Elementary Statistical Methods – Course Syllabus and Study Guide

Course Overview

This syllabus outlines the structure, policies, and content for the course Elementary Statistical Methods (MATH-1342). The course introduces foundational concepts in statistics, including data collection, descriptive and inferential statistics, probability, and hypothesis testing. The course is designed for college students seeking a comprehensive introduction to statistics.

Course Topics

• Statistical & Critical Thinking

• Types of Data

• Collecting Sample Data

• Frequency Distributions

• Histograms

• Graphs That Enlighten and Graphs That Deceive

• Measures of Center

• Measures of Variation

• Measures of Relative Standing and Box Plots

• Basic Concepts of Probability

• Addition Rule

• Multiplication Rule: Basics

• Multiplication Rule: Complements and Conditional Probability

• Counting

• Probability Distributions

• Binomial Probability Distributions

• Parameters for Binomial Distribution

• The Standard Normal Distribution

• Applications of Normal Distributions

• Sampling Distributions and Estimators

• The Central Limit Theorem

• Assessing Normality

• Normal as Approximation to Binomial

• Estimating a Population Proportion

• Estimating a Population Mean

• Basics of Hypothesis Testing

• Testing a Claim about a Proportion

• Testing a Claim about a Mean

• Two Proportions

• Two Means: Independent Samples

• Correlation

• Regression

• Goodness of Fit

• Analysis of Variance

• Contingency Tables

Learning Outcomes

• Explain the use of data collection and statistics as tools to reach reasonable conclusions.

• Recognize, examine, and interpret the basic principles of describing and presenting data.

• Compute and interpret empirical and theoretical probabilities using the rules of probabilities and combinatorics.

• Explain the role of probability in statistics.

• Examine, analyze, and compare various sampling distributions for both discrete and continuous random variables.

• Describe and compute confidence intervals.

• Solve linear regression and correlation problems.

• Perform hypothesis testing using statistical methods.

Key Concepts and Definitions

Statistical & Critical Thinking

• Statistics is the science of collecting, organizing, analyzing, and interpreting data to make decisions.

• Critical thinking in statistics involves questioning data sources, methods, and conclusions.

Types of Data

• Qualitative (Categorical) Data: Non-numeric data that describes categories or groups (e.g., colors, names).

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

• Discrete Data: Countable values (e.g., number of students).

• Continuous Data: Measurable values within a range (e.g., temperature).

Describing Data with Tables and Graphs

• Frequency Distributions: Tables that show how data are distributed across categories or intervals.

• Histograms: Bar graphs representing the frequency of data within intervals.

• Box Plots: Visual summaries showing the median, quartiles, and outliers of a dataset.

Describing Data Numerically

• Measures of Center: Mean, median, and mode.

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

• Measures of Relative Standing: Percentiles, quartiles, and z-scores.

Probability

• Probability: The likelihood of an event occurring, expressed as a number between 0 and 1.

• Basic Rules: Addition and multiplication rules, complements, and conditional probability.

• Counting Principles: Factorials, permutations, and combinations.

Probability Distributions

• Discrete Random Variables: Variables that take on countable values.

• Binomial Distribution: Probability distribution for a fixed number of independent trials, each with two possible outcomes.

• Normal Distribution: Continuous, symmetric, bell-shaped distribution described by mean ($\mu$) and standard deviation ($\sigma$).

Sampling Distributions & Confidence Intervals

• Sampling Distribution: The probability distribution of a statistic based on a random sample.

• Central Limit Theorem: For large samples, the sampling distribution of the sample mean is approximately normal, regardless of the population distribution.

• Confidence Interval: An interval estimate of a population parameter, calculated as:

$\text{Confidence Interval} = \bar{x} \pm z^* \left(\frac{\sigma}{\sqrt{n}}\right)$

Hypothesis Testing

• Null Hypothesis ($H_0$): The statement being tested, usually a statement of no effect or no difference.

• Alternative Hypothesis ($H_a$): The statement we want to test for evidence in favor of.

• Test Statistic: A value calculated from sample data used to decide whether to reject $H_0$.

• p-value: The probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming $H_0$ is true.

Correlation and Regression

• Correlation: Measures the strength and direction of a linear relationship between two variables (correlation coefficient $r$).

• Regression: Predicts the value of one variable based on another using the regression equation:

$\hat{y} = a + bx$

Chi-Square Tests & ANOVA

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

• Analysis of Variance (ANOVA): Compares means across multiple groups to test for significant differences.

Grading Scale

Percentage	Grade
90 – 100%	A
80 – 89%	B
70 – 79%	C
60 – 69%	D
< 60%	F

Evaluation Components

Component	Percentage
Quizzes	10%
Homework	10%
Exam 1	10%
Midterm Exam (Exam 2)	20%
Exam 3	10%
Final Exam (Exam 4)	25%
Projects	15%
Discussions	5%

Additional info:

• This syllabus provides a comprehensive overview of the course structure, expectations, and academic content for a college-level statistics course. It covers all major topics relevant to introductory statistics, including probability, distributions, hypothesis testing, and regression.

• Students are expected to engage in critical thinking, apply statistical methods, and interpret results in context.