# Statistical Inference: A Short Course

John Wiley & Sons, Jun 6, 2012 - Mathematics - 400 pages

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.

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### Contents

 11 Statistics Defined 12 The Population and the Sample 14 Measurement Scales 15 Let Us Add 21 Imposing Order Grouped Data Exercises 24 Appendix 2A Histograms with Classes of Different Lengths
 91 The Sampling Distribution of a Proportion 92 The Error Bound on as an Estimator for p 93 A Confidence Interval for the Population Proportion of Successes p 94 A Sample Size Requirements Formula Exercises Appendix 9A Ratio Estimation 101 What is a Statistical Hypothesis? 102 Errors in Testing

 31 The Search for Summary Characteristics 32 The Arithmetic Mean 33 The Median 34 The Mode 35 The Range 37 Relative Variation 38 Skewness 39 Quantiles 310 Kurtosis 311 Detection of Outliers 312 So What do We do with All this Stuff? Exercises Appendix 3A Descriptive Characteristics of Grouped Data 41 Set Notation 42 Events within the Sample Space 43 Basic Probability Calculations 44 Joint Marginal and Conditional Probability 45 Sources of Probabilities Exercises 51 The Discrete Probability Distribution 52 The Mean Variance and Standard Deviation of A Discrete Random Variable 53 The Binomial Probability Distribution Exercises 61 The Continuous Probability Distribution 62 The Normal Distribution 63 Probability as An Area Under The Normal Curve 64 Percentiles of The Standard Normal Distribution and Percentiles of The Random Variable X Exercises Appendix 6A The Normal Approximation to Binomial Probabilities 71 Simple Random Sampling 72 The Sampling Distribution of The Mean 73 Comments on the Sampling Distribution of the Mean 74 A Central Limit Theorem Exercises Appendix 7A Using a Table of Random Numbers Appendix 7B Assessing Normality Via the Normal probability Plot Appendix 7C Randomness Risk and Uncertainty1 81 The Error Bound On As An Estimator Of 82 A Confidence Interval For The Population Mean μ σ Known 83 A Sample Size Requirements Formula 84 A Confidence Interval For The Population Mean μ σ Unknown Exercises Appendix 8A A Confidence Interval for the Population Median MED
 104 Selecting A Test Statistic 105 The Classical Approach to Hypothesis Testing 107 Hypothesis Tests for μ σ Known 108 Hypothesis Tests for μ σ Unknown And n Small 109 Reporting The Results of Statistical Hypothesis Tests 1010 Hypothesis Tests for The Population Proportion of Successes p Exercises Appendix 10A Assessing The Randomness of A Sample Appendix 10B Wilcoxon Signed Rank Test of a Median Appendix 10C Lilliefors GoodnessofFit Test for Normality 111 Confidence Intervals for the Difference of Means when Sampling from Two Independent Normal Populations Paired Comparisons 113 Confidence Intervals for the Difference of Proportions When Sampling from Two Independent Binomial Populations 114 Statistical Hypothesis Tests for the Difference of Means When Sampling from Two Independent Normal Populations Paired Comparisons 116 Hypothesis Tests for the Difference of Proportions when Sampling from Two Independent Binomial Populations Exercises Appendix 11A Runs Test for Two Independent Samples Appendix 11B MannWhitney Rank Sum Test for Two Independent Populations Paired Comparisons 121 Introducing an Additional Dimension to our Statistical Analysis 122 Linear Relationships 123 Estimating the Slope and Intercept of the Population Regression Line 124 Decomposition of the Sample Variation in Y 125 Mean Variance and Sampling Distribution of the Least Squares Estimators and 126 Confidence Intervals for and 128 Predicting the Average Value of Y given X 129 The Prediction of a Particular Value of Y given X 1210 Correlation Analysis Exercises Appendix 12A Assessing Normality Appendix 7B Continued Appendix 12B On Making Causal Inferences3 131 Distributional Hypotheses 133 The ChiSquare Distribution 134 Testing Goodness Of Fit 135 Testing Independence 136 Testing k Proportions 137 A Measure of Strength of Association in a Contingency Table 138 A Confidence Interval for σ2 Under Random Sampling from a Normal Population 139 The F Distribution 1310 Applications of the F Statistic to Regression Analysis Exercises Copyright