothesis Testing About One Parameter 169
4.5 Hypothesis Testing Concerning Two Parameters 192
CHAPTER 4 EXERCISES 211
TECHNOLOGY STEP-BY-STEP 215
5 S imple Linear Regression and Correlation 226
Outline 226
5.1 Introduction 227
5.2 Regression Models 230
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Applied Statistics Contents
5 .3 Fitting a straight line (First order Model) 232
5.4 Correlation 237
5.5 Hypothesis Testing in Regression Analysis 240
5.6 Confidence Interval on β and β 249
0 1
CHAPTER 5 EXERCISES 253
TECHNOLOGY STEP-BY-STEP 258
6 O ther Tests and Analysis Of Variance 261
Outline 261
6.1 Introduction 262
6.2 Goodness-of-Fit Tests 264
6.3 Contingency Tables 268
6.4 The one-Way Analysis of Variance 271
CHAPTER 6 EXERCISES 278
7 Appendix A Tables 282
8 References 300
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Applied Statistics Preface
Preface
It is already encrypted on the American currency “IN GOD WE TRUST”. This was the first part of a
statement that I heard from the Quality Manager at the Lubbock, TX, site of Texas Instrument while I
was there (1992–1998) as a quality engineer and Statistical Process Control Trainer. The second part says
“EVERYTHING ELSE NEEDS DATA”. It is the 21st century and the technology age, and data is abandunt
in every way and field. Statistics is not an exception since it deals with data all, the time. How to make
sense of that information was the motive behind writing this treatise on Applied Statistics.
Applied Statistics is a compendium, an elementary introduction to the growing field of statistics. In this
consize volume we emphasize on the concepts, definitions and terminology. With no doubt in mind,
linking the three building blocks, mentioned above, will provide any person with a strong hold on the
subject of statistics.
The material had been presented in such a way that only College Algebra can be a prerequisite for the
course that covers the whole text in one semester. The material is presented in 6 chapters.
Chapter 1 is about collecting, and organizing qualitative and quantitative data, as well as summarizing
the data graphically or numericall regardless if the data were discrete or continuous.
Chapter 2 introduces the notion of probability, its axioms, its rules, and applications. In addition to
that, Chapter 2 contains material on probability distributions and their characteristics for discrete and
continuous cases.
Chapter 3 covers the first main part of inferential statistics; namely estimation in its two branches: point
and interval estimation by introducing the sample statistics as estimators for the population parameters.
Chapter 4 is concerned about the second part of inferential statistics, namely hypothesis testing about
one parameter of a population, or two parameters of two populations. In this chapter there is an outline,
and procedure on how to implement the steps in hypothsis testing when using the two methods; the
classical or the traditional method and the p-value method. The detailed exposure of the two methods will
enable the reader, and the student to reach a comprehensive and sound conclusion by using information
found in data.
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Applied Statistics Preface
Up till chapter 5, the discussions were with data based on one variable aspect of the population that
of interest. Chapter 5 will introduce how to deal with two related variables and find a simple linear
relationship, if it exists, between them. In other words, chapter 5 is restricted to simple linear regression
between an explanatory variable and a response variable related to it. Moeover, the correlation concept
and definition are introduced in order to measure the strength of that liear relationship which was found
earlier.
Chapter 6 deals with another route of checking on data of one variable, or factor, and on the independence
or dependence between two factors. Chapter 6 goes on to introduce other tests in statistics and to check
on tests that make a decision whether more than two means are the same or not. Chapter 6 introduces
the One-Way Analysis of Variance, or ANOVA.
The treatise is wrapped up with an appendix that has 8 tables for use when reading the textbook.
Mohammed A. Shayib
Friday, May 31, 2013
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Applied Statistics Descriptive Statistics
1 Descriptive Statistics

Outline
1.1 Introduction
1.2 Descriptive Statistic
1.3 Frequency Distributions
1.4 Graphical Presentation
1.5 Summation Notation
1.6 Numerical Methods for Summarizing Quantitative Data
1.7 Some Properties of the Numerical Measures of Quantitative Data
1.8 Other Measures of Quantitative Data
1.9 Methods of Counting
1.10 Description of Grouped Data
• Exercises
• Technology Step-By-Step
1.1 Introduction
The subject of statistics may be presented at various levels of mathematical difficulty, and it may be
directed toward applications in various fields of inquiry. In this sequel we will keep the mathematical
background to a minimal. Now the question: What is statistics can be raised.
Statistics is that branch of science which deals with:
1. Collection of data,
2. Organizing and summarizing the data,
3. Analysis of data, and
4. Making inferences, or decisions and predictions.
Step 4 is the objective of statistics, i.e., making inferences about a population based on information
contained in a representative sample taken from that population.
We have some concepts that need to be well defined and established. These concepts are: A population
is a set of objects called elements that share a certain property, and it is the entire group to be studied.
For our purposes here, most populations will be sets of numbers that are of interest to us. For instance,
if we talk about students, the population could be all the students you can think of.
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