GB Business Statistics (online, CRN 80275) Spring 2015 (24 Aug thru 11 Dec)

Transcription

1 GB Business Statistics (online, CRN 80275) Spring 2015 (24 Aug thru 11 Dec) Instructor: Dr. Brad Almond Campus Office: Founders Hall 318G (TAMUCT) Office Phone: Office Fax: address: Department: Marketing and Management Department Contact Info: Founders Hall 318, , Office Hours: Mondays and Wednesdays 1 2:15 and from 3:45 5:30 pm (appointments recommended) Hawkes Learning Systems This course utilizes the Hawkes Learning Systems software for all coursework (homework and exams). All technical support questions about the installation and operation of this software should be directed to Hawkes Representatives at (800) or (843) , or via the online chat feature available on their website: Do not contact your instructor for technical support. The Hawkes representatives are very helpful and easy to reach. More information about the Hawkes software appears below. Blackboard This class maintains a Blackboard page for all course communications and documents. It may be accessed at All course video lectures and labs will be accessed and viewed through this Blackboard page. All supplemental documents and course communications will be conducted through the Blackboard page, also. However, all class administration (homework and exams) will be conducted online with the Hawkes Learning Systems software (see below). Additional communication may be conducted through Blackboard or TAMUCT , phone calls (see contact information above) or in-person office visits. Students should log into Blackboard as follows: Your Blackboard Username is your MyCT username (xx123 or everything before the "@" in your MyCT address) Your Blackboard Password is your MyCT password Blackboard login instructions are also given on the right-hand side of the page of the above URL. To ensure timely and reliable communication (e.g., if I have to cancel class for some reason), I recommend that you change your default address in Blackboard to whatever address you 1

2 actually check on a regular basis. To do this, click on the triangle that appears to the right of your name in the upper-right corner of the Blackboard screen. At the bottom of the window that opens, click Settings. Click the link for Personal Information. Click Edit Personal Information. Change your address under 1. Personal Information and click Submit. For this course, you will need reliable and frequent access to a computer with Internet access. If you do not have frequent and reliable access to a computer with Internet connection, or if your computer skills (opening, modifying, and saving files; Web browsing, etc.) are weak, please consider dropping the course and re-enrolling after you have received additional computing training. I am unable to provide computer training in this course aside from that which is directly related to course objectives. UNILERT Emergency Warning System for Texas A&M University Central Texas UNILERT is an emergency notification service that gives Texas A&M University Central Texas the ability to communicate health and safety emergency information quickly via , text message, and social media. All students are automatically enrolled in UNILERT through their myct account. Connect at to change where you receive your alerts or to opt out. By staying enrolled in UNILERT, university officials can quickly pass on safety-related information, regardless of your location. (statement updated Fall 2014) 1.0 Course Overview and description: Business statistics is the science of collecting, organizing, summarizing, and analyzing data to generate information, stated in numerical or graphical form, for the purpose of making objective business decisions. The course will initially cover descriptive statistics, but will also introduce several basic inferential statistical techniques. Topics include the foundations of statistical methods of sampling, classifying, analyzing, and presenting numerical data; frequency and sampling distributions, averages, dispersion, hypothesis testing, and analyzing up to two populations and population proportions. The course will employ the use of an online statistics learning system for problem assignments, in conjunction with the text and lectures, in completing course coverage of each statistics topic. Prerequisite: Junior Classification. 2.0 Course Objective: The student will understand the foundations of statistics, which includes basic statistical graphs and charts, measures of central tendency and variation, basic probability, probability distributions, and hypothesis testing. Additionally the student will be able to apply the statistical foundations in inferential statistics, which will include comparing two populations, two population proportions, comparing two variables or treatments for a single population, one-way analysis of variance, linear regression, and chisquare tests. Student Learning Outcomes 1 Demonstrate methods of reporting data numerically and graphically. 2 Identify and analyze types and levels of data using appropriate statistical methods. 2.1 Qualitative (nominal, ordinal) 2.2 Quantitative (continuous, discrete, interval, ratio) 3 Demonstrate proficiency in calculating descriptive statistics. 3.1 Measures of central tendency 2

