Chapter 1: Introduction (1 meeting)
The basic goal of statistics: draw conclusions based on data. There
are various aspects of statistics ranging from formulating the question,
designing experiments to address the question, collecting the data, and
analyzing the data, but we'll be stressing the role of probability
and probability distributions in this process. We'll often begin with
a random sample drawn from a parameterized family of distributions, and
our job is to make conclusions about the parameter.
Chapter 2: Review of Probability (1 meeting)
We'll quickly review the theory of probability. Sample spaces and events,
Kolmogorov's axioms, principles of combinatorics including permutations
and combinations, conditional probability and independence, Bayes' theorem,
random variables, probability mass functions for discrete random variables,
probability density functions for continuous random variables, cumulative
distribution functions, expected value, mean and variance of a distribution,
selected discrete and continuous distributions.
Chapter 3: Collecting Data (2 meetings)
Types of statistical studies, observational studies, basic sampling designs
Chapter 4: Summarizing and Exploring Data (2 meeting)
Chapter 5: Sampling Distributions of Statistics (6 meetings)
5.1. Sampling Distribution of the Sample Mean
5.2. Sampling Distribution of the Sample Variance
5.3. Student's t-distribution
5.4. Snedecor-Fisher's F-distribution
Chapters 6 and 15: Basic Concepts of Inference (7 meetings)
6.1. Point Estimation
15.1. Maximum Likelihood Estimation
6.2. Confidence Interval Estimation
6.3. Hypothesis Testing
15.2. Likelihood Ratio Tests
15.3. Principles of Bayesian statistics. The Bernoulli process.
Chapter 7: Inferences for Single Samples (4 meetings)
7.1. Inferences on Mean (Large Samples)
7.2. Inferences on Mean (Small Samples)
7.3. Inferences on Variance (if time permits)
Bayesian inference for samples
Chapter 8: Inferences for Two Samples (4 meetings)
8.1. Independent Samples and Matched Pairs Designs
8.2. Graphical methods for comparing two samples
8.3. Comparing Means of Two Populations, independent samples and matched pairs
Chapter 9: Inferences for Proportions and Count Data (3 meetings)
9.1. Inferences on Proportion
9.2. Inferences on Comparing Two Proportions
Chapter 10: Simple linear regression and correlation (4 meetings)
The least squares method
10.1. The model for simple linear regression
10.2. Fitting a line, goodness of fit
10.3. Statistical inference with the simple linear regression model,
prediction and confidence intervals