Elementary Statistical Methods: Syllabus and Course Structure Study Guide

Course Overview

Course Description

This course covers the collection, analysis, presentation, and interpretation of data, as well as probability. Students will learn descriptive statistics, correlation and regression, confidence intervals, and hypothesis testing. Both discrete and continuous random variables are addressed, with appropriate technology integrated throughout.

• Prerequisites: TSI complete/College-Ready

• Textbook: Statistics: Unlocking the Power of Data by Lock, Lock, Lock, Lock, and Lock (2018)

Course Topics

Major Units and Weekly Breakdown

The course is structured to cover foundational and advanced topics in statistics, aligned with standard college-level statistics curricula.

Week	Topics
1	Introduction, What is Statistics? What is Data?
2	Sampling Methods & Sampling Strategies
3	Types of Data, Experimental & Observational Studies
4	Describing Data: Tables, Graphs, and Misleading Graphs
5	Numerical Summaries: Mean, Median, Mode, Range, Standard Deviation
6	Probability: Basic Rules, Counting, Permutations, Combinations
7	Discrete and Binomial Distributions
8	Normal and Standard Normal Distributions
9	Sampling Distributions & Confidence Intervals (Mean & Proportion)
10	Hypothesis Testing: One Sample and Two Samples
11	Correlation and Regression
12	Chi-Square Tests & Goodness of Fit
13	ANOVA (Analysis of Variance)

Student Learning Outcomes

• Explain the use of data collection and statistics to reach reasonable conclusions.

• Organize, present, and interpret statistical data, including graphical and numerical summaries.

• Apply concepts of probability and the binomial distribution using the rules of probability and combinatorics.

• Calculate and interpret confidence intervals and hypothesis tests for both discrete and continuous random variables.

• Describe and compute correlation and regression.

• Perform basic hypothesis testing using statistical methods.

Key Concepts and Definitions

Descriptive Statistics

• Mean: The average value of a dataset. $\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i$

• Median: The middle value when data are ordered.

• Mode: The most frequently occurring value.

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

Probability

• Probability: The likelihood of an event occurring. $P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

• Binomial Distribution: Probability of $k$ successes in $n$ trials. $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$

• Normal Distribution: Symmetrical, bell-shaped distribution. $f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$

Inferential Statistics

• Confidence Interval (Mean): $\bar{x} \pm z^* \frac{s}{\sqrt{n}}$

• Hypothesis Testing: Procedure to test claims about population parameters.

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

• Regression: Predicts value of one variable based on another. $y = a + bx$

• Chi-Square Test: Tests association between categorical variables. $\chi^2 = \sum \frac{(O - E)^2}{E}$

• ANOVA: Compares means across multiple groups.

Course Requirements and Policies

• Attendance: Required for participation and daily grades.

• Homework: Assigned regularly; must be submitted on time.

• Quizzes and Exams: Three major exams and a comprehensive final exam.

• Technology: Calculator (TI-83 or TI-84 recommended), computer/laptop, scanner for homework submission, and access to MyLeo/D2L LMS.

Grading Breakdown

Assessment	Percentage
Daily Work (Homework, Quizzes, Tutoring, etc.)	15%
Test 1	20%
Test 2	20%
Test 3	20%
Comprehensive Final Exam	25%

Academic Integrity and Support

• Academic Honesty: Cheating and plagiarism are strictly prohibited.

• Support Services: Math Skills Center, technical support, counseling, and disability services are available.

Additional Info

• Students are expected to use statistical software and calculators for assignments and exams.

• Course includes both individual and group activities, with emphasis on critical thinking and communication.

• Attendance, participation, and timely submission of assignments are essential for success.