3 3.2 Measures of variation 4 Demonstrate proficiency in analyzing discrete and continuous probability distributions 4.1 Concepts of probability 4.2 Binomial distributions 4.3 Normal distributions 4.4 Chebyshev s Theorem 4.5 Empirical Formula 4.6 Central Limit theorem 5 Demonstrate understanding and proficiency in calculating confidence intervals, conducting hypothesis tests, and calculating p-values. 5.1 Calculate confidence intervals when the population standard deviation is known/unknown and for proportions 5.2 Conduct hypothesis testing when the population standard deviation is known/unknown and for proportions 5.3 Calculate p-values for all hypothesis tests 6 Demonstrate proficiency in calculating inferential statistics. 6.1 Compare means or proportions of two populations 6.2 Compare means of two treatments within one population 7 Demonstrate basic proficiency with common statistical analytic methods 7.1 Analysis of variance (one-way) 7.2 Simple and multiple linear regression 7.3 Chi-square tests 7.4 Control charts 3.0 REQUIRED COURSE MATERIALS / TECHNOLOGY The following materials are REQUIRED. A user license for the Hawkes Business Statistics (HLS) software. This software may either be downloaded and installed or simply accessed via the Web directly. The interfaces are identical either way. The current version of the downloaded software (for Academic Year ) is for PC and for Mac. This software may be bundled with a course textbook (optional) or purchased separately. Instructions for how to download the software and purchase an access code are given below, and are also included on the course Blackboard page. The current cost for a user license is $ All students must pay the user license regardless of how they access the software. The software itself (if you choose to download it) is free. Access to a computer with Microsoft Excel. All TAMUCT lab computers will have Excel, as will most computers everywhere. If your home computer does not have a COMPLETE version already installed (many PCs come with basic and partial versions of Microsoft Office that will NOT be sufficient for this class), you can purchase a full version of Microsoft Office (which includes Excel) through the TAMU Software Store for the greatly discounted price of $10. The URL for the Store is Again, both PC and Mac versions of Office are available through this site. A slightly less expensive (but also less user-friendly) alternative is to download and install an online-only version of Microsoft Office (which includes Excel) for FREE through TAMUCT. Go to and click the link for Office 365 Instructions to learn how to access this software. Both PC and Mac versions of the software are available. Please be sure that your operating system is compatible with whichever version of the software you get. Please call the TAMUCT help desk if you need technical support. The current URL is 3

4 Access to a computer with a reliable, fast internet connection (for uploading and downloading Hawkes Learning System lessons and exams, and for viewing the course Blackboard page). Please note that your instructor is NOT available for technical support. Depending on the nature of the problem, you should contact either the Blackboard HelpDesk (contact information below) or Hawkes Learning Systems ( ) for assistance. The following materials are OPTIONAL. A course textbook. Nearly all students report NOT benefiting from the textbook. If you think you you would benefit from one, you should purchase Discovering Business Statistics by Nottingham and Hawkes. The textbook is available in e-book or hard copy, and can be bundled with downloadable software and access codes. The relevant ISBN numbers are as follows: 10 Digit ISBN 13 Digit ISBN Software Only Software + ebook Bundle Software + Textbook Bundle Software + Textbook + ebook Bundle Your University bookstore does NOT stock textbooks for online sections. However, this text may still be available at your university bookstore, and is definitely be available at the following website (please also see note in red below): o If you purchase your textbook used and it does not include a working copy of the Hawkes software you will still need to download (and purchase a working license for) the Business Statistics courseware as per the instructions in this syllabus or on our course Blackboard page. NOTE: Students are not under any obligation to purchase a textbook from a universityaffiliated bookstore. A hand held calculator. At a minimum must have square root key in addition to the basic functions of addition, subtraction, multiplication, and division. This item is optional because all of our course calculations may be done using Microsoft Excel. The Data Analysis ToolPak add-in in Excel. More information will be given about this in class. If your version of Excel has this, I suggest you use it. If it doesn t, I will provide an alternative for you in class at no extra cost. Additional Information About Blackboard For technological or computer issues, especially those related to Blackboard, students should contact Help Desk Central at any time, 24 hours a day, 7 days a week: helpdesk@tamu.edu Phone: (254) Web Chat: 4

