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, methods of sampling, experimental design, and techniques for analyzing data. The course emphasizes both theoretical understanding and practical application, preparing students to critically evaluate statistical information in various contexts.

• Key Topics: Sampling, experimental design, descriptive statistics, inferential statistics, hypothesis testing, regression analysis, and categorical data analysis.

• Applications: Business, healthcare, social sciences, and informed citizenship.

Student Learning Outcomes

Core Competencies

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 experimental design and data analysis to critically evaluate statistical information in real-world situations.

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.

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

Major Topics and Weekly Schedule

Course Content Breakdown

The course is organized into weekly modules, each focusing on a specific area of statistics. Below is a summary of the main topics covered:

• Week 1: Introduction to Data, Picturing Variation with Graphs

• Week 2: Numerical Summaries of Center and Variation

• Week 3: Regression Analysis, Exploring Association Between Variables

• Week 4: Modeling Random Events: The Normal and Binomial Models, Probability

• Week 5: Survey Sampling & Inference, Hypothesis Testing for Population Proportions

• Week 6: Inferring Population Means

• Week 7: Association Between Categorical Variables

• Week 8: Review and Final Exam

Key Statistical Concepts

Descriptive Statistics

Descriptive statistics summarize and describe the main features of a data set.

• Measures of Central Tendency: Mean, median, mode

• Measures of Variation: Range, variance, standard deviation

• Graphical Representations: Histograms, boxplots, scatterplots

Formula for Mean:

$\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$

Formula for Standard Deviation:

$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}$

Inferential Statistics

Inferential statistics use sample data to make generalizations about a population.

• Sampling Methods: Simple random sampling, stratified sampling, cluster sampling

• Hypothesis Testing: Procedures to test claims about population parameters

• Confidence Intervals: Range of values likely to contain the population parameter

Formula for Confidence Interval (Mean):

$\bar{x} \pm z^* \frac{s}{\sqrt{n}}$

Formula for Hypothesis Test (Z-test):

$z = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}}$

Regression and Correlation

Regression analysis explores relationships between variables, while correlation measures the strength and direction of association.

• Simple Linear Regression: Models the relationship between two variables

• Correlation Coefficient: Quantifies the degree of association

Formula for Correlation Coefficient:

$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}$

Formula for Regression Line:

$y = a + bx$

Probability and Random Events

Probability theory underpins statistical inference and models random phenomena.

• Probability Rules: Addition rule, multiplication rule, complement rule

• Normal Distribution: Bell-shaped curve describing many natural phenomena

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

Formula for Binomial Probability:

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

Formula for Normal Distribution:

$f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$

Categorical Data Analysis

Analyzing categorical variables involves methods such as chi-square tests to assess associations.

• Chi-Square Test: Tests independence between categorical variables

• Contingency Tables: Summarize categorical data

Formula for Chi-Square Statistic:

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

Assessment and Grading

Grade Distribution

Grades are based on a combination of homework, quizzes, tests, and a course project.

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

Letter Grade Scale:

Letter Grade	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 and Participation

• Active participation is required each week through MyLab Statistics assignments.

• Failure to submit weekly assignments may result in a zero for that week.

Homework and Quizzes

• Homework is assigned and submitted via MyLab Statistics.

• Quizzes can be taken twice before the due date; the highest score counts.

• Students are encouraged to keep a homework notebook for problem-solving and review.

Course Project

• Project details are provided on the course site and contribute 10% to the final grade.

Technical and Academic Support

• Technical support is available via email and phone.

• Student Learning Collaborative offers tutoring and skill support.

• Background review resources are recommended for students needing math skill refreshers.

Use of Artificial Intelligence

• AI is encouraged as a learning aid but not for plagiarism or academic dishonesty.

• AI can help create study aids and clarify instructions.

Summary Table: Weekly Topics

Week	Main Topic	Subtopics
1	Introduction to Data	Types of data, graphical representation
2	Numerical Summaries	Measures of center and variation
3	Regression Analysis	Exploring association between variables
4	Probability Models	Normal and binomial distributions
5	Survey Sampling & Inference	Hypothesis testing for proportions
6	Inferring Population Means	Confidence intervals, hypothesis tests
7	Categorical Data Analysis	Chi-square tests, association
8	Review and Final Exam	Comprehensive review

Additional info: The syllabus emphasizes the importance of ethical conduct, collaboration, and the use of technology in learning statistics. Students are encouraged to seek help and use available resources to ensure success in the course.