Statistical Inference: A Short CourseA 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:
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
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 | |