STA 2023: Statistical Methods – Syllabus and Study Guide Overview

Course Overview

Introduction to Statistical Methods

This course, STA 2023, provides a comprehensive introduction to statistical methods for business and economics. Students will learn to collect, organize, summarize, and interpret data using both descriptive and inferential statistical tools. The course emphasizes practical applications, problem-solving, and data-driven decision making.

• Descriptive Statistics: Visualizing and summarizing data.

• Inferential Statistics: Estimating parameters and testing hypotheses.

• Probability: Understanding random processes and distributions.

• Regression: Modeling relationships between variables.

Course Structure and Assessment

Assignments and Exams

The course is organized into weekly assignments, interactive activities, and four major exams. Students are expected to spend 8-10 hours per week studying and completing coursework.

• Exams: Four exams (Exam 1-3 and Final), each covering specific chapters.

• Assignments: Homework, interactive assignments, and tutorials for each topic.

• Grading: Exams and assignments each contribute 20% to the final grade.

Assessment	Percentage
Exam 1	20%
Exam 2	20%
Exam 3	20%
Final Exam	20%
Assignments	20%

Grade	Percentage
A	90–100
B+	85–89
B	80–84
B-	75–79
C+	70–74
C	60–69
D	50–59
F	0–49

Textbook and Materials

Required Textbook

• Title: Interactive Statistics

• Authors: Michael Sullivan III; George Woodbury

• Publisher: Pearson (2024)

• Chapters Covered: 1-10

Course Topics

Chapter-by-Chapter Breakdown

The course covers the following major topics, aligned with the textbook chapters:

• Ch. 1 – Data Collection: Methods for gathering data, distinguishing between populations and samples, and types of variables.

• Ch. 2 – Organizing and Summarizing Data: Visualizing qualitative and quantitative data using tables, bar graphs, pie charts, and histograms.

• Ch. 3 – Numerically Summarizing Data: Measures of central tendency (mean, median, mode), dispersion (range, variance, standard deviation), position (z-scores, percentiles, quartiles), and graphical summaries (boxplots).

• Ch. 4 – Describing the Relation between Two Variables: Scatter diagrams, correlation, and least-squares regression.

• Ch. 5 – Probability: Probability rules, addition and multiplication rules, independence, conditional probability.

• Ch. 6 – Discrete Probability Distributions: Discrete random variables, binomial distribution, expected value, and standard deviation.

• Ch. 7 – The Normal Probability Distribution: Properties and applications of the normal distribution, area under the curve.

• Ch. 8 – Sampling Distributions: Distribution of sample means and proportions, central limit theorem.

• Ch. 9 – Estimating the Value of a Parameter: Point and interval estimation for population mean and proportion, confidence intervals, sample size determination.

• Ch. 10 – Hypothesis Tests Regarding a Parameter: Null and alternative hypotheses, Type I and II errors, hypothesis tests for means and proportions.

Key Concepts and Definitions

Descriptive Statistics

• Mean: The arithmetic average of a set of values. $\text{Mean} = \frac{\sum x_i}{n}$

• Median: The middle value when data are ordered.

• Mode: The value that appears most frequently.

• Range: Difference between the maximum and minimum values.

• Standard Deviation: Measure of spread around the mean. $\text{Standard Deviation} = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$

• Variance: The square of the standard deviation. $\text{Variance} = \frac{\sum (x_i - \bar{x})^2}{n-1}$

• z-Score: Standardized value indicating how many standard deviations a data point is from the mean. $z = \frac{x - \mu}{\sigma}$

Probability and Distributions

• Probability: The likelihood of an event occurring. $P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

• Binomial Distribution: Probability distribution for a fixed number of independent trials, each with two possible outcomes. $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$

• Normal Distribution: Continuous probability distribution characterized by its mean and standard deviation.

Inferential Statistics

• Confidence Interval: Range of values likely to contain the population parameter. $\text{CI} = \bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$

• Hypothesis Testing: Procedure for testing claims about population parameters.

• Null Hypothesis ($H_0$): The default assumption.

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

• Type I Error: Rejecting $H_0$ when it is true.

• Type II Error: Failing to reject $H_0$ when it is false.

Regression and Correlation

• Correlation Coefficient ($r$): Measures the strength and direction of a linear relationship. $r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}$

• Least-Squares Regression Line: Line that minimizes the sum of squared residuals. $y = a + bx$

Student Learning Outcomes

• Visualize and summarize data using descriptive statistics.

• Apply probability concepts to draw reasonable conclusions.

• Employ random variables, sampling distributions, and the central limit theorem to analyze data.

• Choose and apply inferential statistics methods (confidence intervals, hypothesis testing).

• Model linear relationships using correlation and regression.

Additional Info

• Course prerequisites: High School Algebra.

• Technology: Use of Pearson MyLab, Canvas, and Zoom for course activities.

• Academic honesty and integrity are strictly enforced.

• Extra credit opportunities for survey completion and attendance.