## SYLLABUS **Last Updated 10/2/96**

### Course Number: MA 211

Course Title: Statistics with Aviation Applications
Course Hours Credit: 3

Required Text:
Triola, M.F., (1995) Elementary Statistics, 6th Ed., Addison-Wesley Publishing Company, Inc..

Supplemental Material:
1. A scientific calculator. (Required)
2. Student Solutions Manual (Optional)
3. Statistics Software for IBM PC (available on Center Lab Computers)

Course Description:
Descriptive statistics; populations and samples; measures of central tendency and dispersion; elementary probability; binomial and normal distributions and their interrelationships; random variables; one and two sample hypothesis testing involving proportions and means for large and small samples; estimation and confidence intervals; Chi square distribution; correlation coefficient; least squares line. Prerequisite: MA111

Goals:
This course is designed to enable the student to understand and use probability, descriptive statistics and inferential statistics in a variety of applied problems.

Performance Objectives:
Upon course completion, students will be able to:
1. Understand some of the uses and abuses of statistics and methods of sampling.
2. Summarize data using frequency tables and present data in the form of histograms.
3. Calculate, describe and interpret measures of central location and variability; evaluate noncentral measures of location, and explore data using stem-and-leaf plots.
4. Use the basic concepts, laws, and applications of probability theory, sample space, simple probability, and probability of combined events.
5. Derive the probability distribution of random variables and determine the mean, variance, standard deviation and expected value of a probability disribution.
6. Calculate probabilities of a binomial experiment and calculate the mean, variance and standard deviation for a binomial distribution.
7. Determine probabilities using the characteristics of continuous random variables, normal distributions, and the normal curve and use the normal distribution to approximate binomial probabilities.
8. Determine probabilities using distributions of sample means and applying the central limit theorem.
9. Apply the theory of sampling distributions to estimate values of unknown population means or proportions and determine levels of confidence to be attached to these estimates.
10. Apply the theory of sampling distributions to test hypotheses concerning means, using large or small samples, and proportions or percentages.
11. Determine the size of the sample needed when estimating the population mean or proportion.
12. Employ distributions of the difference between two samples to test hypotheses or to estimate confidence intervals concerning the difference between two population variables, means or proportions.
13. Determine and analyze the linear correlation between two populations and construct a linear regression equation for the purpose of making predictions.
14. Employ the chi-square distribution to test hypotheses concerning several proportions from a population and concerning the independence of variables.
15. Use the analysis of variation techniques for testing the equality of several population means.

Teaching Methods:
Class meetings will be comprised of lectures and discussions of assigned material, sample solutions to representative problems, board work, graphing calculator and computer lab demonstrations, and testing for understanding. Class participation is expected with emphasis on aviation related applications.

Class Policy:
All students are expected to bring their text, calculator, paper and pencil to each scheduled class where academic honesty is the required mode of behavior. Assignments contained herein, and as augmented at instructor's discretion, shall be completed prior to the next scheduled Monday class session and will not be accepted beyond that date without prior instructor approval. Assignments constitute minimum coverage of the required lessons and the student is encouraged to complete additional exercise problems contained within each assigned chapter to promote mastery of the objectives. Course content may vary from this syllabus to meet the needs of this particular class composition. Students are expected to attend all scheduled classes where active participation in class is an integral element and will be considered in final course grades. Should circumstances arise beyond a student's control which may force a student to miss a class session or portion thereof, all matters relating to the absence should be arranged between the student and the instructor, including making up missed work. Absences are particularly significant in this program due to the amount of material covered in each class. Thus students are encouraged to assist one another with missed classnotes and assignments.

Area content tests/quizzes50%90-100 A
Final exam30%80-89 B
Homework assignments15%70-79 C
Class participation 5%60-69 D
Total 100%

Session #1/Week #1: Monday
Topic: Introduction and Summarizing Data
Objectives:
1. The student will know the scope and concept of the course to include the classroom procedures, homework requirements, examinations and grading policy.
2. The student will become familiar with the history of statistics and understand some of the uses and abuses of statistics and methods of sampling.
3. The student will be able to summarize data using frequency tables and demonstrate presentational use of histograms, pie charts, frequency polygons and ogives.
Assignment: Read Chapter 1 and Sections 2-1 thru 2-3; do Review Exercises, pp 29-30, #1-8; pp 42-43, # 2,4,8,12,16, and 24; and pp 51-53, #1-4, and 18.

Session #2&3/Week #1&2: Thursday/Monday
Topic: Statistical Measures of Data
Objectives:
1. The student will be introduced to the basic statistical measures of central location and variability and acquire the skill necessary for the calculation of these measures.
2. The student will be able to interpret the significance and limitations of these measures and to describe the distribution of a set of data in terms of its variability about a measure of central and noncentral measures of locations.
3. The student will also learn to explore data using stem-and-leaf plots.
Assignment: Read sections 2-4 thru 2-7; do Review Exercises pp 114-115, #1,2,6,7,10,11 and 15.

