STA 147: Introduction to Statistics – Syllabus and Study Guide

STA 147: Introduction to Statistics

Course Overview

This course introduces students to the fundamental concepts and methods of statistics, emphasizing their application in the biological, social, and behavioral sciences, as well as in business. Topics include descriptive statistics, probability, inferential statistics, sampling theory, estimation, hypothesis testing, regression, and correlation.

• Required Text: Statistics: Informed Decisions Using Data by Sullivan (with MyStatLab Access)

• Software: Minitab 21 (statistical analysis software)

• Course Format: Web class (online)

Core Curriculum and Learning Outcomes

The course is part of Cleveland State University's Inquiry Core Curriculum, focusing on quantitative literacy and reasoning. Students will develop skills in statistical thinking, data analysis, and interpretation.

• Identify characteristics of a well-designed statistical study and critically evaluate various aspects of a study, including limitations of observational studies and common sources of bias.

• Summarize univariate and bivariate data using graphical, tabular, and numerical methods, and describe relationships between variables.

• Compute probabilities for compound events, independent events, and disjoint events, and analyze probability distributions.

• Explain the difference between statistics and parameters, describe sampling distributions, and interpret the normal distribution.

• Construct and interpret confidence intervals for means and proportions, and understand the concept of margin of error.

• Formulate and evaluate hypotheses using statistical tests, interpret p-values, and draw appropriate conclusions regarding statistical significance.

Major Topics and Subtopics

Descriptive Statistics

Descriptive statistics summarize and organize data to reveal patterns and relationships.

• Key Terms: Mean, median, mode, range, variance, standard deviation

• Graphical Methods: Histograms, bar charts, pie charts, box plots

• Tabular Methods: Frequency distributions, contingency tables

• Numerical Methods: Calculation of central tendency and dispersion

Example: Calculating the mean and standard deviation of exam scores in a class.

Probability

Probability theory provides the foundation for statistical inference and decision-making under uncertainty.

• Key Terms: Event, sample space, independent events, mutually exclusive events

• Formulas:

  • $P(A \cap B) = P(A) \times P(B)$ (for independent events)

  • $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

• Probability Distributions: Binomial, normal, and other distributions

Example: Calculating the probability of drawing two aces from a deck of cards.

Inferential Statistics

Inferential statistics use sample data to make generalizations about a population.

• Key Terms: Population, sample, parameter, statistic, sampling distribution

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

• Formula:

  • $\text{Confidence Interval for Mean} = \bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$

• Margin of Error: Quantifies uncertainty in estimation

Example: Estimating the average height of students in a university using a sample.

Hypothesis Testing

Hypothesis testing is a formal procedure for evaluating claims about population parameters.

• Key Terms: Null hypothesis ($H_0$), alternative hypothesis ($H_a$), p-value, significance level ($\alpha$)

• Steps:

  1. State the hypotheses

  2. Choose the significance level

  3. Calculate the test statistic

  4. Find the p-value

  5. Draw a conclusion

• Formula:

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

Example: Testing whether a new drug is more effective than the current standard.

Regression and Correlation

Regression and correlation analyze relationships between quantitative variables.

• Key Terms: Dependent variable, independent variable, correlation coefficient ($r$), regression line

• Formula:

  • $y = a + bx$ (simple linear regression)

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

Example: Analyzing the relationship between study hours and exam scores.

Course Assessment Structure

Grades are determined by a combination of homework, quizzes, exams, and lab assignments. The following table summarizes the grading breakdown:

Component	Weight (%)
MyStatLab Homework	10
Minitab Labs	10
Quizzes	30
Exams	30
Final Exam	20

Grading Scale:

Score (%)	Grade
93-100	A
90-93	A-
87-90	B+
83-87	B
80-83	B-
77-80	C+
70-77	C
60-70	D
0-60	F

Technology Requirements

• Minitab 21: Statistical software for data analysis (available via campus license)

• Blackboard: Platform for assignments, grades, and course materials

• Calculator: Scientific calculator recommended

Course Policies and Support

• Attendance: Regular participation is essential for success.

• Academic Integrity: All work must adhere to university standards of honesty.

• Support: Math Learning Center (MLC), online resources, and instructor office hours are available for help.

Useful Online Resources:

• Minitab Support Videos

• Khan Academy: Statistics & Probability

• Against All Odds: Inside Statistics

Tips for Success

• Complete all assignments on time and review material regularly.

• Form study groups and seek help when needed.

• Utilize available resources, including the MLC and online tutorials.

Additional info: The syllabus emphasizes the importance of quantitative reasoning and the use of statistical software (Minitab) for hands-on data analysis. Students are encouraged to apply statistical thinking to real-world problems and to develop skills in both computation and interpretation.