Statistics for Undergraduate Studies

University e-Preparation Course by NTU

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statistics textbook used in statistics for undergrad studies eprep course

Overview of the Textbook:

Used by hundreds of thousands of students since its first edition, INTRODUCTION TO PROBABILITY AND STATISTICS, Fourteenth Edition, continues to blend the best of its proven, error-free coverage with new innovations. Written for the higher end of the traditional introductory statistics market, the book takes advantage of modern technology–including computational software and interactive visual tools–to facilitate statistical reasoning as well as the interpretation of statistical results. In addition to showing how to apply statistical procedures, the authors explain how to describe real sets of data meaningfully, what the statistical tests mean in terms of their practical applications, how to evaluate the validity of the assumptions behind statistical tests, and what to do when statistical assumptions have been violated. The new edition retains the statistical integrity, examples, exercises, and exposition that have made this text a market leader–and builds upon this tradition of excellence with new technology integration.

Features of the Textbook:

  • Exercises: The book includes more than 1,300 exercises, many of which are new or updated for this edition. New topics for the book’s chapter-ending case study exercises include “How to Save Money for Groceries,” “School Accountability Study: How Is Your School Doing?” and “Are You Going to Curve the Grades?”
  • Market leader: The integrity of the statistics and the quality of the examples and exercises keep this text in the bestseller category. Comprehensive in coverage, it delivers a more rigorous offering with traditional coverage of probability. Instructors and students alike appreciate its error-free material and exercises, and its clear exposition.
  • Real data: The first to incorporate case studies and real data, this text continues to set the standard. Many examples and exercises use authentic data sets, helping students see the connections between their studies and their lives.
  • Quick reference: At the end of each chapter, Key Concepts and Formulas sections provide quick reference for students, helping them ensure they are well prepared for assignments and tests.

Table of Contents:

Introduction: What Is Statistics?

1 Describing Data with Graphs.

Many sets of measurements are samples selected from larger populations. Other sets constitute the entire population, as in a national consensus. In this chapter, you will learn what a variable is, how to classify variables into several types, and how measurements or data are generated. You will then learn how to use graphs to describe data sets. 

2 Describing Data with Numerical Measures.

Graphs  are extremely useful for the visual description of a data set. However, they are not always the best tool when you want to make inferences about a population from the information contained in a sample.  For this purpose, it is better to use numerical measures to construct a mental picture of the data.

3 Describing Bivariate Data.

Sometimes the data that are collected consist of observations for two variables on the same experimental unit.  Special techniques that can be used in describing these variables will help you identify possible relationships between them.

4 Probability and Probability Distributions.

Now that you have learned to describe a data set, how can you use sample data to draw conclusions about the sampled populations? The technique involves a statistical tool called probability. To use this tool correctly, you must first understand  how it works.  The first part of this chapter will present the basic concepts with simple examples.

The variables that we measured in chapter 1 and 2 can now be redefined as random variables, whose value depend on the chance selection of the elements in the samples.  Using probability as a tool, you can create probability distributions that serve as models for discrete random variables, and you can describe these random variables using a mean and standard deviation similar to those in Chapter 2.

5 Several Useful Discrete Distributions.

Discrete random variables are used in many practical applications. Three important discrete random variables – the binomial, the Poisson, and the hyper geometric – are presented in this chapter. These random variables are often used to describe the number of occurrences of a specified even in a fixed number of trials or a fixed unit of time or space.

6 The Normal Probability Distribution.

In Chapter 4 and 5, you learned about discrete random variables and their probability distributions.  In this chapter, you will learn about the continuous random variables and their probability distributions and about one very important continuous random variable – the normal.  You will learn how to calculate normal probabilities, and under certain conditions, how to use the normal probability distribution to approximate the binomial probability distribution. Then, in Chapter 7 and in the chapters that follow, you will see how the normal probability distribution plays a central role in statistical inference.

7 Sampling Distributions.

In the past several chapters, we studied population and the parameters that describe them.  These populations were either discrete or continuous, and we use probability as a tool for determining how likely certain sample outcomes might be.  In this chapter, our focus changes as we begin to study samples and the statistics that describe them.  These sample statistics are used to make inferences about the corresponding population parameters.  This chapter involves sampling and sampling distributions, which describe the behaviors of sample statistics in repeated sampling.

8 Large-Sample Estimation.

In previous chapters, you learned about the probability distributions of random variables and the sampling distributions of several statistics, for large sample sizes, can be approximated by a normal distribution according to the Central Limit Theorem.  This chapter presents a method of estimating population parameters and illustrate the concept with practical examples.  The Central Limit Theorem and the sampling distributions presented in Chapter 7 play a key role in evaluating the reliability of the estimates.

9 Large-Sample Tests of Hypotheses.

In this chapter, the concept of a statistical test of hypothesis is formally introduced. The sampling distributions of statistics presented in Chapter 7 and 8 are used to construct large sample tests concerning the values of population parameters of interest to the experimenter.

10 Inference from Small Samples.

The basic concept of large-sample statistical estimation and hypothesis testing for practical situations involving population means and proportions were introduced in Chapter 8 and 9.  Because all these techniques rely on the Central Limit Theorem to justify the normality of the estimators and test statistics, they apply only when the samples are large.  This chapter supplements the large sample techniques by presenting small-sample tests and confidence intervals for population means and variances.  Unlike the large-sample counterparts, these small-sample techniques requires the sampled population to be normal, or approximately so.

11 The Analysis of Variance.

The quantity of information contained in a sample is affected by various factors the experimenter may or may not be able to control.This chapter introduces three different experimental designs, two of which are direct extensions of the unpaired and paired designs of Chapter 10. A new technique called the analysis of variance is used to determine how the different experimental factors affect the average response.

12 Linear Regression and Correlation.

In this chapter, we consider the situation in which the mean value of a random variable y is related to another variable x.  By measuring both y and x for each experimental unit, thereby generating bivariate data, you can use the information provided by x to estimate the average value of y and to predict values of y for preassigned values of x.

13 Multiple Regression Analysis.

In this chapter, we extend the concepts of linear regression and correlation to a situation where the average value of a random variable y is related to several independent variables – x1, x2, …, xk – in model that are more flexible than the straight line model of Chapter 12.   With multiple regression analysis, we can use the information provided by the independent variables to fit various types of models to the sample data, to evaluate the usefulness of these models, and finally to estimate the average value of y or predict the actual value of y for given values of x1, x2,…, xk.

14 Analysis of Categorical Data.

Many types of surveys and experiments result in qualitative rather than quantitative response variables, so that the response can be classified but not quantified.  Data from these experiments consist of the count or number of observations that fall into each of the response categories included in the experiment.  In this chapter, we are concerned with methods for analyzing categorical data.

15 Nonparametric Statistics.

In Chapter 8-10, we have presented statistical techniques in comparing two populations by comparing their respective population parameters (usually their population means). The techniques in Chapters 8 and 9 are applicable to data that have normal distributions.  The purpose of this chapter is to present several statistical tests for comparing populations for the many types of data that do not satisfy the assumption specified in Chapter 8-10.

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