5 When calling for support please let your support technician know you are a TAMUCT student. For issues related to course content and requirements, contact your instructor. Blackboard supports the following operating systems: PC: Windows 8, Windows 7, Windows Vista Mac: Mac OS X Mavericks NOTE: Computers using Windows XP, Windows 8 RT and OS X 10.6 or lower are no longer supported Check your browser and computer compatibility by clicking the Check My Browser link at the top of the TAMUCT Blackboard logon page ( or by clicking the Test your Browser button on the main page after you log in to Blackboard. It is critical that you run these quick tests to ensure that all features of Blackboard are working properly on your computer. Upon logging on to Blackboard Learn, you will see a link to Blackboard Student Orientation under the My Courses tab. Click on that link and study the materials in this orientation course. This orientation course will help you get familiar with the layout and function of Blackboard. There is also a link to Blackboard Help from inside the course on the left-hand menubar. As needed, the first week of the course may include activities and assignments that will help you get up to speed with navigation, sending and receiving messages and discussion posts, and submitting an assignment. Your ability to function within the Blackboard system will facilitate your success in this course. 4.0 COURSE REQUIREMENTS AND STRUCTURE 4.1 Online Course: This course is completely online and will be conducted in an asynchronous mode. The asynchronous mode does not require the students or the instructor to be online simultaneously or at any specified day or time. Daily work (including listening to the recorded lectures) is completed by the student according to the weekly schedule in this syllabus, but at a time that is convenient to the student. This mode does require the instructor to be accessible at times to answer questions online. Regardless of location, students are solely responsible for ensuring constant access to the Internet and the operability of their personal computers. Be sure your antivirus software is up to date and that your computer is working well. Your instructor is unable to make accommodations for technology malfunctions that cannot be externally verified. Furthermore, to ensure successful course completion, a high level of proactivity, organization, and discipline is expected from all students. 4.2 Course Classroom: The classroom will be in Blackboard under this course s name and section number. Access to Blackboard is through Please refer all technical problems to the Blackboard help desk using the contact information above or on the Blackboard login page. Please read the Start Here letter (in the Blackboard classroom) and become familiar with the online classroom environment. 4.3 Access to Hawkes Learning System (HLS): If you received software with your textbook, install it per the on-screen instructions, and use the access code provided. All students must purchase a software access code. To do this, go to click on the Students menu heading near the top of the page, then under the Purchase Access Code heading, 5

6 click Get Started. In the textbox that appears, begin typing the name of this university. Once you see Texas A&M University Central Texas in the dropdown menu, click on it, then click Continue. Under the Access Code heading, click Please select your product. Discovering Business Statistics is the only option, so choose that, then click +Add. Click View Cart, then click Checkout. Follow the prompts to complete your purchase. Once you receive your access code, download it to somewhere on your computer where you will remember it. I also recommend you save it to a flash drive. You may use the software from any Web-enabled computer provided you have this access code. If you also/instead expect to use the downloaded version of the software, go to then click on download the software under the Students menu. Under Select a product to download, select Discovering Business Statistics (textbook by Nottingham, Hawkes). Click the link that is appropriate for your computer and operating system. If you use a PC, select Student Compact Install for PC, and if you use a Mac, select Student Install for Mac. If you have an option to use either a PC or a Mac, use a PC as this version of the software is slightly more reliable and is better supported. Follow the on-screen instructions to complete the installation. Normally this involves saving the installation file to your desktop, then opening it to complete the installation. If at any point in this process you need technical support, please call Hawkes at Do not contact your instructor. The Hawkes Course ID for this course is TAMUCTDBS. The first time you log into the system you will need to enter your access code (select Load from File if you have the file already saved) and then select the appropriate instructor and course (Dr. Brad Almond and G BK 311 online, respectively). After the first login, you will only need to re-enter your access code. If you have any questions about installing or activating the software, please call the Hawkes Customer Service number below. Note: While HLS is designed to be used both online and offline, students are responsible to have full internet access throughout the semester to ensure they are able to upload or download homework and exams. THE CUSTOMER SUPPORT AT HAWKES IS VERY GOOD, SO DO NOT HESITATE TO CALL THEM FOR ASSISTANCE. They are great, so don t hesitate to call for help with installing or trouble-shooting the software. I and my former students have had great success with them in the past. A real person almost always answers the phone. Their number is Ungraded Class Discussions: I have set up an optional discussion forum for you all to talk about issues and questions with each other. I have found that students often learn from each other as well as or better than they learn from an instructor because they often understand each other s problems and perspectives better than the instructor does. This forum may be accessed by selecting Discussions from the menu found on the left side of the Blackboard class home page. If I notice that several members of the class are struggling with a particular question, I may post a written or video reply with additional help. 4.5 Lectures: All lectures are pre-recorded and can be found in the respective Module folder on the homepage of the Blackboard classroom. These lectures have been prepared by Dr. Almond (your instructor). This lecture set includes both lectures (covering theory) and labs (covering practice). Not every lesson will have both a separate lecture and lab (some will combine them). These videos will also give a lot of emphasis to homework completion algorithms and procedures. This set of lectures / labs will use Excel for nearly all statistical analysis. 6

