Course Overview

Introduction to Statistics I (MATH 1200)

This course provides a comprehensive introduction to the fundamental concepts of descriptive and inferential statistics, probability, and probability distributions. It is designed for students to develop statistical reasoning and proficiency in analyzing data using both manual and computer-based methods.

• Course Textbook: Introductory Statistics: Exploring the World Through Data by Robert Gould, Rebecca Wong, and Colleen Ryan (3rd Edition)

• Statistical Software: StatCrunch (accessed via Blackboard)

• Credits: 3

• Prerequisites: C- or higher in MATH 0988/0989, completion of MATH 1010/1011, or higher placement

Course Objectives

Key Learning Goals

• Describe and summarize data using numerical measures, tables, and graphs

• Analyze relationships between variables using data distributions, correlation, and regression

• Compute probabilities using probability rules and probability distributions

• Estimate population parameters and conduct hypothesis tests

• Utilize statistical software for data analysis and inference

Major Topics and Chapter Structure

Descriptive and Inferential Statistics

• Descriptive Statistics: Organizing, describing, summarizing, and displaying categorical and quantitative data

• Inferential Statistics: Drawing conclusions about populations based on sample data

Probability and Probability Distributions

• Understanding randomness and probability rules

• Modeling random events using normal and binomial distributions

Statistical Inference

• Constructing confidence intervals for population parameters

• Conducting hypothesis tests using significance levels and p-values

Regression and Correlation

• Describing the form, strength, and direction of relationships between two quantitative variables

• Finding the best-fit equation for linear trends

Course Schedule and Chapter Breakdown

Weekly Topics Overview

• Ch. 1: Introduction to Data (Classifying, storing, and organizing categorical data)

• Ch. 2: Picturing Variation with Graphs (Visualizing and summarizing numerical and categorical data)

• Ch. 3: Numerical Summaries of Center and Variation (Measures of center, variation, boxplots, z-scores, empirical rule)

• Ch. 4: Regression Analysis (Scatterplots, correlation, modeling linear trends)

• Ch. 5: Modeling Variation with Probability (Randomness, theoretical probabilities, associations in categorical variables)

• Ch. 6: Modeling Random Events (Normal and binomial models, probability distributions)

• Ch. 7: Survey Sampling and Inference (Survey methods, confidence intervals for proportions)

• Ch. 8: Hypothesis Testing for Population Proportions (Hypothesis testing steps, comparing proportions)

• Ch. 9: Inferring Population Means (Sample means, Central Limit Theorem, hypothesis testing for means)

Assessment and Grading

Course Requirements

• Homework: 10% (completed online via MyStatLab; multiple attempts allowed until due date)

• Tests: 60% (four in-class tests, lowest test grade may be replaced by final exam grade)

• Cumulative Final Exam: 30% (covers all course chapters)

Grading Scale

Final course grades are rounded to the nearest whole number (0.50 and above rounds up).

Academic Integrity and Policies

Academic Honesty

• Plagiarism and cheating are strictly prohibited and may result in a grade of "F" for the course.

• Unauthorized assistance, falsifying data, and other forms of academic misconduct are not tolerated.

Attendance and Engagement

• Regular attendance and active participation are expected.

• Excessive absences may impact course grades.

Support and Resources

Student Support Services

• Disability accommodations available through the Disabilities Office

• Library and tutoring resources provided for academic support

• Mental health and wellness counseling available

Summary of Key Statistical Concepts Covered

• Population vs. Sample: Understanding the difference between the entire group of interest (population) and a subset (sample).

• Descriptive Statistics: Measures of central tendency (mean, median, mode), measures of variation (range, variance, standard deviation), and graphical displays (histograms, boxplots).

• Probability: Basic probability rules, random variables, and probability models.

• Normal and Binomial Distributions: Properties, applications, and calculations involving these distributions.

• Statistical Inference: Confidence intervals and hypothesis testing for proportions and means.

• Regression and Correlation: Analyzing relationships between variables using scatterplots, correlation coefficients, and regression equations.

Example: Calculating a Z-Score

The z-score measures how many standard deviations a data point is from the mean. The formula is:

• X: The value of interest

• \mu: Population mean

• \sigma: Population standard deviation

Example: Confidence Interval for a Population Mean

A confidence interval estimates the range in which a population parameter lies, based on sample data. For a population mean, the formula is:

• \bar{x}: Sample mean

• z^*: Critical value from the standard normal distribution

• \sigma: Population standard deviation

• n: Sample size

Example: Binomial Probability Formula

The probability of exactly k successes in n independent Bernoulli trials (each with probability p of success) is given by:

• n: Number of trials

• k: Number of successes

• p: Probability of success on a single trial

Additional info:

• This syllabus outlines the structure and expectations for a college-level introductory statistics course, covering all major topics listed in the provided chapter titles.

• Students are expected to use statistical software for data analysis and to adhere to academic integrity policies.