Course Syllabus

MATH 1040 Introduction to Statistics

Course Description

Introduction to Statistics is a first-semester course on the nature of statistical reasoning. Topics to be covered include descriptive statistics, sampling and data collection, basic probability, sampling distributions, and statistical inference (including 1- and 2-sample confidence intervals and hypothesis testing). Statistical calculator required (TI-84 recommended).

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 equivalent to the Introductory Statistics course at all state institutions and carries the same prefix and number except at USU and UVU where it transfers as 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. This course provides students with the foundation to understand how such claims are arrived at as well as how to analyze data themselves. This ability to analyze data about the natural world will be assessed through homework, exams, quizzes, and/or student projects.
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 book or an online source such as the census bureau. After working with the data, students will report their analysis, typically on homework, exams, quizzes, and/or student projects.
3. A student who completes the GE curriculum can draw from multiple disciplines to address complex problems. Whether it is 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. This outcome will typically be assessed through homework, exams, quizzes, and/or student projects.
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 populations. In addition, they will be able to correctly interpret these results in real-world terms. Problems to analyze will come from a variety of areas, such as business, human behavior, and medicine. Mastery of these skills will be assessed through homework, exams, quizzes, and/or student projects.
5. A student who completes the GE curriculum can communicate effectively through writing and speaking. While being able to complete statistical calculations is important, the ability to share those results with others is also vital. For example, students will effectively interpret the results of a confidence interval or hypothesis test. Mastery of this outcome will be measured through homework, exams, quizzes, and/or student projects.
6. A student who completes the GE curriculum can reason quantitatively.  As an introduction to the analysis and interpretation of data, this statistics course will ask students to compute hypothesis tests and confidence intervals for one and two populations. Students must carefully analyze the results of the computations to determine the appropriate conclusions to draw for the given context based on the findings. Each student's mastery of this skill will be assessed through homework, exams, quizzes, and/or student projects.

General Education Knowledge Area Outcomes

1. Students will be able to make and interpret various graphs and charts. This outcome will be assessed through homework, exams, quizzes, and/or student projects. Students will be able to make and interpret various graphs and charts. This outcome will be assessed through homework, exams, quizzes, and/or student projects.
2. Convert relevant information into various mathematical forms (e.g., equations, graphs, diagrams, and tables). Students will be able to make and interpret various graphs and charts. This outcome will be assessed through homework, exams, quizzes, and/or student projects.
3. Demonstrate the ability to successfully complete basic calculations to solve problems. From computing a mean to interpreting a hypothesis test, students will perform a variety of statistical computations. This outcome will be assessed through homework, exams, quizzes, and/or student projects.
4. Demonstrate the ability to problem solve using quantitative literacy across multiple disciplines. Make judgments and draw appropriate conclusions based on quantitative analysis of data, recognizing the limits of this analysis. One of the primary uses of statistics is to draw inferences about a whole (large) population without having to survey every member. This applies to many disciplines, from biology to psychology to business. For this course, computing confidence intervals and completing hypothesis tests, and effectively interpreting the results, are prime examples. This outcome will be assessed through homework, exams, quizzes, and/or student projects.
5.  Because statistics draws conclusions by taking a sample from a population, we need to have enough evidence before we can believe a claim. Such results come as conclusions to a confidence interval or hypothesis test. This outcome will be assessed through homework, exams, quizzes, and/or student projects.

Student Learning Outcomes

1. Understand and apply elements of quality study design.
2. Be familiar with many common graphs and charts and will be able to create an appropriate graph or chart for a given data set.
3. Understand the meaning of statistical measures (mean, median, proportion, standard deviation) and be able to calculate each of them for a given data set.
4. Be able to take a given problem and, as appropriate, complete a hypothesis test or compute a confidence interval.
5. Be able to make an appropriate real world conclusion based on the results from the hypothesis test or confidence interval.

Course Content

This course will include:
• study design
o sampling methods and possible bias
o observational studies vs experiments
• descriptive statistics
o graphical methods
o numerical methods
o simple linear regression
• probability and probability distribution
o general rules
o discrete probability distribution - the Binomial
o continuous probability distribution - the Normal
• inferential statistics
o estimating with confidence intervals
o hypothesis testing
o inference for large and small samples and proportions
o two sample hypothesis testing and confidence intervals
• additional inference topics (optional)
o test of goodness of fit
o test of indepedence