Porterville College MATH 122: Introduction to Probability and Statistics – Syllabus and Course Structure Study Guide

Course Overview

Introduction to Probability and Statistics

This course provides a comprehensive introduction to both descriptive and inferential statistics, focusing on the fundamental concepts, methods, and applications relevant to college-level statistics. The curriculum covers data analysis, probability theory, statistical distributions, hypothesis testing, regression, and advanced topics such as ANOVA and non-parametric statistics.

• Descriptive Statistics: Includes data classification, graphical representation, and measures of central tendency and variation.

• Inferential Statistics: Covers probability, probability distributions, hypothesis testing, estimation, and regression analysis.

• Advanced Topics: ANOVA, chi-square tests, and non-parametric methods.

Course Structure and Assessment

Homework, Quizzes, and Final Exam

The course is structured around regular homework assignments, quizzes, and a comprehensive final exam. All assignments are managed through MyMathLab, an online platform integrated with Canvas.

• Homework (50%): Assigned for each chapter; late submissions incur a 15% penalty.

• Quizzes (30%): Four quizzes, each covering multiple chapters; unlimited attempts, best score recorded, late penalty applies.

• Final Exam (20%): Comprehensive, two attempts allowed, 2-hour time limit per attempt. Minimum 70% course grade required to qualify.

Grading Scale:

• 90-100%: A

• 80-89.9%: B

• 70-79.9%: C

• 60-69.9%: D

• <60%: F

Course Topics and Weekly Schedule

Chapter Breakdown and Key Concepts

The course follows a logical progression through the major topics in statistics, as outlined below:

• Chapter 1: Introduction to Statistics

• Chapter 2: Exploring Data with Tables and Graphs

• Chapter 3: Describing, Exploring, and Comparing Data

• Chapter 4: Probability

• Chapter 5: Discrete Probability Distributions

• Chapter 6: Normal Probability Distributions

• Chapter 7: Estimating Parameters and Determining Sample Sizes

• Chapter 8: Hypothesis Testing

• Chapter 9: Inferences from Two Samples

• Chapter 10: Correlation and Regression

• Chapter 11: Chi-Square and Analysis of Variance

• Chapter 12: Non-parametric Statistics and Conducting a Study (Additional info: Non-parametric statistics are methods that do not assume a specific distribution for the data.)

Sample Weekly Schedule

Week	Homework Due	Quiz Due
1	Chapter 1 HW - 1/25
2	Chapter 2 HW - 2/1
3	Chapter 3 HW - 2/8	Quiz 1 (Ch. 1-3) - 2/8
4	Chapter 4 HW
5	Chapter 4 HW - 2/22
6	Chapter 5 HW - 3/1	Quiz 2 (Ch. 4-5) - 3/1
7	Chapter 6 HW
8	Chapter 6 HW - 3/15
9	Spring Break	Spring Break
10	Chapter 7 HW - 3/29	Quiz 3 (Ch. 6-7) - 3/29
11	Chapter 8
12	Chapter 8 HW - 4/12
13	Chapter 9 HW - 4/19	Quiz 4 (Ch. 8-9) - 4/19
14	Chapter 10 HW
15	Chapter 10 HW - 5/3
16	Chapter 11, 12 HW - 5/10
17	Final Exam - To be announced

Student Learning Outcomes

Core Competencies

• Data Classification and Descriptive Measures: Understand levels of measurement, graphical data representation, and calculation of central tendency and variation.

• Hypothesis Testing: Identify and conduct appropriate tests using technology; interpret results in real-world contexts.

• ANOVA and Regression: Interpret analysis of variance and linear regression outputs.

• Probability and Distributions: Calculate, analyze, and interpret probabilities, including discrete and continuous distributions, mean, variance, significance levels, and p-values.

Key Statistical Concepts (Expanded Academic Context)

Descriptive Statistics

Descriptive statistics summarize and organize data using tables, graphs, and numerical measures.

• Levels of Measurement: Nominal, ordinal, interval, and ratio scales.

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

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

• Graphical Representations: Histograms, bar charts, pie charts, boxplots.

Example: Calculating the mean and standard deviation for a set of exam scores.

Formula for Sample Mean:

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

Formula for Sample Standard Deviation:

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

Probability and Probability Distributions

Probability quantifies the likelihood of events, and probability distributions describe how probabilities are distributed over possible outcomes.

• Basic Probability: $P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

• Bayes' Theorem: Used to update probabilities based on new information.

• Discrete Distributions: Binomial, Poisson.

• Continuous Distributions: Normal distribution.

Example: Calculating the probability of getting exactly 3 heads in 5 coin tosses using the binomial distribution.

Binomial Probability Formula:

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

Inferential Statistics: Estimation and Hypothesis Testing

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

• Estimation: Point estimates and confidence intervals for population parameters.

• Hypothesis Testing: Steps include stating hypotheses, selecting significance level, calculating test statistic, and interpreting p-value.

Example: Testing whether the average height of students differs from a national average.

Confidence Interval Formula for Mean (when population standard deviation is known):

$\bar{x} \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

Test Statistic for One-Sample z-Test:

$z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$

Regression, ANOVA, and Chi-Square Tests

These advanced methods analyze relationships between variables and test for differences among groups.

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

• ANOVA (Analysis of Variance): Tests for differences among means of three or more groups.

• Chi-Square Tests: Test for independence and goodness of fit in categorical data.

Example: Using regression to predict exam scores based on study hours.

Regression Equation:

$y = a + bx$

ANOVA F-Test Formula:

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

Chi-Square Test Statistic:

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

Course Policies and Support

Academic Integrity and Student Support

• Professional Conduct: Cheating is not tolerated; violations are reported to the Dean.

• Support Services: Learning Resource Center, Disability Resource Center, Veterans Resource Center, and campus safety protocols are available to all students.

• Accommodations: Students with documented learning challenges should contact the instructor and Disability Resource Center early in the semester.

Important Dates

• 01/30: Last day to drop a course and qualify for a refund

• 02/01: Last day to add a class

• 02/01: Last day to drop a course and not have it appear on the transcript

• 03/27: Last day to drop a course without a letter penalty and receive a “W”

Summary Table: Course Components

Component	Weight	Details
Homework	50%	Assigned per chapter, late penalty applies
Quizzes	30%	Four quizzes, unlimited attempts, best score recorded
Final Exam	20%	Comprehensive, two attempts, 2-hour limit per attempt

Additional info: The syllabus covers all major statistics topics listed in the standard college curriculum, including descriptive statistics, probability, distributions, hypothesis testing, regression, ANOVA, and chi-square tests. Non-parametric statistics and study design are also included, providing a broad foundation for further study or application in various fields.