Inferential Statistics and Probability: A Holistic Approach

Inferential Statistics and Probability: A Holistic Approach

Inferential Statistics and Probability: A Holistic Approach by Maurice Geraghty offers a comprehensive exploration of statistical inference and probability concepts. This resource is designed for students and educators seeking to deepen their understanding of statistical methods, including hypothesis testing, confidence intervals, and the central limit theorem. The text emphasizes a holistic perspective, integrating various statistical techniques and their applications in real-world scenarios. Key topics include descriptive statistics, random variables, and chi-square tests, making it suitable for introductory statistics courses. With practical exercises and Minitab labs, this guide is ideal for learners aiming to master inferential statistics.

Key Points

  • Explains the central limit theorem and its significance in statistics
  • Covers hypothesis testing for one and two populations with practical examples
  • Includes detailed sections on discrete and continuous random variables
  • Features Minitab labs for hands-on experience with statistical software
,
  • newtopiccyclegrowin
339
/ 325
(rev 5/8/2020)
This Course Material by Maurice Geraghty is licensed under a Creative Commons Attribution-ShareAlike 4.0
International License. Conditions for use are shown here: https://creativecommons.org/licenses/by-sa/4.0/
DE ANZA COLLEGE – DEPARTMENT OF MATHEMATICS
Inferential Statistics and
Probability
A Holistic Approach
Maurice A. Geraghty
1/1/2018
Page | 1
Inference Statistics and Probability – A Holistic Approach
Table of Contents
0. Introduction – a Classroom Story and an Inspiration Page 002
1. Displaying and Analyzing Data with Graphs Page 009
2. Descriptive Statistics Page 031
3. Populations and Sampling Page 059
4. Probability Page 077
5. Discrete Random Variables Page 095
6. Continuous Random Variables Page 107
7. The Central Limit Theorem Page 122
8. Point Estimation and Confidence Intervals Page 130
9. One Population Hypothesis Testing Page 139
10. Two Populations Inference Page 164
11. Chi-square Tests for Categorical Data Page 178
12. One Factor Analysis of Variance (ANOVA) Page 188
13. Correlation and Linear Regression Page 194
14. Glossary of Statistical Terms used in Inference Page 207
15. Homework Problems Page 226
16. MINITAB Labs Page 279
17. Flash Animations Page 317
18. PowerPoint Slides Page 318
19. Notes and Sources Page 319
Page | 2
0. Introduction - A Classroom Story and an Inspiration
Several years ago, I was teaching an introductory Statistics course at De Anza College where I had
several achieving students who were dedicated to learning the material and who frequently asked me
questions during class and office hours. Like many students, they were able to understand the material
on descriptive statistics and interpreting graphs. Unlike many introductory Statistics students, they had
excellent math and computer skills and went on to master probability, random variables and the Central
Limit Theorem.
However, when the course turned to inference and hypothesis testing, I watched these students’
performance deteriorate. One student asked me after class to again explain the difference between the
Null and Alternative Hypotheses. I tried several methods, but it was clear these students never really
understood the logic or the reasoning behind the procedure. These students could easily perform the
calculations, but they had difficulty choosing the correct model, setting up the test, and stating the
conclusion.
These students, (to their credit) continued to work hard; they wanted to understand the material, not
simply pass the class. Since these students had excellent math skills, I went deeper into the explanation
of Type II error and the statistical power function. Although they could compute power and sample size
for different criteria, they still didn’t conceptually understand hypothesis testing.
On my long drive home, I was listening to National Public Radio’s Talk of the Nation
1
and heard
discussion on the difference between the reductionist and holistic approaches to the sciences. The
commentator described this as the Western tradition vs. the Eastern tradition. The reductionist or
Western method of analyzing a problem, mechanism or phenomenon is to look at the component
pieces of the system being studied. For example, a nutritionist breaks a potato down into vitamins,
minerals, carbohydrates, fats, calories, fiber and proteins. Reductionist analysis is prevalent in all the
sciences, including Inferential Statistics and Hypothesis Testing.
Holistic or Eastern tradition analysis is less concerned with the component parts of a problem,
mechanism or phenomenon but rather with how this system operates as a whole, including its
surrounding environment. For example, a holistic nutritionist would look at the potato in its
environment: when it was eaten, with what other foods it was eaten, how it was grown, or how it was
prepared. In holism, the potato is much more
than the sum of its parts.
Consider these two renderings of fish:
The first image is a drawing of fish anatomy by
John Cimbaro used by the La Crosse Fish Health
Center.
2
This drawing tells us a lot about how a
fish is constructed, and where its vital organs are
/ 325
End of Document
339
You May Also Like

FAQs of Inferential Statistics and Probability: A Holistic Approach

What is the central limit theorem and why is it important?
The central limit theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the original population distribution. This theorem is crucial in inferential statistics because it allows statisticians to make inferences about population parameters using sample data. It underpins many statistical methods, including hypothesis testing and confidence intervals, making it a foundational concept in the study of statistics.
How does the book approach hypothesis testing?
The book provides a detailed examination of hypothesis testing, including the formulation of null and alternative hypotheses. It explains the steps involved in conducting tests, such as selecting the appropriate test, calculating test statistics, and interpreting p-values. The text emphasizes understanding the logic behind hypothesis testing rather than just performing calculations, which helps students grasp the underlying principles of statistical inference.
What types of random variables are discussed in this text?
The text covers both discrete and continuous random variables, explaining their characteristics and how they are used in statistical analysis. Discrete random variables are discussed in the context of probability distributions, such as binomial and Poisson distributions, while continuous random variables are explored through normal distributions and their applications. This comprehensive approach helps students understand the differences and applications of each type of random variable.
What practical applications does the book include for statistical concepts?
The book includes practical applications of statistical concepts through real-world examples and exercises. It features Minitab labs that allow students to apply statistical methods using software, enhancing their understanding of data analysis. Additionally, the text provides homework problems that reinforce learning and encourage students to practice applying the concepts in various contexts.

Related of Inferential Statistics and Probability: A Holistic Approach