Course Syllabus

MATH 1040 Introduction to Statistics

Course Description

This course introduces basic concepts and methods of statistical analysis of data. Students will summarize and interpret data as well as make calculations and appropriate conclusions for data sets. Topics to be covered include sampling and data collection, descriptive statistics, basic probability, distributions, and statistical inference (including correlation and 1- and 2-population confidence intervals and hypothesis tests for means and proportions). Statistical calculator or technology required.

Justification

This course is offered as a college-level mathematics course that accomplishes the objectives of the State of Utah Quantitative Literacy requirement and is an option for students seeking to fulfill the mathematics requirement for the AA and AS degrees. This course is similar to other Introductory Statistics courses at other USHE institutions (typically taught as Math 1040 / Stat 1040).

General Education Outcomes

1. A student who completes the GE curriculum has a fundamental knowledge of human cultures and the natural world. "Statistics is the art and science of gathering, analyzing, and making conclusions from data" (J. Riskowski). Whether it be analyzing human behavior in a psychology experiment or studying the effectiveness of a certain drug at treating an illness, the best decisions are informed by a careful analysis of the data. Students will gain a foundational understanding of how such claims about our world are arrived at as well as how to analyze data themselves.
2. A student who completes the GE curriculum can read and research effectively within disciplines. To correctly analyze data, students need to be able to carefully read problems (often application or "story" problems) and data sets to identify needed information. These may be from a variety of sources.
3. A student who completes the GE curriculum can draw from multiple disciplines to address complex problems. Students in statistics draw from and learn to make informed decisions in a variety of disciplines (such as medicine, business, or politics). The ability to make accurate decisions about large groups without having to survey/inspect every member is a vital skill. Statistical proficiency allows people to determine whether a sample is likely to be representative and whether the results are significant. It also allows effective and succinct communication of methods and outcomes.
4. A student who completes the GE curriculum can reason analytically, critically, and creatively. In a data-rich world, it is important to be able to interpret and analyze statistical claims. By the end of the course, successful students will be proficient at computing confidence intervals and hypothesis tests for one and two population means or proportions. In addition, they will be able to correctly interpret these results in real-world terms.
5. A student who completes the GE curriculum can reason quantitatively.  Students successfully completing this course will be able to compute, analyze, and interpret hypothesis test and confidence intervals for one and two populations. Students will then be able to analyze the results of their computations to determine the appropriate conclusions to draw for the given context based on their findings.

General Education Knowledge Area Outcomes

1. Students who successfully complete this course will be able to make and interpret various graphs and charts. In addition, students will also be able to compute and interpret confidence intervals and hypothesis tests, reporting the results accurately. Students who successfully complete this course will be able to make and interpret various graphs and charts. In addition, students will also be able to compute and interpret confidence intervals and hypothesis tests, reporting the results accurately.
2. MATHEMATIZATION: Convert quantitative or mathematical information into appropriate mathematical representations and/or models such as equations, graphs, diagrams, or tables, including making and evaluating important assumptions as needed. Students who successfully complete this course will be able to make and interpret various graphs and charts. Students will also be able to determine whether necessary conditions are met in order to use inference techniques.
3. CALCULATION: Use algebraic skills and techniques to solve problems, including the ability to identify and correct errors in calculations and understanding the role and proper use of technology in assisting with calculations. From computing a mean to interpreting a hypothesis test or confidence interval, students who successfully complete this course will be able to perform a variety of statistical computations.
4. ANALYSIS: Draw appropriate conclusions through quantitative or mathematical analysis of data or models, including understanding and evaluating important assumptions in order to recognize the limits of the analysis. One of the primary uses of statistics is to draw inferences about a whole (large) population without having to survey every member. Students who successfully complete this course will be able to determine whether conditions for inference are met and then compute confidence intervals and complete hypothesis tests. Based on this work, students will be able to successfully interpret the results.
5. APPLICATION / CREATION: Solve concrete and abstract problems across multiple disciplines.  Because statistics draws conclusions by taking a sample from a population, we need to have enough evidence before we can believe a claim. Such an analysis comes as conclusions to a confidence interval or hypothesis test and applies to many disciplines, from biology to psychology to business. Upon completion of this course, students will be able to gather evidence in a variety of disciplines and use that evidence to draw appropriate conclusions, recognizing the applications, limitations, and assumptions of those conclusions.

Course Content

This course provides an introduction to statistics. Topics include data classification and study design, visualizations (creating and interpreting graphs), statistical measures (computing and interpreting proportion, mean, standard deviation, etc.), basic probability and distributions, inference (confidence intervals and hypothesis tests) for one- and two-population proportions and means, and correlation testing. Optional topics include tests of goodness of fit and independence or inference for variance.