Elementary Statistics – Course Syllabus and Study Guide

Elementary Statistics – Course Syllabus and Study Guide

Course Overview

This course provides an introduction to statistics, focusing on fundamental concepts such as the normal distribution, statistical inference, and the use of probability in data analysis. Emphasis is placed on real-world applications, including the interpretation of data, probability, hypothesis testing, and confidence intervals. The course is suitable for students in various fields, including social sciences, business, and technology.

• Instructor: Frank Van Valen

• Course Number: MAT 123 02

• Semester: Fall 2025

• Credit Hours: 3

Key Learning Objectives

• Organize data and construct basic displays for presenting data.

• Identify symbolic notations used to represent statistics and parameters.

• Calculate measures of center, variation, and relative standing.

• Identify different levels of correlation.

• Construct the linear regression equation.

• Calculate the sum of squares.

• Calculate probability using basic rules of probability.

• Distinguish normal distribution from other distributions.

• Construct sampling distributions from sample means.

• Construct confidence intervals based on a variety of conditions.

• Determine conclusions when conducting hypothesis tests and ANOVA.

Course Structure

Textbook and Materials

• Required Textbook: Elementary Statistics, 9th Edition by Neil A. Weiss (Pearson).

• MyLab Statistics: Access to MyLab Statistics is required for online homework and quizzes.

• Calculator: A graphing calculator is required for class exams (TI-84 is recommended).

• Course Materials: Course materials can be purchased from the BCC Bookstore or online at MyLab.

Course Schedule

The course is organized into weekly modules, each focusing on specific chapters and topics. The schedule includes homework assignments, quizzes, and exams.

Week	Topics	Assignments	Exams
1-5	Introduction to Statistics, Organizing and Graphing Data, Descriptive Measures, Correlation and Regression	Homework 1-4	Test 1 (Chapters 1-4)
6-9	Probability and Random Variables, Normal Distribution, Sampling Distribution of the Sample Mean	Homework 5-7	Test 2 (Chapters 5-7)
10-15	Confidence Interval Estimates, Hypothesis Testing, ANOVA	Homework 8-11	Test 3 (Chapters 8, 9, 10, 13)

Grading Policy

• MyLab Statistics Homework: 30% (300 points)

• MyLab Statistics Quizzes: 10% (100 points)

• Class Exams: 60% (600 points)

Grading Scale:

Grade	Range (%)
A	93-100
A-	90-92
B+	87-89
B	83-86
B-	80-82
C+	77-79
C	73-76
C-	70-72
D+	67-69
D	63-66
D-	60-62
F	Below 60

Major Topics and Subtopics

1. Introduction to Statistics

Statistics is the science of collecting, organizing, analyzing, and interpreting data to make informed decisions. This section introduces the basic terminology and concepts used throughout the course.

• Population vs. Sample: A population is the entire group of individuals or items of interest, while a sample is a subset of the population used for analysis.

• Descriptive vs. Inferential Statistics: Descriptive statistics summarize data, while inferential statistics use data from a sample to make generalizations about a population.

• Example: Surveying 100 students (sample) to estimate the average study time of all students (population).

2. Organizing and Graphing Data

Effective data organization and visualization are essential for understanding and communicating statistical information.

• Frequency Distributions: Tables that display the frequency of various outcomes in a sample.

• Graphs: Common types include bar graphs, histograms, pie charts, and scatterplots.

• Example: Creating a histogram to show the distribution of exam scores.

3. Descriptive Measures and Relative Standing

Descriptive statistics provide numerical summaries of data, including measures of center and spread.

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

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

• Percentiles and Z-scores: Indicate the relative standing of a value within a data set.

• Formulas:

  • 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: $s = \sqrt{s^2}$

  • Z-score: $z = \frac{x - \mu}{\sigma}$

• Example: Calculating the mean and standard deviation of test scores.

4. Correlation and Regression

Correlation and regression are used to analyze relationships between two quantitative variables.

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

• Regression Equation: Predicts the value of one variable based on another.

• Formulas:

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

  • Regression Line: $y = a + bx$

  • Slope: $b = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$

  • Intercept: $a = \bar{y} - b\bar{x}$

• Example: Using regression to predict final exam scores based on midterm scores.

5. Probability and Random Variables

Probability quantifies the likelihood of events, and random variables represent outcomes of random processes.

• Probability Rules: The probability of an event ranges from 0 to 1.

• Random Variable: A variable whose value is determined by the outcome of a random event.

• Example: Flipping a coin and defining X = 1 if heads, X = 0 if tails.

6. Normal Distribution

The normal distribution is a symmetric, bell-shaped distribution that is fundamental in statistics.

• Properties: Mean = median = mode; defined by mean ($\mu$) and standard deviation ($\sigma$).

• Standard Normal Distribution: A normal distribution with $\mu = 0$ and $\sigma = 1$.

• Empirical Rule: Approximately 68% of data within 1$\sigma$, 95% within 2$\sigma$, 99.7% within 3$\sigma$.

• Formula: $z = \frac{x - \mu}{\sigma}$

• Example: Calculating the probability that a value falls within a certain range.

7. Sampling Distributions

Sampling distributions describe the distribution of sample statistics over repeated sampling from a population.

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

• Standard Error: $SE = \frac{\sigma}{\sqrt{n}}$

• Example: Estimating the mean height of students using a sample.

8. Confidence Intervals

Confidence intervals provide a range of values within which a population parameter is likely to fall.

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

• Formula for Mean (unknown $\sigma$): $\bar{x} \pm t^* \frac{s}{\sqrt{n}}$

• Example: Constructing a 95% confidence interval for the average test score.

9. Hypothesis Testing

Hypothesis testing is a formal procedure for testing claims about population parameters using sample data.

• Null Hypothesis ($H_0$): The default assumption (e.g., no difference or effect).

• Alternative Hypothesis ($H_a$): The claim to be tested.

• Test Statistic: $z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}}$

• p-value: The probability of observing a result as extreme as, or more extreme than, the observed result under $H_0$.

• Example: Testing whether a new teaching method improves average scores.

10. ANOVA (Analysis of Variance)

ANOVA is used to compare means across multiple groups to determine if at least one group mean is different.

• F-statistic: Ratio of variance between groups to variance within groups.

• Formula: $F = \frac{\text{Mean Square Between}}{\text{Mean Square Within}}$

• Example: Comparing test scores across different teaching methods.

Course Policies and Resources

Attendance and Participation

• Regular attendance and participation in both in-person and online activities are required.

• Zoom and MyLab Statistics are used for instruction and assessment.

Homework and Exams

• Homework is assigned weekly and completed in MyLab Statistics.

• Quizzes and exams are scheduled throughout the semester; see the course calendar for details.

• There is no final exam; the course is assessed through three major exams.

Support Services

• Disability Services: Accommodations are available through the Disability Resource Center.

• Tutoring: Free tutoring is available at the Jonathan Edwards Library and online via Zoom.

Important Dates

• Drop/Add Period: Sep 2 – Sep 9

• Class Exams: Sep 30, Oct 28, Dec 9 (5:30 – 7:00 PM, Zoom)

• Course Withdrawal Deadline: Dec 4

Additional info: The course schedule, grading policy, and support services are designed to ensure student success in mastering the fundamentals of statistics. Students are encouraged to utilize all available resources, including office hours, tutoring, and online materials.