Introductory Statistics Course Syllabus and Learning Outcomes

Course Overview

Course Description

This course introduces students to the fundamental concepts and procedures of descriptive statistics, elementary probability theory, and inferential statistics. Topics include data summarization, computation and interpretation of descriptive statistics, probability distributions (binomial, normal, T, Chi-square, F), confidence intervals, hypothesis testing, correlation, regression, ANOVA, and tests for independence. Statistical thinking is developed through applications across various disciplines, with integrated use of calculators and statistical software.

Course Structure and Requirements

Participation and Grading

• Learning Modules: Each module includes video lectures, guided notes, quizzes, calculator tutorials, and discussion board posts. Completion by due dates is required.

• Graded Assignments:

  • Online Homework (9%)

  • Welcome Module Assignments (2%)

  • Knowledge Check Quizzes (5%)

  • Discussion Board Posts (9%)

  • Project (5%)

  • Exams (50%)

  • Final Exam (20%)

• Final Grades: A: 90-100%, B: 80-89.99%, C: 70-79.99%, D: 60-69.99%, F: below 60%

• Calculator Requirement: TI-83 Plus / TI-84 Plus is required; no cell phones or shared calculators allowed.

• Online Exams: Proctored via Honorlock; webcam and microphone required.

Student Learning Outcomes (SLOs)

• Analyze data sets and present information using tables, graphs, and statistical calculations.

• Use estimation strategies to make inferences about population characteristics (mean, proportion, variation).

• Apply appropriate hypothesis tests to reach conclusions about population parameters.

Entry Level Skills

• Solve linear and non-linear equations.

• Simplify numerical expressions (order of operations).

• Plot and interpret points on Cartesian coordinate system.

• Plot linear equations using slope-intercept method.

• Translate verbal problems into mathematical forms.

• Solve absolute value equations and inequalities.

• Evaluate exponential functions and expressions with sigma notation.

• Solve literal equations for designated variables.

• Write equations of lines and express solutions using interval notation.

Exit Level Skills

• Statistically describe mathematically sets of data.

• Apply basic laws of probability.

• Formulate probability distributions.

• Formulate and test null hypotheses for one, two, or more populations.

• Make point and interval estimates of parameters.

• Identify correlation and linear relationships between variables.

• Use statistical functions on a calculator.

• Critically evaluate statistical claims.

Course Objectives

• Summarize and interpret data.

• Identify standard methods of obtaining data and their advantages/disadvantages.

• Analyze and interpret graphical presentations of data.

• Find and interpret measures of central tendency and dispersion.

• Solve basic probability problems.

• Analyze and interpret probability distributions, including binomial and normal distributions. Calculate mean and variance for both discrete and continuous distributions.

• Distinguish between sample and population distributions; understand the Central Limit Theorem.

• Formulate, test, and interpret statistical significance of hypotheses about one-population parameters, including p-value, Type I and Type II errors.

• Formulate, test, and interpret statistical significance of hypotheses about differences between means and proportions of two populations.

• Formulate and analyze point and confidence interval estimates for differences between means and proportions of two populations.

• Formulate, test, and interpret hypotheses of independence between two variables.

• Formulate, test, and interpret equality of three or more population means using ANOVA.

• Find and interpret correlation between two variables.

• Find regression lines, interpret values in context, and evaluate goodness of fit.

• Use calculators/statistical software to implement objectives.

• Apply statistical techniques to data from business, social sciences, psychology, life sciences, health science, and education.

Key Statistical Concepts (Expanded Academic Context)

Descriptive Statistics

Descriptive statistics involve methods for summarizing and organizing data. Common tools include:

• Measures of Central Tendency: Mean, median, mode

• Measures of Dispersion: Range, variance, standard deviation

• Graphical Representations: Histograms, bar charts, box plots

Example:

Given a data set of exam scores, calculate the mean and standard deviation to describe the average performance and variability.

Probability Theory

Probability theory provides the foundation for making inferences about populations based on sample data.

• Classical Probability: Based on equally likely outcomes

• Probability Distributions: Binomial, normal, T, Chi-square, F

Formula Example:

Binomial probability formula:

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

Inferential Statistics

Inferential statistics allow us to make predictions or decisions about populations based on sample data.

• Confidence Intervals: Estimate population parameters with a specified level of confidence

• Hypothesis Testing: Test claims about population parameters

• Types of Errors: Type I (false positive), Type II (false negative)

Formula Example:

Confidence interval for a population mean:

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

Correlation and Regression

Correlation measures the strength and direction of a linear relationship between two variables. Regression models the relationship and allows prediction.

• Correlation Coefficient: $r$ measures linear association

• Regression Line: $y = a + bx$

Formula Example:

Correlation coefficient:

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

ANOVA (Analysis of Variance)

ANOVA is used to test for equality of means across three or more groups.

• Null Hypothesis: All group means are equal

• F-statistic: Used to determine statistical significance

Formula Example:

F-statistic:

$F = \frac{\text{Between-group variance}}{\text{Within-group variance}}$

Grading Table

Assignment	Weight (%)
Online Homework	9
Welcome Module Assignments	2
Knowledge Check Quizzes	5
Discussion Board Posts	9
Project	5
Exams	50
Final Exam	20

Final Notes

• Academic honesty is strictly enforced; violations result in a grade of 0 for the assignment/exam.

• Accommodations for disabilities are available through the Center for Students with Disabilities.

• Participation in discussion boards and completion of modules is required to remain enrolled.

Additional info: Expanded academic context and formulas were added to make the study notes self-contained and suitable for exam preparation.