MATH 2209 – Introduction to Statistics II: Course Syllabus and Study Guide

Course Overview

Introduction

MATH 2209 – Introduction to Statistics II is a continuation of introductory statistics, focusing on inferential statistics for both quantitative and categorical data. The course emphasizes applications to other disciplines and the refinement of statistical analysis skills.

• Prerequisite: MATH 2208 (Introduction to Statistics I)

• Delivery: Multi-mode (primarily synchronous online lectures and labs, with asynchronous materials as needed)

• Textbook: Stats: Data and Models, 4th Canadian Edition (DeVeaux, Velleman, Bock, Vukov, Wong)

• Software: Minitab (used for output interpretation; not required for assignments/tests)

Course Objectives

Learning Outcomes

By the end of the course, students should be able to:

• Identify and distinguish contexts suitable for statistical methods covered in the course.

• Recognize cases requiring techniques beyond the course scope.

• Select and justify appropriate statistical methods for real data.

• Perform calculations using statistical software and/or calculators.

• Write clear interpretations of data analyses.

Course Topics

Summary of Main Topics

The following topics are covered, corresponding to key chapters in a college statistics curriculum:

• Central Limit Theorem for Sample Means

• One-sample t-procedures for Population Means

• Two-sample t-procedures for Population Means

• Paired Data

• Chi-square Tests

• Inference for Simple Linear Regression

• Analysis of Variance (ANOVA) – One-way

• Analysis of Variance (ANOVA) – Two-way

• Multiple Regression

Detailed Topic Guide

Central Limit Theorem for Sample Means

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.

• Definition: For a population with mean $\mu$ and standard deviation $\sigma$, the distribution of sample means (for samples of size $n$) will be approximately normal for large $n$.

• Formula: $\text{Standard Error} = \frac{\sigma}{\sqrt{n}}$

• Application: Used to justify inference procedures for means.

• Example: If $n = 30$ and $\sigma = 10$, then $\text{SE} = \frac{10}{\sqrt{30}} \approx 1.83$.

One-sample t-procedures for Population Means

One-sample t-tests are used to infer the population mean when the population standard deviation is unknown.

• Definition: Tests whether the sample mean differs significantly from a hypothesized population mean.

• Formula: $t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}$

• Application: Used when $n$ is small and $\sigma$ is unknown.

• Example: Testing if the average height of a sample differs from a known population value.

Two-sample t-procedures for Population Means

Two-sample t-tests compare the means of two independent groups.

• Definition: Tests whether the difference between two sample means is statistically significant.

• Formula: $t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$

• Application: Used in comparing treatment and control groups.

• Example: Comparing average test scores between two classes.

Paired Data

Paired t-tests analyze data where two measurements are taken on the same subject.

• Definition: Tests the mean difference between paired observations.

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

• Application: Used in before-and-after studies.

• Example: Measuring blood pressure before and after treatment in the same patients.

Chi-square Tests

Chi-square tests are used for categorical data to test independence or goodness-of-fit.

• Definition: Tests whether observed frequencies differ from expected frequencies.

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

• Application: Used in contingency tables and testing distributions.

• Example: Testing if gender and preference are independent in a survey.

Inference for Simple Linear Regression

Simple linear regression models the relationship between two quantitative variables.

• Definition: Estimates the slope and intercept of the best-fit line.

• Formula: $y = \beta_0 + \beta_1 x + \epsilon$

• Application: Used to predict values and assess association.

• Example: Predicting sales based on advertising expenditure.

Analysis of Variance (ANOVA) – One-way

One-way ANOVA tests for differences among means of three or more groups.

• Definition: Compares group means to determine if at least one differs.

• Formula: $F = \frac{\text{Between-group variance}}{\text{Within-group variance}}$

• Application: Used in experiments with multiple treatments.

• Example: Comparing mean yields of crops under different fertilizers.

Analysis of Variance (ANOVA) – Two-way

Two-way ANOVA examines the effect of two categorical factors and their interaction on a quantitative outcome.

• Definition: Tests main effects and interaction effects.

• Formula: $F = \frac{\text{Mean Square Factor}}{\text{Mean Square Error}}$

• Application: Used in factorial experiments.

• Example: Studying the effect of fertilizer type and irrigation method on crop yield.

Multiple Regression

Multiple regression models the relationship between a quantitative outcome and two or more predictor variables.

• Definition: Extends simple regression to include multiple predictors.

• Formula: $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \ldots + \beta_p x_p + \epsilon$

• Application: Used to predict outcomes and assess the effect of several variables.

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

Course Evaluation

Assessment Breakdown

The course grade is determined by the following components:

Category	Weight
Assignments	15%
Laboratory Work	15%
Tests (3 x 10%)	30%
Final Exam	40%
Total	100%

• Minimum Final Exam Requirement: If you earn less than 50% on the proctored final exam, your course grade will be capped at a "D". If you earn less than 25%, your grade will be an "F".

Academic Policies

Standards and Integrity

• Correct Use of Language: Required in all written assignments.

• Plagiarism and Cheating: Strictly prohibited; includes unauthorized use of previous solutions and online resources.

• Lab Work: Group work is encouraged during lab sessions, but submissions must be individual.

• Accessibility and Accommodation: Students requiring accommodations must register with Accessibility Services.

• Religious Observance: Requests for accommodation must be made within the first two weeks.

Course Resources

Textbook and Software

• Textbook: Stats: Data and Models, 4th Canadian Edition (Pearson Canada)

• MyLab Access: Required for assignments and tests

• Minitab: Used for lab output interpretation

• Calculator: Required for computations

Additional Info

• Weekly schedule and lab manual will be posted on Moodle.

• Office hours and additional resources will be announced in class and online.

• Students must check MSVU email and Moodle regularly for updates.

Additional info: Academic context and formulas were added to expand brief syllabus points into a self-contained study guide.