## MATH 3342 (Trindade) -- Mathematical Statistics for Engineers & Scientists -- fall 2021

### Basic Information

Course Meets: TR 09:30-10:50 in Animal & Food Science 102.
• Course instructor: Dr. Alex Trindade, 228 Mathematics & Statistics Building.
E-mail: alex.trindade "at" ttu.edu; Phone: 834-6164.
Office Hours: TWR 2:00-3:00, preferably on zoom, or by appointment.
Emergency Substitute: Dr. Brent Lindquist.
Link for holding class virtually via zoom (if/when announced).

### Text Books

• Required: Probability and Statistics for Engineering and the Sciences (7th - 9th ed.), by Jay L. Devore, Thomson Brooks/Cole.
• Recommended: Student Solution Manual. Contains detailed solutions to odd problems.

### Lecture Notes

These slides cover all the material in the course, but about 50% of them contain blank spaces to be filled in class. These incomplete slides are marked with a red asterisk [*].

### Course Objectives and Syllabus

This course covers mathematical theory and methods of statistical inference at a basic undergraduate level, corresponding to Chapters 1-4, and 6-9 of the book. Calculus III (MATH 2450) is a prerequisite. After introducing probability and distribution theory, these concepts are used to develop the main tools of statistical inference: estimation, confidence intervals, and hypothesis tests. A specific syllabus with approximate coverage timeline is as follows (based on MWF schedule):
• Chapter 1 (1.1-1.4): Descriptive statistics (5 days).
• Chapter 2 (2.1-2.5): Probability (5 days).
• Chapter 3 (3.1-3.6): Discrete random variables and probability distributions (6 days).
• Chapter 4 (4.1-4.6): Continuous random variables and probability distributions (6 days).
• Chapter 5 (5.3-5.5): Sampling distributions and Central Limit Theorem (2 days).
• Chapter 6 (6.1): Point estimation (1 day).
• Chapter 7 (7.1-7.3): One-sample confidence intervals for means and proportions (5 days).
• Chapter 8 (8.1-8.5): One-sample hypothesis tests for means and proportions (5 days).
• Chapter 9 (9.1-9.4): Two-sample inference for means and proportions (4 days).

### Expected Student Learning Outcomes

Students will apply their calculus knowledge to learn the meanings of, and computational procedures relating to, basic statistical concepts used for making decisions in the sciences and engineering. In particular, students will:
• Understand the need to be wary of statistical claims, common pitfalls in sampling, and misrepresentation of conclusions.
• Understand the meanings of various statistical measures, including the mean, median, mode, standard deviation, variance, and quartiles.
• Become familiar with various graphical representations of data and learn to recognize misleading graphs.
• Develop proficiency in real-world probability problems.
• Understand the concept of a probability distribution and real-world problems involving various distributions, including binomial, normal, hypergeometric, and Poisson distributions.
• Understand and apply the Central Limit Theorem.
• Compute and interpret confidence intervals.
• Conduct and interpret hypothesis tests.

### Methods of Assessing the Expected Learning Outcomes

Continuous formative assessment of the progress of the course will occur via ongoing communication between the instructor and the students. to this end all students are encouraged to ask questions during class and to seek the instructor's help outside class. The expected learning outcomes for the course will be assessed through: semester tests and a final exam, homework assignments, and class discussion. The course grade will be determined from homework sets (15%), three (3) semester tests (20% each), and a comprehensive final exam (30%). The traditional grading scale will be used:
• A: 90-100%.
• B: 80-89%.
• C: 70-79%.
• D: 60-69%.
• F: 0-59%.
The grade weighting scheme allows for a maximum of 5% extra credit to be counted toward the overall grade. Firm test dates are as follows:
• Test 1: After completion of Chapters 1 & 2 (Sep 23). (Based on Hwks 1 & 2.)
• Test 2: After completion of Chapters 3 & 4 (Oct 21). (Based on Hwks 3 & 4.)
• Test 3: After completion of Chapters 5, 6 & 7 (Nov 11). (Based on Hwks 5-6 & 7.)
• Final Exam: 7:30 - 10:00 am Saturday Dec 4.
Test grades will be posted on WebAssign.

### Homework Problem Sets

There will be chapter Assignments administered through the online grading system WebAssign (which will show the exact due date/time). The due dates for each Assignment will be approximately one week after coverage of the relevant material in class. All the problem sets are already available, and can be worked on at any time. You will no longer be able to work on sets past the due date (visible in WebAssign). Keep the following in mind:
• Be sure to click on "Save Answer" each time you complete a Question. You can then log out and return later to continue the Assignment. Click on "Submit Answer" only when you finish the whole Question, which will then be graded. You can also choose to "Save Assignment" and "Submit Assignment" at the bottom.
• Some questions are open-ended and ask you to write/draw something. These cannot be checked very carefully by the automatic grading system, and thus almost anything you write/draw will be acceptable. BUT, you should make an honest attempt at these questions, since you will see them again in the tests which are graded by me!
• Some questions are very specific in asking for the answer correct to a certain number of decimal places. Be sure not to round intermediate answers; round only when you get to the final answer.
• Some questions are somewhere in between these two extremes. For example, the calculation of a p-value is very precise, but the system should flag as being correct any answer that you correctly interpolate with tables. For instance, if the exact p-value is 0.078, but you can only deduce from the tables that it falls somewhere between 0.05 and 0.10, then any value in this range should be marked as correct.
• Unless otherwise specified, give answers correct to 4 decimal places. This should be a sufficient default accuracy for all questions.
• You may submit each Question Part, a maximum of 3 times. The highest score of these 3 submissions will be recorded. (Alternatively, you can also submit each entire Question, or entire Assignment 3 times.) The system may give you helpful hints/links for incorrect questions, in order to help you get it right on the next submission.
• Most questions are randomized per student, so as to dissuade you from simply inputting what you friend did.
• The Communications tool is disabled, so do not attempt to communicate with me through the system.
• You are advised to complete each Assignment within a week after we finish the corresponding chapter in class. Each Assignment # corresponds exactly to the Chapter #.
• Some questions may require considerable effort on your part, but this is an important part of the learning process. It is important to keep up with the pace of the course, which on average will require you to complete a homework assignment about every other week.

