Course Overview

Introduction to Statistics and Probability

This course provides a comprehensive introduction to statistics and probability, focusing on techniques and the use of statistical software for the analysis of univariate and bivariate data. Students will learn about graphical and numerical methods, probability, random variables, normal and binomial distributions, sampling distributions, inference, regression, and hypothesis testing. The course emphasizes both conceptual understanding and practical application, including the use of modern statistical technology.

• Statistical Software: Students will use tools such as Canvas, Pearson MyLab, StatCrunch, and calculators for data analysis.

• Prerequisites: Completion of college-level mathematics (MATH 1200, 1250, 1260, 1321, or higher).

• Textbook: Sullivan, Statistics: Informed Decisions Using Data, 7th Edition.

Learning Objectives

Core Competencies in Statistics

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

• Select and produce appropriate graphical, tabular, and numerical methods for summarizing and analyzing univariate and bivariate data.

• Interpret statistical summaries and evaluate the design of studies, including the ability to identify well-constructed studies and critically assess statistical evidence.

• Describe and interpret quantitative measures of central tendency (mean, median, mode) and variability (range, variance, standard deviation).

• Understand and apply probability concepts, including random experiments, events, and sample spaces.

• Calculate and interpret probabilities using probability distributions such as the binomial and normal distributions.

• Distinguish between discrete and continuous probability distributions and apply formulas for expected values and variances.

• Apply inferential statistics to perform hypothesis testing, estimation, and confidence intervals.

• Use appropriate technology for descriptive and inferential statistical analysis.

• Make judgments and draw conclusions based on statistical evidence, including the ability to recognize the limitations of statistical methods.

• Communicate quantitative evidence in support of arguments or decisions, both in written and oral formats.

• Critically evaluate information from sources with enough rigor to identify errors or biases.

• Recognize and avoid methodological fallacies and misinterpretations in statistical reasoning.

• State and evaluate connections between statistics and related outcomes, including consequences and implications.

Major Topics Covered

Univariate and Bivariate Data Analysis

Students will learn to summarize and analyze data using graphical (histograms, boxplots, scatterplots) and numerical methods (mean, median, mode, standard deviation, correlation).

• Univariate Data: Analysis of a single variable.

• Bivariate Data: Analysis of relationships between two variables.

Probability and Random Variables

Probability theory forms the foundation for statistical inference. Students will study random experiments, sample spaces, and events.

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

• Random Variable: A variable whose value is determined by the outcome of a random experiment.

• Discrete Random Variable: Takes on countable values (e.g., number of heads in coin tosses).

• Continuous Random Variable: Takes on any value within a range (e.g., height, weight).

Formula for Probability:

Probability Distributions

Students will study important probability distributions, including the binomial and normal distributions.

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

• Normal Distribution: A continuous distribution characterized by its mean () and standard deviation ().

Binomial Probability Formula:

Normal Distribution Formula:

Statistical Inference

Statistical inference involves drawing conclusions about populations based on sample data. Key techniques include estimation and hypothesis testing.

• Estimation: Using sample statistics to estimate population parameters.

• Hypothesis Testing: Assessing evidence to support or refute a claim about a population.

Confidence Interval Formula (for mean):

Hypothesis Test Steps:

1. State the null and alternative hypotheses.

2. Choose a significance level ().

3. Calculate the test statistic.

4. Determine the p-value or critical value.

5. Draw a conclusion.

Regression and Correlation

Students will analyze relationships between variables using regression and correlation techniques.

• Regression: Modeling the relationship between a dependent variable and one or more independent variables.

• Correlation: Measuring the strength and direction of the linear relationship between two variables.

Correlation Coefficient Formula:

Grading and Assessment

Grade Calculation

Grades are based on homework, quizzes, tests, and a final exam. The weighted breakdown is as follows:

Letter grades are assigned according to the following scale:

Academic Integrity and Student Conduct

Expectations

• Students must adhere to the university's code of conduct, avoiding academic dishonesty such as cheating and plagiarism.

• Integrity is especially important in statistics, as statistical methods inform real-world decisions.

• Students are encouraged to seek help and use resources appropriately.

Accessibility Services

• Students with disabilities should contact the Office of Student Accessibility Services for accommodations.

Attendance Policy

Attendance will not be taken daily, but students are expected to participate and keep up with course materials and assignments.

Technology Requirements

• Use of Canvas, Pearson MyLab, and StatCrunch for assignments and exams.

• Calculators and statistical software may be required for some activities.

Summary Table: Major Statistical Concepts

Conclusion

This course equips students with foundational knowledge and skills in statistics and probability, preparing them for further study and practical application in various fields. Mastery of these concepts is essential for informed decision-making and critical analysis in academic, professional, and everyday contexts.