7 I strongly encourage you to view the lectures so as to keep pace with the schedule at the end of this syllabus. The schedule is the minimum recommendation: there is no penalty for listening and working ahead. However, exams must be completed according to the schedule. To hear the lectures, simply select the link for the recorded lecture. The lecture will automatically play. If it does not, please contact the Blackboard help line using the contact information above. 4.6 Assignments: This portion of the class comprises 38 lessons, broken up into 4 modules. All assignments will be administered through the Hawkes Learning System (HLS). HLS is a Web-based, artificially intelligent assessment and learning system. Each lesson allows for a practice mode and a certify mode. A student in practice mode may practice a lesson as long as he or she likes without penalty. In certify mode students are only permitted so many errors ( strikes ) before they are kicked out of the lesson. If this happens, students are still permitted to re-attempt to certify a lesson as many times as they like until they succeed. Students must successfully certify each lesson to receive credit for it merely practicing a lesson is not enough. Once a student successfully certifies a lesson (where successfully means correctly answering about 80% of the questions within a lesson this percentage varies slightly from lesson to lesson), he or she will receive full credit (100%) for the lesson. Although the mode of instruction is face-to-face in this class, there will be no traditional, paper-and-pencil homework assignments in this class. The lowest 3 lesson scores will be dropped, but this may not appear correctly in your Hawkes gradebook until the end of the semester. To allow maximum flexibility for the student, all lessons are due on the last day of the semester. However, students are strongly encouraged to complete HLS lessons as the corresponding material is introduced and covered in class. Students will not receive credit for any lessons left incomplete at the end of the semester. Thus, the only grade a student can receive for a lesson is 100% or 0%. 4.7 Exams: There will be four (4) non-cumulative exams administered during the semester as indicated on the course calendar. Exams represent the independent, unassisted work of students, and must be completed alone without the use of any resource other than those explicitly permitted or provided by your instructor. With the exception of Exam 1 (which may be taken twice), exams may be taken only once. No makeup exams will be given except in cases of emergencies for which written and official documentation is provided. All exams will be completed online within the Hawkes Learning System environment. The permitted time on each exam varies depending on length and rigor, but usually ranges between 2 to 3 hours per exam. Exact exam durations will be listed on Hawkes. The point values for each exam will vary based on the number and type of problems we are covering in Hawkes, but the weighting of each exam will be equal, and according to the scale below. Your instructor reserves the right to modify the exam structure and schedule at will, with advance notice, in order to best fulfill course objectives and assess student competencies. See the schedule below for exam availability and due dates. The first date indicates when the exam will be available to you (beginning at 12:00 a.m.). The second date indicates when the exam will be due (no later than 11:59 p.m.). 4.8 End-of-class Assessment: Near the end of the semester (see schedule below), all students will be required to complete the assessment assignment found in the Blackboard classroom (NOT in Hawkes!). This assessment is used in this course as part of a wider program of assessment that is required by the accrediting bodies for TAMUCT and for the College of Business Administration. For this assessment you will be required to conduct a statistical analysis for a particular scenario and dataset and answer a few questions related to 7

