Statistics

Statistics covers the basic principles of Statistics. The book starts by tackling the importance and the two kinds of statistics; the presentation of sample data; the definition, illustration and explanation of several measures of location; and the measures of variation. The text then discusses elementary probability, the normal distribution and the normal approximation to the binomial. Testing of statistical hypotheses and tests of hypotheses about the theoretical proportion of successes in a binomial population and about the theoretical mean of a normal population are explained. The text then considers testing of hypotheses about the mean of a normal population when the population variance is not known and testing the hypotheses about the mean of populations that are not normal.
The book also describes correlation and regression, confidence limits, non-parametric statistics, and the analysis of variance. The text concludes by giving more complex problems and step-by-step directions for the various statistical tests.
Statisticians and students taking Statistics courses will find the book invaluable.

Inhalt

1 What is Statistics?

The Present Importance of Statistics

Two Kinds of Statistics

2 Pictorial Description of Data

Introduction

Selecting a Random Sample

Classification of Data

Frequency Distributions and Cumulative Frequency Distributions

Graphical Representation of Data

Histogram

Frequency Polygon

Ogive

Exercises

3 Measures of Location

Introduction

The Mid-range

The Mode

The Median

The Arithmetic Mean

The Median of Classified Data

Summation Notation

The Mean of Classified Data

Exercises

4 Measures of Variation

Introduction

The Range

The Mean Absolute Deviation

The Variance and the Standard Deviation

The Variance and Standard Deviation of Classified Data

Exercises

5 Elementary Probability and the Binomial Distribution

Introduction

Probabilities of Simple Events

Probabilities of Two Events

Probabilities for Combinations of Three or More Events

Permutations

Fundamental Principle

Combinations

More Probability

The Binomial Distribution

The Theoretical Mean of the Binomial Distribution

The Theoretical Variance of the Binomial Distribution

Exercises

6 The Normal Distribution

Introduction

The Normal Distribution

Use of Standard Normal Tables

More Normal Probabilities

The Normal Approximation to the Binomial

Theorem

Exercises

7 Some Tests of Statistical Hypotheses

Introduction

The Nature of a Statistical Hypothesis-Two Types of Error

Test of H0: p = p0 versus a Specified Alternative

Tests about the Mean of a Normal Distribution

Exercises

8 More Tests of Hypotheses

Introduction

Test of H0: µ = µ0, Normal Population, s2 Unknown

Tests about the Mean of a Non-normal Population

Tests about the Difference of Two Proportions

Tests about the Difference of Two Means

Exercises

9 Correlation and Regression

The Sample Correlation Coefficient

Computation of r

Testing Hypotheses about the Population Correlation Coefficient

Linear Regression

Finding the Regression (Least-squares) Line

Testing Hypotheses about µ in a Regression Problem

Testing Hypotheses about ß in a Regression Problem

Exercises

10 Confidence Limits

Introduction

A Note on Inequalities

Confidence Intervals for µ

Confidence Interval for p

Confidence Interval for µ1 - µ2

Confidence Interval for p1 - p2

Confidence Interval for

Exercises

11 Non-Parametric Statistics

Introduction

The Chi-squared Distribution

Contingency Tables

The Rank-correlation Coefficient

The Sign Test (One Population)

The Wilcoxon Signed-rank Test

The Rank-sum Test (Two Populations)

Exercises

12 The Analysis of Variance

Introduction

One-way Analysis of Variance

One-way Analysis of Variance-Another Approach

One-way Analysis of Variance, Different Sample Sizes

Two-way Analysis of Variance

Exercises

Appendix

List of Selected Symbols

Tables

t-Distribution

Squares

Square Roots

Area of the Standard Normal Distribution

x2-Distribution

Fisher-z Values

Spearman Rank-correlation Coefficient

Wilcoxon Signed-rank Values

Rank-sum Critical Values

F-Distribution

Answers to Exercises

Index