Introductory Statistics | Douglas S. Shafer and Zhiyi Zhang

- 1Introduction
- 2Descriptive Statistics
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  - 2.1Three Popular Data Displays
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  - 2.2Measures of Central Location
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  - 2.3Measures of Variability
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  - 2.4Summary Description of Data Sets
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  - 2.5Relative Position of Data
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  - 2.6The Empirical Rule and Chebyshev’s Theorem
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- 3Basic Concepts of Probability
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  - 3.1Sample Spaces, Events, and Their Probabilities
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  - 3.2Complements, Intersections, and Unions
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  - 3.3Conditional Probability and Independent Events
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- 4Discrete Random Variables
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  - 4.1Random Variables
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  - 4.2Probability Distributions for Discrete Random Variables
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  - 4.3The Binomial Distribution
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- 5Continuous Random Variables
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  - 5.1Continuous Random Variables
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  - 5.2The Standard Normal Distribution
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  - 5.3Probability Computations for General Normal Random Variables
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  - 5.4Areas of Tails of Distributions
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- 6Sampling Distributions
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  - 6.1The Mean and Standard Deviation of the Sample Mean
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  - 6.2The Sampling Distribution of the Sample Mean
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  - 6.3The Sample Proportion
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- 7Estimation
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  - 7.1Large Sample Estimation of a Population Mean
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  - 7.2Small Sample Estimation of a Population Mean
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  - 7.3Large Sample Estimation of a Population Proportion
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  - 7.4Sample Size Considerations
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- 8Testing Hypotheses
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  - 8.1The Elements of Hypothesis Testing
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  - 8.2Large Sample Tests for a Population Mean
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  - 8.3The Observed Significance of a Test
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  - 8.4Small Sample Tests for a Population Mean
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  - 8.5Large Sample Tests for a Population Proportion
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- 9Two-Sample Problems
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  - 9.1Comparison of Two Population Means: Large, Independent Samples
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  - 9.2Comparison of Two Population Means: Small, Independent Samples
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  - 9.3Comparison of Two Population Means: Paired Samples
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  - 9.4Comparison of Two Population Proportions
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  - 9.5Sample Size Considerations
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- 10Correlation and Regression
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  - 10.1Linear Relationships Between Variables
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  - 10.2The Linear Correlation Coefficient
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  - 10.3Modelling Linear Relationships with Randomness Present
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  - 10.4The Least Squares Regression Line
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  - 10.5Statistical Inferences About β1
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  - 10.6The Coefficient of Determination
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  - 10.7Estimation and Prediction
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  - 10.8A Complete Example
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  - 10.9Formula List
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- 11Chi-Square Tests and F-Tests
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  - 11.1Chi-Square Tests for Independence
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  - 11.2Chi-Square One-Sample Goodness-of-Fit Tests
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  - 11.3F-tests for Equality of Two Variances
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  - 11.4F-Tests in One-Way ANOVA
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- AAppendix
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