8 such things as the type of data involved and the type of statistical tools that are appropriate for analyzing them. You will also be required to use Microsoft Excel to conduct the analyses, and to provide visual evidence (i.e., computer screen shots) of your analysis. See the grading rubric on the last page of this course syllabus. This assignment counts 8% toward the final course average. This assessment will be graded according to the rubric attached to the end of this syllabus. Please note that this assessment is mandatory. Students with course averages of 92% or higher are not exempt from completing it. Students who fail to complete the assessment will receive no credit for this assignment, and will be penalized an additional 2 percentage points from their final course average. Again, the end-of-course assessment will be taken in Blackboard, not Hawkes. You will be given one (1) hour to complete the assessment, and it must be completed in a single sitting. You may use permissible course materials on this assessment (notes, computer, textbook, calculator, scratch paper). You must complete this assessment alone and unaided by another person. Academic integrity penalities will be assessed against anyone found violating this restriction. NOTE: You will fail this course if you attempt to only take the exams and not complete the required online homework assignments. 5.0 GRADING CRITERIA 5.1 Grade Computation: Students earn their course grades by completing scheduled assignments. No extra credit assignments are given. To pass this course satisfactorily, students must complete each of the graded items listed below. Failure to complete appropriate assignments and exams may result in a failing grade. Refusal to complete homework assignments will result in a failing grade. 5.2 Grading Weighting and Scale: Final grades will be calculated as follows: Possible Evaluation Item Points Percentage Homework (35@ 1.371% points ea.) Exams 11% ea.) End-of-course Assessment (see above) 80 8 Total Final course grades will be determined according to the following scale. A = 90% or better B = 80% and up to but not including 90% C = 70% and up to but not including 80% D = 60% and up to but not including 70% F = below 60% Please note that standard rounding (i.e.,.5 and up) will be used to compute final grades. There will be no exceptions to this (admittedly arbitrary but necessary) standard. 8

9 Please see the next page for the course schedule. 9

10 6.0 Course Calendar. Note that all lessons are due on Dec 10. Lecture Assigned HLS Class Topic Date* Lesson(s) / Exam Aug 25 populations and samples variables, levels of measurement Sept 1 frequency distributions 3.3; 3.4 graphical displays of data ; 3.10 Sept 8 measures of location 4.1 measures of dispersion 4.2a All assigned lessons from Chapters 1, 2, and 3, plus lessons 4.1 and 4.2a. Sept 15 percentiles 4.3 applying the standard deviation Sept 22 discrete random variables the binomial distribution 6.5 Sept 29 the normal distribution 7.2; 7.3a more on the normal distribution 7.3b; 7.3c Lessons 4.3 and from Chapter 4, plus all assigned lessons from Chapters 6 and 7 EXAM 1 (opens Sept 9) EXAM 2 (opens Sept 30) Oct 6 central limit theorem 8.3 t distribution 9.4a Oct 13 confidence intervals (z distribution) confidence intervals (t distribution) 9.4b; 9.5 Oct 20 intro to hypothesis testing hypothesis testing, 1 sample 10.4a; 10.4b Oct 27 hypothesis testing, 1 sample 10.4c hypothesis testing for 2 samples 11.1; 11.2 All assigned lessons from Chapters 8-11 EXAM 3 (opens Oct 28) Nov 3 analysis of variance correlation, scatterplots; simple regression 4.8; Nov 10 simple regression 13.8 multiple regression 14.5a Nov 17 multiple regression 14.7 chi square goodness of fit test 15.2 Dec 1 chi square test for association 15.3 control charts 17.3a; 17.3b Dec 8 control charts 17.4 catch-up and review (if needed) Lesson 4.8, plus all assigned lessons from Chapters and 17 EXAM 4 (opens Dec 8) Due Date Sept 16 Oct 7 Nov 4 Dec 11 End-of-course Assessment (see Section above) POST-TEST (opens Dec 8) Dec 11 *These represent the approximate dates around which students should view the video lectures and complete the corresponding homework in Hawkes. All due dates are fixed, however. 10

