This course on Statistics covers a broad range of topics, organized into 13 chapters:
- Sampling and Data: Introduces statistics and probability, data and sampling, levels of measurement, experimental design, and ethics in statistics.
- Descriptive Statistics: Covers displaying data, measures of data location, center, sigma notation, arithmetic mean, geometric mean, skewness, and data spread.
- Probability Topics: Discusses probability terminology, independent and mutually exclusive events, basic probability rules, contingency tables, probability trees, and Venn diagrams.
- Discrete Random Variables: Explores discrete probability distributions including hypergeometric, binomial, geometric, and Poisson distributions.
- Continuous Random Variables: Focuses on continuous probability density functions, uniform distribution, and exponential distribution.
- The Normal Distribution: Introduces the standard normal distribution, using the normal distribution, and estimating the binomial distribution with the normal distribution.
- The Central Limit Theorem: Covers the central limit theorem for sample means and proportions, and the finite population correction factor.
- Confidence Intervals: Discusses constructing confidence intervals for known and unknown population standard deviations, for population proportions, and calculating sample size for continuous and binary random variables.
- Hypothesis Testing with One Sample: Includes null and alternative hypotheses, type I and II errors, probability distributions for hypothesis testing, and full hypothesis test examples.
- Hypothesis Testing with Two Samples: Compares two independent population means, effect sizes, tests for differences in means with equal population variances, compares two population proportions, and matched or paired samples.
- The Chi-Square Distribution: Covers the chi-square distribution, tests of a single variance, goodness-of-fit tests, tests of independence, tests for homogeneity, and comparison of chi-square tests.
- F Distribution and One-Way ANOVA: Discusses tests of two variances, one-way ANOVA, the F distribution, and facts about the F distribution.
- Linear Regression and Correlation: Focuses on the correlation coefficient, significance testing of the correlation coefficient, linear equations, regression equations, interpretation of regression coefficients, prediction with regression equations, and regression analysis using Microsoft Excel®.
Each chapter includes key terms, a chapter review, homework exercises, references, and solutions, providing a comprehensive understanding of statistical concepts and their practical applications.