### Instructions on Accessing WebAssign

Go to WebAssign and follow the instructions for self-enrolling with a CLASS KEY as follows:
• Class Key: ttu 2248 0572.
• It is very important that you provide a genuine e-mail address, such as your @ttu.edu, upon registering (otherwise username & password retrieval will be impossible).
Read the Student Quick Start Guide which also explains different payment options for obtaining access. WebAssign also offers extensive online support.

### Policies

• Class Attendance. Your attendance alone will not impact your grade, but missing exams and assignments will. Whether an absence is excused or unexcused is determined solely by me, with the exception of absences due to religious observance and officially approved trips (see below).
• Make-up Exams: These may be granted in exceptional circumstances if you provide me with a valid excuse (such as a note from a physician, an obituary, etc.).
• Absence for observance of a religious holy day (TTU Operating Policy 34.19): 1. "Religious holy day" means a holy day observed by a religion whose places of worship are exempt from property taxation under Texas Tax Code 11.20. 2. A student who intends to observe a religious holy day should make that intention known to the instructor prior to the absence. A student who is absent from classes for the observance of a religious holy day shall be allowed to take an examination or complete an assignment scheduled for that day within a reasonable time after the absence. 3. A student who is excused under Section 2 may not be penalized for the absence; however, the instructor may respond appropriately if the student fails to complete the assignment satisfactorily.
• Absence due to officially approved trips: The Texas Tech University Catalog states that the department chairpersons, directors, or others responsible for a student representing the university on officially approved trips should notify the student's instructors of the departure and return schedules in advance of the trip. The instructor so notified must not penalize the student, although the student is responsible for material missed. Students absent because of university business must be given the same privileges as other students.
• Illness and Death Notification. The Center for Campus Life is responsible for notifying the campus community of student illnesses, immediate family deaths and/or student death. Generally, in cases of student illness or immediate family deaths, the notification to the appropriate campus community members occur when a student is absent from class for four (4) consecutive days with appropriate verification. It is always the student's responsibility for missed class assignments and/or course work during their absence. The student is encouraged to contact the faculty member immediately regarding the absences and to provide verification afterwards. The notification from the Center for Campus Life does not excuse a student from class, assignments, and/or any other course requirements. The notification is provided as a courtesy. In addition, see the Pandemic Guide.
• ADA accommodations (TTU Operating Policy 34.22). Any student who, because of a disability, may require some special arrangements in order to meet course requirements should contact the instructor as soon as possible to make any necessary arrangements. Students should present appropriate verification from Student Disability Services, during the instructor's office hours. Please note instructors are not allowed to provide classroom accommodations to student until appropriate verification from Student Disability Services has been provided. For additional information, you may contact the Student Disability Services office at 335 West Hall or 806-742-2405.
• Civility in the Classroom. It is expected that everyone will behave in a manner that is conducive to learning. One common disruption is cell phones. Please turn these off in class.
• Academic Honesty (TTU Operating Policy 34.12). It is the aim of the faculty of Texas Tech University to foster a spirit of complete honesty and high standard of integrity. The attempt of students to present as their own any work not honestly performed is regarded by the faculty and administration as a most serious offense and renders the offenders liable to serious consequences, possibly suspension. "Scholastic dishonesty" includes, but it not limited to, cheating, plagiarism, collusion, falsifying academic records, misrepresenting facts, and any act designed to give unfair academic advantage to the student (such as, but not limited to, submission of essentially the same written assignment for two courses without the prior permission of the instructor) or the attempt to commit such an act.
• Electronic Devices in Tests. Scientific calculators are capable of performing many of the long and laborious calculations for almost all of the course. These are permitted, and are in fact necessary. However, you should not rely on your calculator to automatically "spit-out" answers to the more complex questions. The reason for this is that many substantive statistical procedures have slight variations, and tend to be course-specific. So, although your calculator may be able to calculate the quartiles (fourths) of a sample of data for you, its method may not exactly agree with the one in the book. Greater deviations may occur in confidence intervals and hypothesis tests. Also, some questions on tests may be of a partial-credit type nature, and hence require you to show the steps in obtaining the answer. If you simply write the final answer, you may only get a small proportion of the points, even if your answer is correct. Finally, any kind of communication-capable device (smart phones, tablets, laptops, etc.) is forbidden.
• Collaboration. My policies on this are as follows.
• Homeworks: Discussion with peers regarding material/concepts covered in the course is permitted, and is encouraged since it usually leads to greater comprehension. However, each person must write up his/her own solution to a particular problem, and not simply have someone else do it for them.
• Tests: Any form of collaboration on tests, including e-device communication or trying to see what the person next to you is writing, is strictly forbidden and will not be tolerated.

### Statistical Computing

In this course we will not use, but only mention statistical computing software packages, such as SAS, Minitab, SPSS, and R. Those wishing to learn and explore more on this can access some of my statistical computing resources here, particularly R.
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