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Statistics, Data, and Statistical Thinking | |
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the Science of Statistics | |
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Types of Statistical Applications | |
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Fundamental Elements of Statistics | |
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Types of Data | |
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Collecting Data | |
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the Role of Statistics in Critical Thinking | |
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Methods for Describing Sets of Data | |
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Describing Qualitative Data | |
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Graphical Methods for Describing Quantitative Data | |
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Summation Notation | |
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Numerical Measures of Central Tendency | |
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Numerical Measures of Variability | |
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Interpreting the Standard Deviation | |
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Numerical Measures of Relative Standing | |
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Methods for Detecting Outliers: Box Plots and z-Scores | |
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Graphing Bivariate Relationships (Optional) | |
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Distorting the Truth with Descriptive Techniques | |
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Probability | |
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Events, Sample Spaces, and Probability | |
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Unions and Intersections | |
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Complementary Events | |
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the Additive Rule and Mutually Exclusive Events | |
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Conditional Probability | |
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the Multiplicative Rule and Independent Events | |
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Random Sampling | |
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Some Additional Counting Rules (Optional) | |
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Bayes' Rule (Optional) | |
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Random Variables and Probability Distributions | |
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Two Types of Random Variables | |
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Probability Distributions for Discrete Random Variables | |
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Expected Values of Discrete Random Variables | |
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the Binomial Random Variable | |
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Continuous Probability Distributions | |
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the Normal Distribution | |
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Descriptive Methods for Assessing Normality | |
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Approximating a Binomial Distribution with a Normal Distribution (Optional) | |
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What is a Sampling Distribution? | |
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the Sampling Distribution of (x-bar) and the Central Limit Theorem | |
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Inferences Based on a Single Sample: Estimation with Confidence Intervals | |
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Identifying and Estimating the Target Parameter | |
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Confidence Interval for a Population Mean: Normal (z) Statistic | |
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Confidence Interval for a Population Mean: Student's t-statistic | |
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Large-Sample Confidence Interval for a Population Proportion | |
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Determining the Sample Size | |
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Confidence Interval for a Population Variance (Optional) | |
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Inferences Based on a Single Sample: Tests of Hypothesis | |
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the Elements of a Test of Hypothesis | |
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Formulating Hypotheses and Setting Up the Rejection Region | |
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Test of Hypothesis About a Population Mean: Normal (z) Statistic | |
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Observed Significance Levels: p-Values | |
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Test of Hypothesis About a Population Mean: Student's t-statistic | |
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Large-Sample Test of Hypothesis About a Population Proportion | |
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Calculating Type II Error Probabilities: More About � (Optional) | |
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Test of Hypothesis About a Population Variance (Optional) | |
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Single Population Inferences | |
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Comparing Population Means | |
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Identifying the Target Parameter | |
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Comparing Two Population Means: Independent Sampling | |
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Comparing Two Population Means: Paired Difference Experiments | |
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Determining the Sample Size | |
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the Completely Randomized Design: Single Factor | |
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Comparing Two Populations: Independent Samples | |
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Comparing Two Populations: Paired Difference Experiment | |
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Comparing Population Proportions | |
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Categorical Data and the Multinomial Distribution | |
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Testing Categorical Probabilities: One-Way Table | |
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Testing Categorical Probabilities: Two-Way (Contingency) Table | |
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A Word of Caution About Chi-Square Tests | |
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Comparing Two Population Proportions: Independent Sampling | |
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Determining the Sample Size | |
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Simple Linear Regression | |
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Probabilistic Models | |
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Fitting the Model: the Least Squares Approach | |
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Model Assumptions | |
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Assessing the Utility of the Model: Making Inferences About the Slope �1 | |
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the Coefficients of Correlation and Determination | |
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Using the Model for Estimation and Prediction | |
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A Complete Example | |
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Rank Correlation | |