Elementary Statistical Methods: Course Structure and Study Guide

Course Overview

Introduction to Elementary Statistical Methods

This course, MATH-1342-M02, covers fundamental concepts in statistics, including data collection, analysis, presentation, interpretation, and probability. Students will learn descriptive statistics, correlation and regression, confidence intervals, and hypothesis testing, using appropriate technology and tools.

Course Topics and Structure

Chapter 1: Sampling and Data

• Definitions of Statistics, Probability, and Key Terms: Introduction to the field of statistics, basic terminology, and the role of probability.

• Data, Sampling, and Variation: Types of data, sampling methods, and understanding variation in data and sampling.

• Frequency, Frequency Tables, and Levels of Measurement: Organizing data using frequency tables and understanding measurement levels (nominal, ordinal, interval, ratio).

• Experimental Design and Ethics: Principles of designing experiments and ethical considerations in data collection.

Chapter 2: Descriptive Statistics

• Stem-and-Leaf Graphs (Stem plots), Graphs: Visual representation of data using stem plots and other graphs.

• Histograms, Frequency Polygons: Construction and interpretation of histograms and frequency polygons.

• Measures of the Location of the Data: Calculation and interpretation of measures such as mean, median, and mode.

• Box Plots: Visual summary of data distribution, including quartiles and outliers.

• Measures of the Center of the Data: Central tendency measures (mean, median, mode).

• Skewness and the Mean, Median, and Mode: Understanding data distribution and its impact on central tendency.

• Measures of the Spread of the Data: Variability measures such as range, variance, and standard deviation.

Chapter 3: Probability Topics

• Terminology: Key probability terms and concepts.

• Independent and Mutually Exclusive Events: Definitions and examples of event relationships.

• Two Basic Rules of Probability: Addition and multiplication rules for probability calculations.

Chapter 4: Discrete Random Variables

• Probability Distribution Function (PDF) for a Discrete Random Variable: Understanding and constructing PDFs for discrete variables.

• Binomial Distribution: Properties and applications of the binomial distribution.

Chapter 6: The Normal Distribution

• The Standard Normal Distribution: Characteristics and applications of the standard normal curve.

• Using the Normal Distribution: Calculating probabilities and interpreting results using the normal distribution.

Chapter 8: Confidence Intervals

• A Single Population Mean using the Normal Distribution: Constructing and interpreting confidence intervals for means.

• A Population Proportion: Confidence intervals for population proportions.

Chapter 9: Hypothesis Testing with One Sample

• Null and Alternative Hypotheses: Formulating hypotheses for statistical testing.

• Rare Events, the Sample, Decision and Conclusion: Making decisions based on sample data and interpreting results.

• Full Hypothesis Test Examples: Step-by-step examples of hypothesis testing.

Chapter 12: Linear Regression and Correlation

• Linear Equations and Scatter Plots: Introduction to linear relationships and visualizing data with scatter plots.

• The Regression Equation: Deriving and interpreting the regression equation for prediction.

Key Definitions and Concepts

• Statistics: The science of collecting, analyzing, presenting, and interpreting data.

• Probability: The measure of the likelihood that an event will occur.

• Random Variable: A variable whose value is subject to random variation.

• Confidence Interval: A range of values used to estimate a population parameter.

• Hypothesis Testing: A method for making decisions about population parameters based on sample data.

• Regression: A statistical method for modeling the relationship between variables.

• Correlation: A measure of the strength and direction of the relationship between two variables.

Grading Scheme

Activity Type	Percentage
Online Homework	20%
Quizzes	20%
Scaffolding Assignments	15%
Unit Exams	25%
Signature Assignment	20%
Total	100%

Assessment Scale

Letter Grade	Grade Point	Numerical Value	Operational Value
A	4.0	4	Exemplary
B	3.0	3	Proficient
C	2.0	2	Developing
D	1.0	1	Beginning
F	0.0	0	Not Evident

Course Calendar Overview

• Weeks 1-2: Introduction, Sampling, Data, Frequency Tables, Experimental Design

• Weeks 3-6: Descriptive Statistics, Graphs, Measures of Center and Spread

• Weeks 7-8: Probability, Rules, Projects

• Weeks 9-10: Discrete Random Variables, Binomial, Normal Distribution

• Weeks 11-13: Confidence Intervals, Hypothesis Testing

• Weeks 14-15: Linear Regression, Correlation

• Week 16: Final Exam

Student Learning Outcomes

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

• Recognize, examine, and interpret the basic principles of describing and presenting data.

• Compute and interpret empirical and theoretical probabilities using the rules of probabilities and combinatorics.

• Explain the role of probability in statistics.

• Examine, analyze, and compare various sampling distributions for both discrete and continuous random variables.

• Describe and compute confidence intervals.

• Solve linear regression and correlation problems.

• Perform hypothesis testing using statistical methods.

Course Requirements and Expectations

• Active participation in online and in-person activities.

• Regular attendance and engagement with course materials.

• Timely submission of assignments, quizzes, and exams.

• Adherence to academic integrity and college policies.

• Utilization of Canvas and college resources for support.

Support and Resources

• Instructor office hours and contact information for academic support.

• Canvas Support Hotline and live chat for technical assistance.

• Digital library access for research and study.

• Disability support services for accommodations.

Additional Info

• Course aligns with THECB Core Curriculum objectives: Critical Thinking, Communication, Empirical and Quantitative skills.

• Signature assignments and projects reinforce applied statistical analysis and communication skills.

• Emergency Academic Continuity Plan ensures course access during disruptions.