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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.
Contenu
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