Introduction to Statistics – Syllabus and Study Guide

Course Overview

Introduction

This course provides a foundational understanding of statistical methods and their applications. Students will learn to organize and analyze data, interpret statistical results, and apply statistical reasoning to real-world problems. The course covers both descriptive and inferential statistics, including probability, hypothesis testing, and correlation analysis.

• Course Code: Math 146 Hybrid

• Credits: 5

• Format: Online Asynchronous

• Prerequisites: MATH 087 or MATH 097 (minimum grade 2.5), ENGL& 101

Course Materials

Required Textbook and Platforms

• Textbook: Fundamentals of Statistics, 6th Edition, Sullivan, Pearson

• Online Platform: MyStatLab (for homework, quizzes, and tests)

• Testing Platform: Honorlock (for proctored exams)

• Calculator: Scientific calculator required

Students may purchase or access the textbook and MyStatLab online. Honorlock is used for supervised online tests and requires a webcam.

Assignments and Grading

Grading Structure

Grades are based on homework, quizzes, and supervised tests. The grading breakdown is as follows:

Assignment	Weight	Quantity
Regular Online Homework	20% of grade	One assignment for each section of the text
12 Online Chapter Quizzes	30% of grade	One for each chapter of the text
2 Test Prep Homework Sets	5%+5%=10% of grade	One for each test (Test 1: Chapters 1-6, Test 2: Chapters 7-12)
2 Proctored/Supervised Tests	20%+20%=40% of grade	Test 1: Chapters 1-6, Test 2: Chapters 7-12

Grade Conversion Table:

Percentage	Grade
94-100	4.0
90-93	3.7
88-89	3.5
86-87	3.3
83-85	3.0
80-82	2.7
78-79	2.3
76-77	2.0
74-75	1.7
70-73	1.0
64-69	0.0

Learning Objectives

Key Skills and Knowledge

• Distinguish between quantitative and categorical data.

• Display categorical data using frequency tables and two-way tables.

• Construct appropriate graphical displays of quantitative and categorical data by hand and using technology.

• Compute and interpret summary statistics for quantitative variables.

• Perform computations using the Normal model.

• Interpret and compute scatterplots of bivariate quantitative data.

• Compute and interpret the correlation of two quantitative variables.

• Construct, compute, and interpret a linear regression model on two quantitative variables.

• Appropriately use the Normal model.

• Use random numbers to perform a simulation.

• Appropriately use terms related to sample surveys, experiments, and observational studies.

• Perform computations with probability models, including the binomial model.

• Compute the expected value and standard deviation of a random variable.

• Perform computations and interpret a confidence interval and/or hypothesis test in situations involving: a one proportion, two proportions, one mean, two means.

• When appropriate, use chi-square methods to perform a goodness-of-fit test, tests of homogeneity, and tests of independence.

Major Topics and Subtopics

1. Types of Data

Statistics involves the classification and analysis of different types of data. Understanding the distinction between quantitative and categorical data is fundamental.

• Quantitative Data: Numerical values representing counts or measurements (e.g., height, weight).

• Categorical Data: Data sorted into categories or groups (e.g., gender, color).

• Example: Survey responses about favorite color (categorical) and age (quantitative).

2. Data Organization and Display

Organizing data into tables and graphical displays helps reveal patterns and relationships.

• Frequency Tables: Summarize categorical data by counting occurrences.

• Two-Way Tables: Show relationships between two categorical variables.

• Graphical Displays: Histograms, bar charts, scatterplots, and boxplots.

• Example: A histogram showing the distribution of exam scores.

3. Descriptive Statistics

Descriptive statistics summarize and describe the main features of a dataset.

• Measures of Central Tendency: Mean, median, mode.

• Measures of Spread: Range, variance, standard deviation.

• Formula for Mean:

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

• Formula for Standard Deviation:

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

4. Probability and Probability Models

Probability models are used to quantify uncertainty and predict outcomes.

• Probability: The likelihood of an event occurring, ranging from 0 to 1.

• Binomial Model: Used for experiments with two possible outcomes (success/failure).

• Formula for Binomial Probability:

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

• Expected Value: The mean of a probability distribution.

• Formula for Expected Value:

$E[X] = \sum_{i} x_i P(x_i)$

5. Inferential Statistics

Inferential statistics allow us to make conclusions about populations based on sample data.

• Confidence Interval: Range of values likely to contain the population parameter.

• Formula for Confidence Interval (mean):

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

• Hypothesis Testing: Procedure to test claims about a population.

• Chi-Square Tests: Used for categorical data to test independence or goodness-of-fit.

• Formula for Chi-Square Statistic:

$\chi^2 = \sum \frac{(O - E)^2}{E}$

6. Regression and Correlation

Regression and correlation measure and model relationships between variables.

• Correlation Coefficient (r): Measures strength and direction of linear relationship.

• Formula for Correlation:

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

• Linear Regression: Models the relationship between two quantitative variables.

• Regression Equation:

$y = a + bx$

• Example: Predicting exam scores based on hours studied.

Course Policies and Support

Academic Integrity

• All work must be your own. Plagiarism and cheating are strictly prohibited.

• Violations may result in disciplinary action.

Support Services

• Learning Support Center: Tutoring for math, writing, and other classes.

• TRiO Student Support Services: Support for first-generation college students.

• e-Tutoring: Online tutoring for math and writing.

• STEM Study Room: Free drop-in tutoring for STEM subjects.

• Technology Help: Assistance with Canvas, CTC Link, and campus computer labs.

Emergency Preparedness

• Sign up for campus emergency alerts via the Triton Alert System.

AI Statement

• Use of artificial intelligence engines or software to produce work for this class is prohibited and considered a violation of the Academic Conduct Policy.

Important Dates

• Course deadlines and exam dates are listed in the Canvas calendar and syllabus.

• Final deadline for all coursework: December 12 at 11:59 pm.

Additional info:

• Some details about the course structure, such as the number of assignments and the use of online platforms, were inferred from the syllabus and standard practices in college statistics courses.