Loyola University Chicago

Mathematics and Statistics

STAT 103: Fundamentals of Statistics

Credit Hours

3

Prerequisites

None. Fulfills CORE Quantitative Analysis requirement.

Description

An introduction to statistical reasoning. Students learn how statistics has helped to solve major problems in economics, education, genetics, medicine, physics, political science, and psychology. Topics include: design of experiments, descriptive statistics, mean and standard deviation, the normal distribution, the binomial distribution, correlation and regression, sampling, estimation, and testing of hypothesis.

Barbara Illowsky and Susan Dean. Introductory Statistics (WebAssign eBook). OpenStax

Chapter 1: Sampling and Data
   1.1    Definitions of Statistics, Probability, and Key Terms
   1.2    Data, Sampling, and Variation in Data and Sampling
   1.3    Frequency, Frequency Tables, and Levels of Measurement
   1.4    Experimental Design and Ethics
Chapter 2: Descriptive Statistics
   2.1    Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
   2.2    Histograms, Frequency Polygons, and Time Series Graphs
   2.3    Measures of the Location of the Data
   2.4    Box Plots
   2.5    Measures of the Center of the Data
   2.6    Skewness and the Mean, Median, and Mode
   2.7    Measures of the Spread of the Data
Chapter 3: Probability Topics
   3.1    Terminology        
   3.2    Independent and Mutually Exclusive Events
   3.3    Two Basic Rules of Probability
   3.4    Contingency Tables
Chapter 4: Discrete and Random Variables
   4.1    Probability Distribution Function (PDF) for a Discrete Random Variable
   4.2    Mean or Expected Value and Standard Deviation
   4.3    Binomial Distribution
Chapter 5: Continuous Random Variables
   5.1    Continuous Probability Functions
   5.2    The Uniform Distribution
   5.3    The Exponential Distribution
Chapter 6: The Normal Distribution
   6.1    The Standard Normal Distribution
   6.2    Using the Normal Distribution
Chapter 7: The Central Limit Theorem
   7.1    The Central Limit Theorem for Sample Means (Averages)
   7.2    The Central Limit Theorem for Sums
   7.3    Using the Central Limit Theorem
Chapter 8: Confidence Intervals
   8.1    A Single Population Mean using the Normal Distribution
   8.2    A Single Population Mean using the Student t Distribution
   8.3    A Population Proportion
Chapter 9: Hypothesis Testing With One Sample
   9.1    Null and Alternative Hypotheses
   9.2    Outcomes and the Type I and Type II Errors
   9.3    Distribution Needed for Hypothesis Testing
   9.4    Rare Events, the Sample, Decision and Conclusion
   9.5    Additional Information and Full Hypothesis Test Examples
Chapter 10: Hypothesis Testing With Two Samples
   10.1    Two Population Means with Unknown Standard Deviations
   10.2    Two Population Means with Known Standard Deviations
   10.3    Comparing Two Independent Population Proportions
   10.4    Matched or Paired Samples
Chapter 12: Linear Regression and Correlation
   12.1    Linear Equations
   12.2    Scatter Plots
   12.3    The Regression Equation
   12.4    Testing the Significance of the Correlation Coefficient
   12.5    Prediction
   12.6    Outliers
Chapter 11: Optional: The Chi-Square Distribution
   11.1    Facts About the Chi-Square Distribution
   11.2    Goodness-of-Fit Test
   11.3    Test of Independence
   11.4    Test for Homogeneity

See Course Page for additional resources.