"A concise, easily accessible introduction to descriptive and inferential techniques"
"Statistical Inference: A Short Course" offers a concise presentation of the essentials of basic statistics for readers seeking to acquire a working knowledge of statistical concepts, measures, and procedures.
The author conducts tests on the assumption of randomness and normality, provides nonparametric methods when parametric approaches might not work. The book also explores how to determine a confidence interval for a population median while also providing coverage of ratio estimation, randomness, and causality. To ensure a thorough understanding of all key concepts, "Statistical Inference" provides numerous examples and solutions along with complete and precise answers to many fundamental questions, including: How do we determine that a given dataset is actually a random sample?With what level of precision and reliability can a population sample be estimated?How are probabilities determined and are they the same thing as odds?How can we predict the level of one variable from that of another?What is the strength of the relationship between two variables?
The book is organized to present fundamental statistical concepts first, with later chapters exploring more advanced topics and additional statistical tests such as Distributional Hypotheses, Multinomial Chi-Square Statistics, and the Chi-Square Distribution. Each chapter includes appendices and exercises, allowing readers to test their comprehension of the presented material.
"Statistical Inference: A Short Course" is an excellent book for courses on probability, mathematical statistics, and statistical inference at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for researchers and practitioners who would like to develop further insights into essential statistical tools.
Preface Chapter 1 The Nature of Statistics Statistics Defined The Population and the Sample Selecting a Sample from a Population Measurement Scales Let?s Add! Exercises Chapter 2 Analyzing Quantitative Data 2.1 Imposing Order 2.2 Tabular and Graphical Techniques: Ungrouped Data 2.3 Tabular and Graphical Techniques: Grouped Data 2.4 Exercises Appendix 2.A Histograms With Classes of Different Lengths Chapter 3 Descriptive Characteristics of Quantitative Data 3.1 The Search for Summary Characteristics 3.2 Arithmetic Mean 3.3 The Median 3.4 The Mode 3.5 The Range 3.6 The Standard Deviation 3.7 Relative Variation 3.8 Skewness 3.9 Quantiles (Quartiles, Deciles, and Percentiles) 3.10 Kurtosis 3.11 Detection of Outliers 3.12 So What Do We Do With All This Stuff? 3.13 Exercises Appendix 3.A Descriptive Characteristics of Grouped Data The Arithmetic Mean The Median The Mode The Standard Deviation Quantiles (Quartiles, Deciles, and Percentiles) Chapter 4 Essentials of Probability 4.1 Set Notation 4.2 Events Within the Sample Space 4.3 Basic Probability Calculations 4.4 Sources of Probabilities 4.5 Exercises Chapter 5 Discrete Probability Distributions and Their Properties 5.1 The Discrete Probability Distribution 5.2 The Mean, Variance, and Standard Deviation of a Discrete Random Variable 5.3 The Binomial Probability Distribution A. Counting Issues B. The Bernoulli Probability Distribution C. The Binomial Probability Distribution 5.4 Exercises Chapter 6 The Normal Distribution 6.1 The Continuous Probability Distribution 6.2 The Normal Distribution 6.3 Probability as an Area Under the Normal Curve 6.4 Percentiles of the Standard Normal Distribution and Percentiles of the Random Variable X 6.5 Exercises Appendix 6.A The Normal Approximation to Binomial Probabilities Chapter 7 Simple Random Sampling and the Sampling Distribution of the Mean 7.1 Simple Random Sampling 7.2 The Sampling Distribution of the Mean 7.3 Comments on the Sampling Distribution of the Mean 7.4 A Central Limit Theorem 7.5 Exercises Appendix 7.A Using a Table of Random Numbers Appendix 7.B Assessing Normality via the Normal Probability Plot Appendix 7.C Randomness, Risk, and Uncertainty Chapter 8 Confidence Interval Estimation of ? 8.1 The Error Bound on as an Estimator of ? 8.2 A Confidence Interval for the Population Mean ? (a Known) 8.3 A Sample Size Requirements Formula 8.4 A Confidence Interval for the Population Mean ? (a Unknown) 8.5 Exercises Appendix 8.A A Confidence Interval for the Population Median Chapter 9 The Sampling Distribution of a Proportion and its Confidence Interval Estimation. 9.1 The Sampling Distribution of a Proportion 9.2 The Error Bound onas an Estimator for p 9.3 A Confidence Interval for the Population Proportion (of Successes) p 9.4 A Sample Size Requirements Formula 9.5 Exercises Appendix 9.A Ratio Estimation Chapter 10 Testing Statistical Hypotheses 10.1 What is a Statistical Hypothesis 10.2 Errors in Testing 10.3 The Contextual Framework of Hypothesis Testing 10.4 Selecting a Test Statistic 10.5 The Classical Approach to Hypothesis Testing 10.6 Types of Hypothesis Tests 10.7 Hypothesis Tests for ? (a Known) 10.8 Hypothesis Tests for ? (a Unknown) 10.9 Reporting the Results of Statistical Hypothesis Tests 10.10 Hypothesis Tests for the Population Proportion (of Successes) p 10.11 Exercises Appendix 10.A Assessing the Randomness of a Sample Appendix 10.B Wilcoxon Signed Rank Test (of a Median) Appendix 10.C Lilliefors? Goodness-of-Fit Test for Normality Chapter 11 Comparing Two Population Means and Two Population Proportions 11.1 Confidence Intervals for the Difference of Means When Sampling from Two Independent Normal Populations A. Sampling from Two Independent Normal Populations With Equal and Known Variances B. Sampling from Two Independent Normal Populations With Unequal But Known Variances C. Sampling from Two Independent Normal Populations With Equal But Unknown Variances D. Sampling from Two Independent Normal Populations With Une
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