Applied Statistics
Revised: August 2023
Course Description
Descriptive statistics, exploratory data analysis, probability distributions, correlation,
regression, estimation, and hypothesis testing. Three semester hours.
Student Learning Objectives
By the end of the course, students should be able to:
- Describe the concepts of population and sample, and some of the basic descriptive
measures associated with them.
- Explain and utilize graphical methods for data presentation.
- Connect the concepts of probability, random variables, and distributions.
- Assess the properties of common distributions, especially the normal and binomial.
- Synthesize the ideas of correlation and regression.
- Interpret estimation and hypothesis testing procedures applied to population means
and proportions.
Learning Objectives for Liberal Studies
MATH 170 is a C2 (Mathematics) Liberal Studies Course. Specifically, this course will
emphasize the following Liberal Studies learning objective and outcome:
Objective: Problem Solving
Students will apply appropriate disciplinary methodologies to answer questions and
propose solutions to problems within the human and natural worlds.
As a C2 Course, this course introduces applications of mathematics to daily experience,
emphasizing the development of conceptual understanding rather than computational
drill. An assignment in which students display an application of mathematics and/or
analytical problem solving will be required.
Text
Required Textbook:
Warren, Denley, & Atchley. Beginning Statistics, Third Edition. Hawkes Learning, 2021.
Optional Supplemental Text:
Illowsky, Dean, et al. Introductory Statistics. OpenStax, 2013. https://openstax.org/details/books/introductory-statistics
Grading Procedure
Grading procedures and factors influencing course grade are left to the discretion
of individual instructors, subject to general university policy.
Attendance Policy
Attendance policy is left to the discretion of individual instructors, subject to
general university policy.
Course Outline
- Chapter 1: Introduction to Statistics (0.5 weeks)
- 1.1 Getting Started
- 1.2 Data Classification (Optional Topic: Levels of Measurement)
- 1.3 The Process of a Statistical Study (at least cover observational vs experimental
studies, simple random sample, response versus explanatory variable)
- 1.4 How to Critique a Published Study (at least cover selection and non-response bias)
- Chapter 2: Graphical Descriptions of Data (0.5 weeks)
- 2.1 Frequency Distributions (Optional)
- 2.2 Graphical Displays of Data (Optional)
- 2.3 Analyzing Graphs
- Chapter 3: Numerical Descriptions of Data (1 weeks)
- 3.1 Measures of Center (Optional Topic: calculating measures by hand)
- 3.2 Measures of Dispersion (Optional Topics: calculating measures by hand, Chebyshev’s
Theorem)
- 3.3 Measures of Relative Position (Optional Topics: calculating quartiles by hand,
interpreting and comparing box and whisker plots)
- Chapter 4: Probability, Randomness, and Uncertainty (1.5 weeks)
- 4.1 Introduction to Probability
- 4.2 Addition Rules for Probability (Optional Topics: Venn Diagrams, The Addition Rule
for Probability)
- 4.3 Multiplication Rules for Probability (Optional Topic: Multiplication Rule for
Probability of Dependent Events)
- 4.4 Combinations and Permutations (Optional)
- 4.5 Combining Probability and Counting Techniques (Optional)
- Chapter 5: Discrete Probability Distributions (1 week)
- 5.1 Discrete Random Variables (Optional Topics: Variance and Standard Deviation for
a Discrete Probability Distribution)
- 5.2 Binomial Distribution (Optional Topic: calculating a Binomial Probability by hand)
- 5.3 Poisson Distribution (Optional)
- 5.4 Hypergeometric Distribution (Optional)
- Chapter 6: Normal Probability Distributions (1 week)
- 6.1 Introduction to the Normal Distribution
- 6.2 The Standard Normal Distribution
- 6.3 Finding Probability Using a Normal Distribution
- 6.4 Finding Values of a Normally Distributed Random Variable (Optional Topic: Finding
the Value of a Normally Distributed Random Variable That Represents a Given Percentile/Quartile)
- 6.5 Approximating a Binomial Distribution Using a Normal Distribution (Optional)
- Chapter 7: The Central Limit Theorem (1 week)
- 7.1 Sampling Distributions and the Central Limit Theorem
- 7.2 Central Limit Theorem with Means
- 7.3 Central Limit Theorem with Proportions
- Chapter 8: Confidence Intervals (2 weeks)
- 8.1 Estimating Population Means, Known (Optional Topics: Constructing a Confidence
Interval where is known, unbiased estimators)
- 8.2 Student’s t-Distribution (Optional Topic: Compare shapes of z and t distributions)
- 8.3 Estimating Population Means, Unknown
- 8.4 Estimating Population Proportions
- 8.5 Estimating Population Variances (Optional)
- Chapter 10: Hypothesis Testing (2 weeks)
- 10.1 Fundamentals of Hypothesis Testing
- 10.2 Hypothesis Testing for Population Means, Known (Optional Topic: Draw conclusions
using rejection region techniques)
- 10.3 Hypothesis Testing for Population Means, Unknown (Optional Topic: Draw conclusions
using rejection region techniques)
- 10.4 Hypothesis Testing for Population Proportions (Optional Topic: Draw conclusions
using rejection region techniques)
- 10.5 Hypothesis Testing for Population Variances (Optional)
- 10.6 Chi-Square Test for Goodness of Fit (Optional)
- 10.7 Chi-Square Test for Association (Optional)
- Chapter 12: Regression, Inference, and Model Building (1.5 weeks)
- 12.1 Scatter Plots and Correlation (Optional Topics: all material that discusses significance
of the correlation coefficient)
- 12.2 Linear Regression
- 12.3 Regression Analysis (at least cover how to calculate a residual)
- 12.4 Multiple Regression (Optional)
* Note: Some instructors for this course require the use of statistical calculators.