MATH2209 Statistics Course Schedule and Key Topics (Winter 2026)

Course Overview

This schedule outlines the weekly topics, chapters, and assessments for MATH2209, a college-level statistics course based on "Stats: Data and Models, 4th Canadian Edition." The course covers foundational and advanced statistical methods, including sampling distributions, inference, regression, and analysis of variance.

Key Topics and Chapters

Sampling Distributions and Central Limit Theorem (CLT)

The Central Limit Theorem (CLT) is a fundamental concept in statistics, stating that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution.

• Chapter 14: CLT for mean

• Key Points:

  • Sampling distribution of the mean

  • Normal approximation for large samples

• Formula:

  • $\text{If } X_1, X_2, ..., X_n \text{ are i.i.d. with mean } \mu \text{ and variance } \sigma^2, \text{ then } \bar{X} \approx N(\mu, \frac{\sigma^2}{n})$

• Example: Estimating the average height of students using a random sample.

Confidence Intervals and Hypothesis Tests for Means

Statistical inference for means includes constructing confidence intervals and performing hypothesis tests to determine if a population mean differs from a hypothesized value or another mean.

• Chapter 18: CI, Test for one mean

• Chapter 19: CI, Test for difference in means

• Key Points:

  • Confidence interval for a mean: $\bar{X} \pm t^* \frac{s}{\sqrt{n}}$

  • Hypothesis test for a mean: $t = \frac{\bar{X} - \mu_0}{s/\sqrt{n}}$

  • Difference in means: $\bar{X}_1 - \bar{X}_2$

• Example: Comparing average test scores between two classes.

Matched Pairs and Paired Samples

Matched pairs analysis is used when observations are paired, such as before-and-after measurements on the same subjects.

• Chapter 20: Matched Pairs

• Key Points:

  • Paired t-test for dependent samples

  • Difference scores: $d_i = X_{i,\text{after}} - X_{i,\text{before}}$

• Formula:

  • $t = \frac{\bar{d}}{s_d / \sqrt{n}}$

• Example: Measuring the effect of a treatment on blood pressure.

Chi-Squared Tests: Goodness-of-Fit, Homogeneity, and Independence

Chi-squared tests are used to analyze categorical data, testing whether observed frequencies differ from expected frequencies.

• Chapter 22: Goodness-of-fit, homogeneity, and independence tests

• Key Points:

  • Goodness-of-fit: Does data fit a specified distribution?

  • Homogeneity: Are distributions the same across groups?

  • Independence: Are two categorical variables independent?

• Formula:

  • $\chi^2 = \sum \frac{(O - E)^2}{E}$

• Example: Testing if dice are fair.

• Table:

  Test Type	Purpose	Data Structure
  Goodness-of-fit	Compare observed to expected frequencies	One categorical variable
  Homogeneity	Compare distributions across groups	Two or more groups
  Independence	Test association between variables	Contingency table

Regression Analysis

Regression is used to model relationships between variables, estimate effects, and make predictions.

• Chapter 23: Regression

• Key Points:

  • Simple linear regression: $Y = \beta_0 + \beta_1 X + \epsilon$

  • Interpretation of slope and intercept

  • Correlation and association

• Example: Predicting sales based on advertising budget.

Analysis of Variance (ANOVA)

ANOVA is used to compare means across multiple groups and assess whether group means differ significantly.

• Chapter 24: One-way ANOVA

• Chapter 25: Two-way ANOVA

• Key Points:

  • Partitioning variance into between-group and within-group components

  • F-statistic: $F = \frac{\text{MS}_{\text{between}}}{\text{MS}_{\text{within}}}$

  • Multiple factors in two-way ANOVA

• Example: Comparing mean exam scores across different teaching methods.

• Table:

  ANOVA Type	Purpose	Factors
  One-way	Compare means across groups	Single factor
  Two-way	Assess interaction between factors	Two factors

Multiple Regression

Multiple regression extends simple regression to include multiple predictors, allowing for more complex modeling and control of confounding variables.

• Chapter 26: Multiple Regression

• Key Points:

  • Model: $Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + ... + \beta_p X_p + \epsilon$

  • Interpretation of coefficients

  • Model selection and diagnostics

• Example: Predicting house prices using size, location, and age.

Review and Choosing Methods

The course includes review sessions and guidance on selecting appropriate statistical methods for different types of data and research questions.

• Key Points:

  • Choosing between t-tests, ANOVA, regression, and chi-squared tests

  • Understanding assumptions for each method

• Example: Deciding whether to use a paired t-test or ANOVA for a given dataset.

Assessment Schedule

• Quizzes: Four quizzes throughout the term, covering recent chapters

• Midterm Exam: Covers Chapters 14, 18, 19, 20, and/or 22

• Final Exam: Cumulative, covering all chapters

Lab Sessions

• Weekly labs reinforce lecture material and provide hands-on practice with statistical methods.

• Lab topics align with chapters and include review, application, and method selection.

Summary Table: Weekly Topics

Week	Chapter(s)	Topic
Jan 7-8	14	CLT for mean
Jan 12-16	18	CI, Test for one mean
Jan 19-23	19	CI, Test for difference in means
Jan 26-28	20	Matched Pairs
Feb 2-6	22	Chi-squared tests
Feb 9-13	22	Finish Chi-Square
Feb 23-27	23	Regression
Mar 2-6	23, 24	Finish regression, One-way ANOVA
Mar 9-13	24, 25	Finish one-way ANOVA, Two-way ANOVA
Mar 16-20	25	Finish Two-Way ANOVA
Mar 23-27	26	Multiple Regression
Mar 30-Apr 3	26	Multiple Regression
Apr 6-10	Review	Choosing methods, Review

Additional info: The schedule references review sessions and method selection, which are essential for exam preparation and practical application of statistical techniques.