1. Statistics Fall 2007

2. Introduction2 Wed, Aug 22, 2007 Introduction Dr. Robb T. Koether Office: Bagby 114 Office phone: 223-6207 Home phone: 392-8604 (before 11:00 p.m.) Office hours: 2:30-4:00 MWRF, 3:30 – 4:00 T  Other hours by appointment E-mail: rkoether@hsc.edurkoether@hsc.edu Web page: http://people.hsc.edu/faculty- staff/robbkhttp://people.hsc.edu/faculty- staff/robbk

3. Introduction3 Wed, Aug 22, 2007 The Course The class meets in Bagby 022 at 8:30 - 9:20 MWF and at 2:30 – 3:20 T. The text for the course is Interactive Statistics, 3rd ed., by Martha Aliaga and Brenda Gunderson.Interactive Statistics, 3rd ed. The web page for this course is at http://people2.hsc.edu/faculty-staff/robbk/Math121

4. Introduction4 Wed, Aug 22, 2007 Introduction Syllabus Lectures Assignments Page xi – Interactive Exercises Page xvi – Graphing Calculator

5. Introduction5 Wed, Aug 22, 2007 Grading There will be  Weekly quizzes  Three tests  A final exam

6. Introduction6 Wed, Aug 22, 2007 Grading In the final average, these will have the following weights: CategoryWeight Average of quizzes30% Average of the tests50% The final exam20%

7. Introduction7 Wed, Aug 22, 2007 Homework The homework is the most important part of this course. Learning mathematics requires gaining knowledge and understanding, but more importantly doing mathematics is a skill. You should not expect to acquire a skill by listening to a lecturer talk about it. It takes practice. Do all of the homework every day.

8. Introduction8 Wed, Aug 22, 2007 Homework More importantly, do not put off doing the homework until the night before the quiz. You will not be able to learn that much material in one night. Most importantly of all, do not put off doing the homework until the day before a test. By then it is too late to learn it.

9. Introduction9 Wed, Aug 22, 2007 Homework At the beginning of each class meeting (except on Tuesdays), I will spend up to 10 minutes working one or two homework problems in detail from previous assignments. You may request a problem that you would like to see worked. Of course, outside of class, I will help you with as many problems as I can.

10. Introduction10 Wed, Aug 22, 2007 Quizzes Each Tuesday there will be a 10-minute quiz. The quiz will contain 1 to 3 questions taken from the previous week's homework assignments. The problems will be copied verbatim from the book.

11. Introduction11 Wed, Aug 22, 2007 Tests The test schedule is as follows: TestDateCoverage #1Fri, Sep 21Chapters 1, 2, 3, 4 #2Fri, Oct 19Chapters 5, 6, 7 #3Fri, Nov 16Chapters 8, 9, 10, 11

12. Introduction12 Wed, Aug 22, 2007 The Final Exam The final exam will be cumulative. It will be given in this classroom at the time stated in the exam schedule. Everyone must take it. It will not be rescheduled. Do not schedule a flight home before the exam! You will lose your ticket.

13. Introduction13 Wed, Aug 22, 2007 Attendance Attendance will be checked at the beginning of each class. Two late arrivals will be counted as one absence. The only valid excuses for missing class are  An illness which includes a visit to the Health Center or a doctor  An approved college activity  A true emergency  Any absence excused by the Dean of Students

14. Introduction14 Wed, Aug 22, 2007 Attendance Sending me an e-mail or leaving me a voice message does not excuse you from class.

15. Introduction15 Wed, Aug 22, 2007 Attendance When assigning final grades, attendance will be taken into account. AbsencesAction 0 – 2Grade bonus 3 – 5Neutral 6 – 8Grade penalty > 8Withdrawal

16. Introduction16 Wed, Aug 22, 2007 Calculators A calculator will be necessary for this course. I strongly recommend the TI-83 or the TI- 84.

17. Introduction17 Wed, Aug 22, 2007 The Honor Code Quizzes, tests, and the final exam are pledged.

18. Introduction18 Wed, Aug 22, 2007 Classroom Etiquette During a lecture, you are free to ask questions. It is polite to raise your hand first and wait to be called on. You should not talk to other students while I am talking. While working assigned problems in class, you are free to talk to other students provided you are talking about the assigned problems.

