## Course Syllabus MATH1442

Course Syllabus

MATH1442 - Elementary Statistics

Catalog Description: An introductory course in statistical methods. Topics include collection and display of data, mean, standard deviation and variance, probability including the normal, binomial, and chi-square distributions, confidence intervals, hypothesis testing including non-parametric tests, regression, and analysis of variance.

Prerequisite(s): None

Semester Credit Hours: 4

Lecture Hours / Week: 3

Lab Hours / Week: 2

Contact Hours / Semester: 80

State Approval Code: 2705015119

Core Curriculum: State Criteria

 Perspectives (The following reflect the state-mandated perspectives taught in this course.): Establish broad and multiple perspectives on the individual in relationship to the larger society and world in which he/she lives, and to understand the responsibilities of living in a culturally and ethnically diversified world.Develop a capacity to use knowledge of how technology and science affect their lives.Use logical reasoning in problem solving.Integrate knowledge and understand the interrelationships of the scholarly disciplines.
 Exemplary Objectives (The following reflect the state-mandated exemplary objectives taught in this course.): Mathematics: The objective of the mathematics component of the core curriculum is to develop a quantitatively literate college graduate. Every college graduate should be able to apply basic mathematical tools in the solution of real-world problems. To apply arithmetic, algebraic, geometric, higher-order thinking and statistical methods to modeling and solving real-world situations.To represent and evaluate basic mathematical information verbally, numerically, graphically, and symbolically.To expand mathematical reasoning skills and formal logic to develop convincing mathematical arguments.To use appropriate technology to enhance mathematical thinking and understand and to solve mathematical problems and judge reasonableness of the results.To interpret mathematical models such as formulas, graphs, tables and schematics, and draw inferences from them.To develop the limitations of mathematical and statistical models.To develop the view that mathematics is an evolving discipline interrelated with human culture, and understand its connections to other disciplines.

Course Instructors:

General Course Objectives:

Successful completion of this course will promote the general student learning outcomes listed below. The student will be able:

1. To apply problem-solving skills through solving application problems.
2. To demonstrate arithmetic and algebraic manipulation skills.
3. To read and understand scientific and mathematical literature by utilizing proper vocabulary and methodology.
4. To construct appropriate mathematical models to solve applications.
5. To interpret and apply mathematical concepts.
6. To use multiple approaches-physical, symbolic, graphical, and verbal-to solve application problems.

Specific Course Objectives:

Upon successful completion of the course, the student will be able:

1. To understand and use vocabulary and formulas integral to statistics.
2. To construct and interpret various statistical functions and graphs.
3. To identify misleading graphs.
4. To determine appropriate statistical tests to apply.
5. To use and understand probability formulas.
6. To use and understand confidence intervals.
7. To perform hypothesis testing.
8. To define and apply the concepts of Type I and Type II errors.
9. To understand the relationships between the various formulas used in a specific area of study.
10. To apply and interpret the Chi-square test.
11. To determine and interpret the linear correlation coefficient.
12. To use linear regression.
13. To apply and interpret ANOVA.

Course Content:

Students will be required to do the following:

BASIC INFORMATION

1. Differentiate between descriptive and inferential statistics.
2. Classify statistical studies.
3. Generate random samples.
4. Group data appropriately.
5. Use a random variable.
6. Interpret various types of graphs portraying data distribution.
7. Recognize and correct misleading graphs.

DESCRIPTIVE MEASURES

1. Apply and interpret measures of central tendency for grouped and non-grouped data.
2. Apply and interpret measures of dispersion for grouped and non-grouped data.
3. Generate Boxplots and Five-Number Summaries.
4. Differentiate between populations and samples.
5. Apply descriptive measures for populations.

PROBABILITY

1. Define and use terms relevant to probability.
2. Apply and interpret rules of probability.
3. Construct and interpret contingency tables.
4. Explain joint and marginal probability.
5. Determine conditional probability.
6. Determine if events are independent or mutually exclusive.
7. Use appropriate counting rules to determine probability.

DISTRIBUTIONS AND DISCRETE RANDOM VARIABLES

1. Generate and interpret probability distributions.
2. Use discrete random variables to describe appropriate data sets or events.
3. Determine the mean and standard deviation of a discrete random variable.
4. Apply the vinomial random variable and binomial distribution appropriately.
5. Determine the mean and standard deviation of a binomial random variable.
6. Define the "Normal Distribution".
7. Generate the standard normal curve.
8. Determine probabilities for events in normally distributed populations.
9. Determine the mean and standard deviation of a normally distributed random variable.
10. Interpret graphs of normal probability distributions.
11. Define the "Sample Distribution of the Mean".
12. Find the mean and standard deviation of the sampling distribution of the mean.

CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

1. Discuss the nature and importance of a confidential interval.
2. Determine confidence intervals.
3. Explain how sample size affects confidence intervals.
4. Discuss the nature and importance of hypothesis testing.
5. Construct and interpret hypothesis tests.
6. Determine Type II Error probabilities.
7. Discuss and determine P-values.

INFERENCES FOR TWO POPULALTION MEANS AND POPULATION PROPORTIONS

1. Apply appropriate formulas to determine inferences under various circumstances.
2. Determine confidence intervals for one or two populations.
3. Determine inferences for two population proportions.

CHI-SQUARE AND ANOVA

1. Discuss the Chi-Square distribution, goodness-of-fit test, and independence test.
2. Determine inferences for a population standard deviation.
3. Discuss the F-distribution and ANOVA.
4. Perform one-way and two-way ANOVA.

LINEAR REGRESSION AND CORRELATION

1. Discuss the purpose of regression equations, coefficient of determination, and linear.
2. Correlation and the relationships between these.
3. Find a regression equation and coefficient of determination.

Methods of Instruction/Course Format/Delivery:

Faculty may choose but are not limited to the following methods of instruction:

1. Lecture
2. Discussion
3. Internet
4. Video
5. Television
6. Demonstrations
7. Field trips
8. Collaborations

Assessment:

Faculty may assign both in- and out-of-class activities to evaluate students' knowledge and abilities. Faculty may choose from the following methods:

1. Attendance
2. Class preparedness and participation
3. Collaborative learning projects
4. Exams/tests/quizzes
5. Homework
6. Internet
7. Scientific observations
8. Student-teacher conferences
9. Written assignments