Statistics

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: π = π0 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, σ2 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 β in a Regression Problem Exercises 10 Confidence Limits Introduction A Note on Inequalities Confidence Intervals for μ Confidence Interval for π Confidence Interval for μ1 — μ2 Confidence Interval for π1 — π2 Confidence Interval for ρ 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