Statistics Syllabus and Study Guide: Stat C100 & Math 54C (Santa Monica College)

Statistics Syllabus and Study Guide

Introduction

This study guide summarizes the key topics, objectives, and expectations for Stat C100 (Elementary Statistics) and Math 54C (Statistics & Support) at Santa Monica College. The guide is based on the official course syllabus and is designed to help students understand the structure, content, and learning outcomes of the course.

Course Overview

Stat C100: Elementary Statistics

Stat C100 introduces students to the fundamental concepts and methods of statistics, including data collection, analysis, and interpretation. The course covers descriptive and inferential statistics, probability distributions, hypothesis testing, and regression analysis.

• Units: 4

• Prerequisite: Completion of Math 20, Math 18, Math 49, Math 50, or equivalent

• Textbook: Sullivan III, Michael; Statistics: Informed Decisions Using Data, 7th Edition

• Access: MyLab Statistics (Pearson Education)

Math 54C: Statistics Support Course

This support course is designed to reinforce prerequisite skills and provide additional practice in statistics. It is intended for students who are concurrently enrolled in Stat C100 and need extra support with mathematical concepts and problem-solving strategies.

Key Topics and Learning Objectives

Descriptive Statistics

Descriptive statistics involve methods for summarizing and organizing data. This includes the use of tables, graphs, and numerical measures to describe the main features of a dataset.

• Summarize and interpret data using graphical and numerical methods

• Calculate measures of central tendency (mean, median, mode)

• Calculate measures of dispersion (range, variance, standard deviation)

• Identify and interpret outliers and the shape of data distributions

Probability and Probability Distributions

Probability theory provides the foundation for inferential statistics. Students learn to calculate probabilities and work with discrete and continuous probability distributions.

• Basic probability rules and concepts

• Discrete distributions: Binomial, Poisson

• Continuous distributions: Normal distribution

• Calculate mean and variance for both discrete and continuous distributions

Inferential Statistics

Inferential statistics allow us to make conclusions about populations based on sample data. This includes estimation, confidence intervals, and hypothesis testing.

• Point and interval estimation for population parameters

• Construct and interpret confidence intervals for means and proportions

• Hypothesis testing for one and two populations

• Type I and Type II errors in hypothesis testing

• Use appropriate tests (e.g., t-test, chi-square test, ANOVA) based on data type and research question

Regression and Correlation

Regression and correlation analysis are used to examine relationships between variables.

• Calculate and interpret correlation coefficients

• Fit and interpret simple linear regression models

• Use regression models to make predictions

Statistical Reasoning and Communication

Students are expected to develop the ability to interpret statistical results, communicate findings, and apply statistical reasoning to real-world problems.

• Translate verbal problems into mathematical form

• Interpret statistical results in context

• Evaluate the appropriateness of statistical methods for different scenarios

Key Formulas and Equations

• Mean: $\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i$

• Variance: $s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2$

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

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

• Normal Distribution (Z-score): $z = \frac{x - \mu}{\sigma}$

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

• Simple Linear Regression: $y = a + bx$

Course Requirements and Evaluation

• Quizzes: 5%

• Homework: 21%

• Participation/Discussion: 4%

• Exams: 50%

• Final Exam: 20%

Grading Formula (Stat C100):

• $\text{UTS} = 20\%[\text{QUIZ}] + 5\%[\text{HWQ}] + 5\%[\text{PT}] + 42\%[\text{UTE}] + 28\%[\text{UTF}]$

• A: 90% or higher, B: 80-89%, C: 70-79%, D: 60-69%, F: below 60%

Exit Skills and Course Objectives

Stat C100 Exit Skills

• Summarize and interpret data

• Identify methods of data collection and their advantages/disadvantages

• Graphical representation and analysis of data

• Calculate and interpret central tendency and dispersion

• Probability and probability distributions

• Inferential statistics: estimation, confidence intervals, hypothesis testing

• Regression and correlation analysis

• Interpret statistical results in context

Math 54C Course Objectives

• Graph fractions, decimals, and signed numbers

• Evaluate and simplify algebraic expressions

• Convert between fractions, decimals, and percentages

• Use calculators and interpret results

• Apply effective learning strategies for success in statistics

Sample Course Schedule (First Weeks)

Day	Topics
9/2	Introduction, Syllabus, Randomness, Sampling, Experimental Design
9/4	Simple Random Sampling, Sampling Methods, Design of Experiments
9/9	Organizing and Displaying Data, Misrepresentations of Data
9/11	Real Numbers, Fractions, Decimals, Percents, Rounding
9/16	Measures of Central Tendency, Calculators, Grouped Data
9/23	Measures of Position, Outliers

Additional Information

• Office Hours: Listed in the syllabus for in-person and online support

• Math Lab: Additional help available in MSB 107 and MSB 108

• Accessibility and Support: Resources for students with disabilities, emotional support, and equitable learning environment are provided

• Academic Integrity: Cheating and plagiarism are strictly prohibited

Example Application: A student collects data on study hours and exam scores, uses a scatterplot to visualize the relationship, calculates the correlation coefficient, and fits a regression line to predict exam scores based on study hours.