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- Statistical Inference by Michael J. PanikCall Number: Available onlineISBN: 1118229401Publication Date: 2012-07-031 The Nature of Statistics;

1.1 Statistics Defined;

1.2 The Population and the Sample;

1.3 Selecting a Sample from a Population;

1.4 Measurement Scales;

1.5 Let us Add; Exercises;

2 Analyzing Quantitative Data;

2.1 Imposing Order;

2.2 Tabular and Graphical Techniques: Ungrouped Data;

2.3 Tabular and Graphical Techniques: Grouped Data; Exercises;

Appendix 2.A Histograms with Classes of Different Lengths;

3 Descriptive Characteristics of Quantitative Data;

3.1 The Search for Summary Characteristics;

3.2 The 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;

3.10 Kurtosis;

3.11 Detection of Outliers;

3.12 So What Do We Do with All This Stuff?; Exercises; Appendix

3.A Descriptive Characteristics of Grouped Data;

3.A.1 The Arithmetic Mean;

3.A.2 The Median;

3.A.3 The Mode;

3.A.4 The Standard Deviation;

3.A.5 Quantiles (Quartiles, Deciles, and Percentiles);

4 Essentials of Probability;

4.1 Set Notation;

4.2 Events within the Sample Space;

4.3 Basic Probability Calculations;

4.4 Joint, Marginal, and Conditional Probability

4.5 Sources of ProbabilitiesExercises;

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;

5.3.1 Counting Issues;

5.3.2 The Bernoulli Probability Distribution;

5.3.3 The Binomial Probability Distribution; Exercises;

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 XExercises;

Appendix 6.A The Normal Approximation to Binomial Probabilities;

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; 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;

7.C.1 Introduction to Randomness

7.C.2 Types of Randomness

7.C.2.1 Type I Randomness;

7.C.2.2 Type II Randomness;

7.C.2.3 Type III Randomness;

7.C.3 Pseudo-Random Numbers;

7.C.4 Chaotic Behavior;

7.C.5 Risk and Uncertainty;

8 Confidence Interval Estimation of μ;

8.1 The Error Bound on X as an Estimator of μ;

8.2 A Confidence Interval for the Population Mean μ (σ Known);

8.3 A Sample Size Requirements Formula;

8.4 A Confidence Interval for the Population Mean μ (σ Unknown);

Exercises;

Appendix 8.A A Confidence Interval for the Population Median MED

9 The Sampling Distribution of a Proportion and its Confidence Interval Estimation

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.

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