19. Introduction19 Wed, Aug 22, 2007 Classroom Etiquette Do not make leave the room during the class.  If necessary, use the bathroom before coming to class.  If you are thirsty, get a drink before class. Do not sleep in class. Do not work on assignments from other classes during class. Do not read the newspaper during class.

20. Introduction20 Wed, Aug 22, 2007 Goals of this Course To learn statistics.  The theoretical basis of the statistical method.  How to perform statistical tests.  How to interpret statistics. To become a more sophisticated thinker. To become a more sophisticated consumer of information.

21. Introduction21 Wed, Aug 22, 2007 Goals of this Course To get you through your freshman year with a decent GPA.

22. Introduction22 Wed, Aug 22, 2007 The Scientific Method Formulate a theory. Collect some data. Summarize the results. Make a decision.

23. Introduction23 Wed, Aug 22, 2007 The Scientific Method Formulate a theory – Chapter 1. Collect some data. Summarize the results. Make a decision.

24. Introduction24 Wed, Aug 22, 2007 The Scientific Method Formulate a theory – Chapter 1. Collect some data – Chapters 2 – 3. Summarize the results. Make a decision.

25. Introduction25 Wed, Aug 22, 2007 The Scientific Method Formulate a theory – Chapter 1. Collect some data – Chapters 2 – 3. Summarize the results – Chapters 4 – 5. Make a decision.

26. Introduction26 Wed, Aug 22, 2007 The Scientific Method Formulate a theory – Chapter 1. Collect some data – Chapters 2 – 3. Summarize the results – Chapters 4 – 5. Make a decision – Chapters 9 – 14.

27. Introduction27 Wed, Aug 22, 2007 The Scientific Method Formulate a theory – Chapter 1. Collect some data – Chapters 2 – 3. Summarize the results – Chapters 4 – 5. Make a decision – Chapters 9 – 14. Theoretical underpinnings – Chapters 6 – 8.

28. Introduction28 Wed, Aug 22, 2007 Formulate a Theory We are wondering whether a particular die is fair. That is, does each number occur just as often as every other number? For example, if we roll the die 600 times, we expect to get each number 100 times.

29. Introduction29 Wed, Aug 22, 2007 Formulate a Theory Or do we?

30. Introduction30 Wed, Aug 22, 2007 Formulate a Theory The theory that the die is fair will be tested by posing it as a question with two competing answers. Question: Does the distribution of observed rolls match what we would expect to see if the die were fair?

31. Introduction31 Wed, Aug 22, 2007 Formulate a Theory The possible answers (yes and no) are stated more precisely as two competing hypotheses:  “Null hypothesis” The die is fair. Any deviations from the expected observation are due entirely to chance.  “Research hypothesis” The die is not fair. Any deviations from the expected observations are due to the bias in the die.

32. Introduction32 Wed, Aug 22, 2007 Collect Some Data So we roll the die 600 times and get the following results. Number123456 Expected100 Observed951068997 116

33. Introduction33 Wed, Aug 22, 2007 Two Possible Explanations There is a discrepancy. Can it be explained by chance?

34. Introduction34 Wed, Aug 22, 2007 Summarize the Results We use the TI-83 or TI-84, and compute a special quantity:  2 = 4.56.

35. Introduction35 Wed, Aug 22, 2007 Summarize the Results We use the TI-83 or TI-84, and compute a special quantity:  2 = 4.56. So what?

36. Introduction36 Wed, Aug 22, 2007 Summarize the Results If the die really is fair, then statistical theory says that we expect this calculation to yield a value between 0 and 11.070, with the value expected to be very close to 5.

37. Introduction37 Wed, Aug 22, 2007 Make a Decision Since  2 is within this range, we conclude that the “null hypothesis” is correct: The die is fair.

38. Introduction38 Wed, Aug 22, 2007 An Important Question Does this procedure prove that the die is fair?

39. Introduction39 Wed, Aug 22, 2007 An Objection Our antagonist was arguing that this die turned up 6’s too often. He claims that our data supports his assertion. How do we deal with that?

40. Introduction40 Wed, Aug 22, 2007 Collect More Data So we roll the die 6000 times and get the following results. Number123456 Expected 1000 Observed 9459831023101510001034

41. Introduction41 Wed, Aug 22, 2007 Collect More Data This time we get  2 = 5.224. This is extremely close to the value that the theory predicts for a fair die. At this point, we tell our antagonist to go study statistics.