11 7.0 Drop Policy: If you discover that you need to drop this class, you must go to (or contact) the Records Office and ask for the necessary paperwork. You may also access this information online at Professors cannot drop students; this is always the responsibility of the student. The Records Office will give you a deadline by which the paperwork they give you must be completely filled out, signed, and returned to their office. Once you have returned the completed and signed form(s) to the records office, wait 24 hours before going into Warrior Web to confirm that you are no longer enrolled. If, after the 24 hours, you find that you are still enrolled, FOLLOW-UP with the records office immediately. You must continue to attend class until the procedure is complete to avoid any penalties for absence. Should you miss the deadline or fail to follow the procedure, you will receive an F in the course. (statement updated Fall 2014) 8.0 Academic Integrity: Texas A&M University Central Texas expects all students to maintain high standards of honor in personal and scholarly conduct. In this course, any and all collaboration on lesson certifications and exams (including the end-of-semester assessment) is strictly forbidden. This includes collaboration with another student, instructor, or tutor, as well as with any other individual (friend, boss, coworker, significant other, family member, etc.). Any deviation from this expectation may result in a minimum of a failing grade for the assignment and potentially a failing grade for the course. All academic dishonesty concerns will be reported to the University's Office of Student Conduct. Academic dishonesty includes, but is not limited to, cheating on an examination or other academic work, plagiarism and improper citation of sources, using another student's work, collusion, and the abuse of resource materials. When in doubt on collaboration, citation, or any issue, please contact me before taking a course of action. More information may be found at (statement updated Summer 2015) 9.0 Disability Support Services: At Texas A&M University Central Texas, we value an inclusive learning environment where every student has an equal chance to succeed and has the right to an education that is barrier-free. The Office of Disability Support and Access is responsible for ensuring that students with a disability enjoy equal access to the University's programs, services and activities. Some aspects of this course or the way the course is taught may present barriers to learning due to a disability. If you feel this is the case, please contact Disability Support and Access at (254) in Warrior Hall, Ste For more information, please visit their website at Any information you provide is private and confidential and will be treated as such. (statement updated Fall 2014) 10.0 Tutoring: Tutoring is available to all TAMUCT students, both on-campus and online. Subjects tutored include Accounting, Finance, Statistics, Mathematics, and Writing. Tutors are available at the Tutoring Center in Warrior Hall, Room 111. Visit for tutor schedules and contact info. If you have questions, need to schedule a tutoring session, or if you're interested in becoming a tutor, contact Academic Support Programs using the contact information on the above URL. 11

12 Chat live with a tutor 24/7 for almost any subject on your computer! Tutor.com is an online tutoring platform that enables TAMUCT students to log-in and receive FREE online tutoring and writing support. This tool provides tutoring in Mathematics, Writing, Career Writing, Chemistry, Physics, Biology, Spanish, Calculus, and Statistics. To access Tutor.com, log into your Blackboard account and click Online Tutoring. (statement updated Summer 2015) 11.0 Library Services: Just as computer literacy deals with general competency in the use of computers a necessary skill in a highly technological society like ours INFORMATION LITERACY focuses on research skills that prepare individuals to live and work in an information-centered society. Librarians are available to work with students in the development of information literacy, and are knowledgeable on many relevant matters including critical reasoning, the ethical use of information, and the appropriate use of secondary research techniques. Librarian services may include, but are not limited to, the following: exploring information resources such as library collections and services, identifying sources such as subject databases and scholarly journals, and executing effective search strategies. Library Resources are outlined and accessed through the following web page: The TAMUCT librarians are available to assist distance learning students doing research via and chat sessions; consult the library link provided here or the library link on the course home page to access these services. (statement updated Fall 2014) 12.0 Miscellany Please note that I do not offer extra credit opportunities in this class. 12

13 Appendix: End-of-Course Assessment Grading Rubric Satisfactory Progressing Unsatisfactory Analysis Weight 100% 50% 0% Data and variable description 10% The data types and variables were correctly identified. The data types and/or the variables were partially correctly identified. Either the data types or the variables, or both, were not correctly identified. Descriptive statistics 15% Appropriate descriptive statistics were calculated using designated software technology and discussed, given the type of data and variables. Descriptive statistics were partially correctly calculated using designated software technology and/or discussed, given the type of data and variables. Either the descriptives statistics were not calculated with designated software technology, and/or they were not discussed. Analysis method selection 20% Appropriate methods were selected for the overall analysis, based on the data types and variables, and the methods were discussed. Selected methods were partially appropriate for the overall analysis, based on the data types and variables, and the methods were discussed. Selected methods were inappropriate for overall analysis, based on the data types and variables, and/or the methods were not discussed. Analysis conducted 25% Appropriate analysis was correctly conducted using designated software technology. Appropriate analysis was partially correctly conducting using designated software technology. Analysis was either not conducted using designated software technology or not conducted correctly. Decision and/or recommendation 30% Based on the results of the analysis, the appropriate recommendations for a decision was given. Based on the results of the analysis the recommendations for a decision were partially correct. Either the recommendations for a decision was not based on the analysis, or the recommendations for a decision were incorrect. 13