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Exploring One-Variable Data and Collecting Data

Working with one variable at a time and gathering trustworthy data. Topics: Introducing Statistics: What Can We Learn from Data?, Variables, Tabular Representation and Summary Statistics for One Categorical Variable, Graphical Representations for One Categorical Variable, Graphical Representations for One Quantitative Variable, Descriptions for One Quantitative Variable Distributions, Summary Statistics for One Quantitative Variable, Graphical Representations of Summary Statistics for One Quantitative Variable, Comparisons of the Distributions for One Quantitative Variable, The Investigative Question Revisited and Data Collection, Random Sampling, Potential Problems with Sampling, Experimental Design.

Probability, Random Variables, and Probability Distributions

The probability machinery that connects data production to inference. Topics: Tabular and Graphical Representations for the Distributions of Two Categorical Variables, Summary Statistics for Two Categorical Variables, Estimating Probabilities Using Simulation, Introduction to Probability, Mutually Exclusive Events, Conditional Probability, Independent Events and Unions of Events, Introduction to Random Variables and Probability Distributions, Parameters of Random Variables, The Binomial Distribution, The Normal Distribution, Sampling Distributions and the Central Limit Theorem.

Inference for Categorical Data: Proportions

Formal statistical inference for proportions. Topics: Estimators, Sampling Distributions for Sample Proportions, Constructing a Confidence Interval for a Population Proportion, Justifying a Claim Based on a Confidence Interval for a Population Proportion, Setting Up a Test for a Population Proportion, p-Values, Carrying Out a Test for a Population Proportion, Potential Errors When Performing Tests, Sampling Distributions for the Difference Between Sample Proportions, Constructing a Confidence Interval for the Difference Between Two Population Proportions, Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population Proportions, Setting Up a Test for the Difference Between Two Population Proportions, Carrying Out a Test for the Difference Between Two Population Proportions, Setting Up a Chi-Square Test for Homogeneity or Independence, Carrying Out a Chi-Square Test for Homogeneity or Independence.

Inference for Quantitative Data: Means

Inference for means, built on the same logic as inference for proportions but using the t-distribution because the population standard deviation must be estimated. Topics: Sampling Distributions for Sample Means, Constructing a Confidence Interval for a Population Mean or Population Mean Difference, Justifying a Claim Based on a Confidence Interval for a Population Mean or Population Mean Difference, Setting Up a Test for a Population Mean or Population Mean Difference, Carrying Out a Test for a Population Mean or Population Mean Difference, Sampling Distributions for the Difference Between Two Sample Means, Constructing a Confidence Interval for the Difference Between Two Population Means, Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population Means, Setting Up a Test for the Difference Between Two Population Means, Carrying Out a Test for the Difference Between Two Population Means.

Regression Analysis

Relationships between two quantitative variables. Topics: Graphical Representations Between Two Quantitative Variables, Correlation, Linear Regression Models, Residuals, Least-Squares Regression.