MAT 220A-OL: Introduction to Statistics – 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 information. Students will learn fundamental concepts such as sampling, experimental design, measurement, and statistical methods for data analysis. The course covers descriptive and inferential statistics, hypothesis testing, and the use of statistical software.

• Descriptive Statistics: Summarizing and describing data using measures such as mean, median, mode, and graphical representations.

• Inferential Statistics: Drawing conclusions about populations based on sample data, including hypothesis testing and estimation.

• Statistical Software: Application of MyLab Statistics for homework, quizzes, and data analysis.

Student Learning Outcomes

Goals of the Course

Upon completion of this course, students will be able to:

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

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

3. Apply knowledge of statistical theory and reasoning to critically evaluate statistical information in real-world contexts.

4. Communicate statistical information effectively.

5. Develop technology skills through the use of statistical software.

Required Resources

Textbook and Online Materials

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

• MyLab Statistics: Online homework, quizzes, and course materials.

Students will access course materials and assignments through MyLab Statistics and the Moodle course site.

Course Topics and Schedule

Weekly Breakdown

The course is organized into weekly topics, each covering key areas of statistics. Below is a summary of the main topics and chapters:

• Week 1: Introduction to Data

• Week 2: Picturing Variation with Graphs

• Week 3: Numerical Summaries of Center and Variation

• Week 4: Regression Analysis: Exploring Association Between Variables

• Week 5: Survey Sampling & Inference

• Week 6: Hypothesis Testing for Population Proportions and Means

• Week 7: Association Between Categorical Variables

• Week 8: Review and Final Exam

Assessment and Grading

Grade Distribution

Grades are based on a combination of homework, quizzes, tests, and a course project. The following table summarizes the grade distribution:

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

Letter grades are assigned according to the following scale:

Letter Grade	Numerical Range
A	93.0–100
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

Key Statistical Concepts

Descriptive Statistics

Descriptive statistics summarize and describe the main features of a data set. Common measures include:

• Mean: The average value, calculated as $\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$

• Median: The middle value when data are ordered.

• Mode: The most frequently occurring value.

• Standard Deviation: Measures the spread of data, $s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}$

Inferential Statistics

Inferential statistics allow us to make predictions or inferences about a population based on sample data. Key concepts include:

• Sampling: Selecting a subset of individuals from a population to estimate characteristics of the whole population.

• Hypothesis Testing: Procedures for testing claims about population parameters. Example: Testing the mean using a t-test.

• Confidence Intervals: Range of values within which a population parameter is likely to fall. Example: $\bar{x} \pm z^* \frac{s}{\sqrt{n}}$

Regression and Association

Regression analysis explores relationships between variables. The simplest form is linear regression:

• Linear Regression Equation: $y = a + bx$

• Correlation Coefficient: Measures the strength and direction of a linear relationship, $r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}$

Probability

Probability quantifies the likelihood of events. Key concepts include:

• Probability of an Event: $P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

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

Course Policies and Support

Attendance and Participation

Active participation is required. Weekly homework and assignments must be submitted on time via MyLab Statistics. Failure to submit work may result in a zero for that week.

Academic Integrity

Students are expected to adhere to the college's academic honesty policy. Use of AI for learning is encouraged for study support, but plagiarism is strictly prohibited.

Technical and Tutoring Support

• Technical support is available via helpdesk.

• Student Learning Collaborative offers tutoring and skill support.

Course Project

Project Overview

The course project constitutes 10% of the final grade and involves applying statistical concepts to a real-world problem. Details will be provided on the course site.

Summary Table: Weekly Topics

Week	Main Topic	Assignments
1	Introduction to Data	Homework, Quiz
2	Picturing Variation with Graphs	Homework, Quiz
3	Numerical Summaries	Homework, Quiz
4	Regression Analysis	Homework, Quiz
5	Survey Sampling & Inference	Homework, Quiz
6	Hypothesis Testing	Homework, Quiz
7	Association between Categorical Variables	Homework, Quiz, Project
8	Review and Final Exam	Final Exam

Additional info: The syllabus emphasizes the importance of statistical reasoning in various fields, including business, healthcare, and social sciences. Students are encouraged to use technology and AI tools for learning, provided academic integrity is maintained.