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.
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.
Angel, Stewart L
General Course Objectives:
Successful completion of this course will promote the general student learning outcomes listed below. The student will be able:
- To apply problem-solving skills through solving application problems.
- To demonstrate arithmetic and algebraic manipulation skills.
- To read and understand scientific and mathematical literature by utilizing proper vocabulary and methodology.
- To construct appropriate mathematical models to solve applications.
- To interpret and apply mathematical concepts.
- 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:
- To understand and use vocabulary and formulas integral to statistics.
- To construct and interpret various statistical functions and graphs.
- To identify misleading graphs.
- To determine appropriate statistical tests to apply.
- To use and understand probability formulas.
- To use and understand confidence intervals.
- To perform hypothesis testing.
- To define and apply the concepts of Type I and Type II errors.
- To understand the relationships between the various formulas used in a specific area of study.
- To apply and interpret the Chi-square test.
- To determine and interpret the linear correlation coefficient.
- To use linear regression.
- To apply and interpret ANOVA.
Students will be required to do the following:
- Differentiate between descriptive and inferential statistics.
- Classify statistical studies.
- Generate random samples.
- Group data appropriately.
- Use a random variable.
- Interpret various types of graphs portraying data distribution.
- Recognize and correct misleading graphs.
- Apply and interpret measures of central tendency for grouped and non-grouped data.
- Apply and interpret measures of dispersion for grouped and non-grouped data.
- Generate Boxplots and Five-Number Summaries.
- Differentiate between populations and samples.
- Apply descriptive measures for populations.
- Define and use terms relevant to probability.
- Apply and interpret rules of probability.
- Construct and interpret contingency tables.
- Explain joint and marginal probability.
- Determine conditional probability.
- Determine if events are independent or mutually exclusive.
- Use appropriate counting rules to determine probability.
DISTRIBUTIONS AND DISCRETE RANDOM VARIABLES
- Generate and interpret probability distributions.
- Use discrete random variables to describe appropriate data sets or events.
- Determine the mean and standard deviation of a discrete random variable.
- Apply the vinomial random variable and binomial distribution appropriately.
- Determine the mean and standard deviation of a binomial random variable.
- Define the "Normal Distribution".
- Generate the standard normal curve.
- Determine probabilities for events in normally distributed populations.
- Determine the mean and standard deviation of a normally distributed random variable.
- Interpret graphs of normal probability distributions.
- Define the "Sample Distribution of the Mean".
- Find the mean and standard deviation of the sampling distribution of the mean.
CONFIDENCE INTERVALS AND HYPOTHESIS TESTING
- Discuss the nature and importance of a confidential interval.
- Determine confidence intervals.
- Explain how sample size affects confidence intervals.
- Discuss the nature and importance of hypothesis testing.
- Construct and interpret hypothesis tests.
- Determine Type II Error probabilities.
- Discuss and determine P-values.
INFERENCES FOR TWO POPULALTION MEANS AND POPULATION PROPORTIONS
- Apply appropriate formulas to determine inferences under various circumstances.
- Determine confidence intervals for one or two populations.
- Determine inferences for two population proportions.
CHI-SQUARE AND ANOVA
- Discuss the Chi-Square distribution, goodness-of-fit test, and independence test.
- Determine inferences for a population standard deviation.
- Discuss the F-distribution and ANOVA.
- Perform one-way and two-way ANOVA.
LINEAR REGRESSION AND CORRELATION
- Discuss the purpose of regression equations, coefficient of determination, and linear.
- Correlation and the relationships between these.
- 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:
- Field trips
Faculty may assign both in- and out-of-class activities to evaluate students' knowledge and abilities. Faculty may choose from the following methods:
- Class preparedness and participation
- Collaborative learning projects
- Scientific observations
- Student-teacher conferences
- Written assignments
Students' final grades are determined by:
Texts, Materials, and Supplies:
Please contact the Texarkana College Bookstore for name of book.