Statistical Inference: A Short Course

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

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
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About the author (2012)

MICHAEL J. PANIK, PhD, is Professor Emeritus in the Department of Economics at the University of Hartford. He has served as a consultant to the Connecticut Department of Motor Vehicles as well as a variety of healthcare organizations. Dr. Panik has published numerous journal articles in the areas of economics, mathematics, and applied econometrics.

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