Introduction to Statistics (MAT 220A-OL) – Syllabus and Study Guide

Course Overview

Introduction to Statistics

This course provides a comprehensive introduction to the field of statistics, focusing on the collection, analysis, and interpretation of numerical data. Students will learn fundamental statistical concepts, including sampling, experimental design, descriptive and inferential statistics, and hypothesis testing. The course emphasizes the application of statistical methods to real-world problems in various fields such as business, healthcare, and the social sciences.

• Course Code: MAT 220A-OL

• Term: Fall 2025, First 8-Week Term

• Instructor: Tim Brechven

• Delivery: Online (asynchronous, with optional online meetings)

Student Learning Outcomes

• Describe and interpret data and relationships with numbers and graphs.

• Perform and interpret statistical hypothesis tests to draw inferences and make decisions.

• Apply knowledge of data collection and analysis to critically evaluate statistical information in context.

• Communicate statistical information effectively.

• Develop technology skills through the use of statistical software.

Required Resources

• Textbook: Introductory Statistics: Exploring the World through Data, 4th Edition, by Robert Gould

• Online Platform: MyLab Statistics (for homework, quizzes, and course materials)

Major Topics and Weekly Schedule

The course is structured into weekly modules, each focusing on a key area of statistics. Below is a summary of the main topics and their subtopics, as outlined in the tentative schedule:

1. Introduction to Data

• Definition: Data are values collected from observations, surveys, or experiments.

• Types of Data: Categorical (qualitative) and numerical (quantitative).

• Applications: Understanding the context and source of data is crucial for proper analysis.

2. Picturing Variation with Graphs

• Graphical Methods: Histograms, bar charts, pie charts, boxplots, and scatterplots.

• Purpose: Visualizing data helps identify patterns, trends, and outliers.

• Example: A histogram can show the distribution of exam scores in a class.

3. Numerical Summaries of Center and Variation

• Measures of Center: Mean, median, and mode.

• Measures of Variation: Range, variance, and standard deviation.

• Formulas:

$\text{Mean} = \frac{\sum x_i}{n}$

$\text{Variance} = \frac{\sum (x_i - \bar{x})^2}{n-1}$

$\text{Standard Deviation} = \sqrt{\text{Variance}}$

4. Regression Analysis: Exploring Association Between Variables

• Regression: Examines the relationship between two quantitative variables.

• Correlation Coefficient (r): Measures the strength and direction of a linear relationship.

• Simple Linear Regression Equation:

$y = a + bx$

• Applications: Predicting outcomes, such as sales based on advertising expenditure.

5. Modeling Random Events: The Normal and Binomial Models

• Normal Distribution: A symmetric, bell-shaped distribution described by its mean and standard deviation.

• Binomial Distribution: Models the number of successes in a fixed number of independent trials.

• Formulas:

$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$ (Binomial Probability)

$z = \frac{x - \mu}{\sigma}$ (Standard Score for Normal Distribution)

6. Survey Sampling & Inference

• Sampling Methods: Simple random, stratified, cluster, and systematic sampling.

• Inference: Drawing conclusions about a population based on sample data.

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

7. Hypothesis Testing for Population Proportions and Means

• Hypothesis Test: A procedure to test claims about a population parameter.

• Steps:

  1. State null ($H_0$) and alternative ($H_a$) hypotheses.

  2. Choose significance level ($\alpha$).

  3. Calculate test statistic.

  4. Determine p-value or critical value.

  5. Draw a conclusion.

• Formulas:

$z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$ (Proportion)

$t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}$ (Mean, when population standard deviation is unknown)

8. Association Between Categorical Variables

• Chi-Square Test: Used to determine if there is a significant association between two categorical variables.

• Formula:

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

• Applications: Testing independence in contingency tables.

Assessment and Grading

Grades are based on a combination of homework, quizzes, tests, and a course project. The grading scale and distribution are as follows:

Component	Percentage
Course Project	10%
MyLab Statistics Tests	30%
MyLab Statistics Quizzes	30%
MyLab Statistics Homework	30%

Letter Grade Scale:

Letter	Numerical Range
A	93.0–100.0
A-	90.0–92.9
B+	87.0–89.9
B	83.0–86.9
B-	80.0–82.9
C+	77.0–79.9
C	73.0–76.9
C-	70.0–72.9
D+	67.0–69.9
D	63.0–66.9
D-	60.0–62.9
F	0.0–59.9

Course Policies and Support

• Attendance: Active weekly participation is required through assignment submission.

• Homework: Assigned via MyLab Statistics; multiple attempts allowed before due date.

• Quizzes/Tests: Quizzes can be taken twice before the due date; the higher score is counted.

• Course Project: Worth 10% of the final grade; details provided on the course site.

• Academic Integrity: High standards are expected; AI tools may be used for learning but not for plagiarism.

• Technical Support: Available via helpdesk (phone and email).

• Tutoring: Student Learning Collaborative offers support in statistics and related skills.

Additional Info

• Background review is recommended for students needing a refresher in basic math skills.

• Students are encouraged to keep a homework notebook for organized problem-solving and exam preparation.

• Rounding rules and attention to detail are emphasized in all assignments and assessments.