Sessions #4&5/Week #2&3: Thursday/Monday
Topic: Probability
Objectives:
1. The student will comprehend the concept of a sample space and study various methods used in counting the number of elements of a sample space.
2. The student will understand the concept of simple probability, probability of combined events, as well as their associated properties, laws, and applications.
3. The student will learn to determine the total number of different ways that various events can occur and the relationship between probabilities and odds.
Assignment: Read Chapter 3; do Review Problems pp 176-178, #1-20.

Session #6/Week #3: Thursday
Topic: Probability Distributions
Objectives:
1. The student will comprehend the concept of discrete random variables, and discrete and continuous probability distributions.
2. The student will acquire the skills to derive the probability distribution of random variables and develop an understanding of the measures of central location and variability as applied to random variables.
Assignment: Read sections 4.1 thru 4.3; do Review Problems pp 194-197, #1-12, 19,20 and 24; pp 208-210, #1,6,10,15,17,23,25 and 30.

Session #7/Week #4: Monday
Topic: Binomial Distributions
Objectives:
1. The student will become proficient in calculating probabilities of a binomial experiment and in calculating the mean, variance and standard deviation for a binomial distribution.
2. Test over Chapter 1 thru Section 4.3.
Assignment: Read section 4.4; do Exercises pp217-219, #2,9 and 10; and Review Exercises pp 221-222, #1-10.

Session #8&9/Week #4&5: Thursday/Monday
Topic: Normal Distributions
Objectives:
1. The student will comprehend the characteristics of continuous random variables, normal distributions, and the normal curve and how to use these characteristics to determine probabilities.
2. The student will use the information from a normal distribution to approximate binomial probabilities.
3. The student will be familiar with the applications of the normal distribution.
Assignment: Read sections 5.1 thru 5.5; do Exercises pp 236-237, #2,6,22,26,35; pp248-250, #9,18,19,25,27; pp261-265, #3,6,11,12,20,24; pp272-276, #2,3,7,11,12,24, & 31.

Session #10/Week #5: Thursday
Topic: Estimates and Sampling Distributions
Objectives:
1. The student will comprehend sampling distributions of the mean and applications of the central limit theorem.
2. The student will use the Student t distribution on appropriate applications.
Assignment: Read sections 6.1-6.2, do Exercises pp302-307, #1,3,8,11,25 & 32.

Session #11/Week #6: Monday
Topic: Estimation of Parameters
Objectives:
1. The student will comprehend the procedures for estimating the values of unknown population parameters from information provided by sample data and how the theory of sampling distributions allows levels of confidence to be assigned to these estimates.
2. The student will demonstrate how to determine the size of a sample needed.
3. Student Project topic/outline submitted for approval.
Assignment: Read sections 6-3 and 6-4, do Exercises pp 313-316, #2,3,5,11,24,30,35; pp 326-329, #1,5,6,11,12,15.

Session #12/Week #6: Thursday
Topic: Testing of Hypothesis
Objectives:
1. The student will comprehend how the theory of sampling distributions can be applied to hypothesis testing; use procedures for estimating a set of rules that lead to the acceptance or rejection of an hypothesis; and assess the errors that can be made when inferences are made on sample information.
2. The student will learn to test hypotheses concerning means, using large and small samples, and proportions or percentages.
Assignment: Read Chapter 7, do Exercises pp 399-401, #1,3,5,7,11,17,19.

Session #13/Week #7: Monday
Topic: Hypothesis Tests and Confidence Intervals Using Two Samples
Objectives:
1. The student will comprehend the concept of employing distributions of the difference between two samples to construct confidence intervals and to test hypotheses concerning the difference between two proportions population variances or means.
2. Test over material covered thru Chapter 7.
Assignment: Read Chapter 8; do Review Exercises pp 465-470, #1-16.

Session #14/Week #7: Thursday
Topic: Linear Correlation and Regression Line and Chi-Square Tests
Objectives:
1. The student will be able to determine and analyze the linear correlation between two populations and construct a linear regression equation for the purpose of making predictions.
2. The student will comprehend the use of Chi-Square distributions to test hypotheses concerning more than two proportions from a population and concerning independence of variables in contingency tables.
Assignment: Read section 9.1-9.3 and 10.1-10.2; do Exercises pp487-491, #1,5 & 22; pp504-506, #4,5,24a,b,d and pp547-550, #1,8 and 11.

Session #15&16/Week 8: Monday/Thursday
Topic: Analysis of Variances (ANOVA)
Objectives:
1. The student will become acquainted with the analysis of variance techniques for testing the equality of several population means.
Assignment: Read sections 11-1 thru 11-3; do Exercises pp 584-586, #5,6,7; pp597-598, #2,3, and 6.

Session #17/Week #9: Monday
Topic: Review for Final Exam
Objectives:
1. The student will review material covered in course in preparation for Final Exam.
Assignment: Complete Practice Final Exam

Session #18/Week#9: Thursday
Topic: Final Exam
Objective:
1. Assess student comprehension of materials covered in this course.

For questions contact Instructor: E-mail.