MGMT 276: Statistical Inference in Management Room 120 Integrated Learning Center (ILC) Fall, 2012

1. MGMT 276: Statistical Inference in ManagementRoom 120 Integrated Learning Center (ILC)Fall, 2012 Welcome http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man

2. Screen Cabinet Cabinet Lecturer’s desk Table Computer Storage Cabinet Row A 3 4 5 19 6 18 7 17 16 8 15 9 10 11 14 13 12 Row B 1 2 3 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row C 1 2 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row D 1 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row E 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row F 27 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 28 Row G 27 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 29 10 19 11 18 16 15 13 12 17 14 28 Row H 27 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row I 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 1 Row J 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 28 27 1 Row K 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row L 20 1 19 2 18 3 17 4 16 5 15 6 7 14 13 INTEGRATED LEARNING CENTER ILC 120 9 8 10 12 11 broken desk

3. Please read: Chapters 5 - 11 in Lind book & Chapters 10, 11, 12 & 14 in Plous book: Lind Chapter 5: Survey of Probability Concepts Chapter 6: Discrete Probability Distributions Chapter 7: Continuous Probability Distributions Chapter 8: Sampling Methods and CLT Chapter 9: Estimation and Confidence Interval Chapter 10: One sample Tests of Hypothesis Chapter 11: Two sample Tests of Hypothesis Plous Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability and Risk Chapter 14: The Perception of Randomness

4. Use this as your study guide By the end of lecture today10/4/12 Measures of variability Standard deviation and Variance Counting ‘standard deviationses’ – z scores Connecting raw scores, z scores and probabilityConnecting probability, proportion and area of curve Law of Large Numbers Central Limit Theorem

5. Please click in My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z

6. Homework due – Tuesday (October 9th) On class website: Please print and complete homework worksheet #11 Dan Gilbert Reading and the Law of Large Numbers

7. Comments on Dan Gilbert Reading

8. Law of large numbers: As the number of measurements increases the data becomes more stable and a better approximation of the true (theoretical) probability As the number of observations (n) increases or the number of times the experiment is performed, the estimate will become more accurate.

9. Law of large numbers: As the number of measurements increases the data becomes more stable and a better approximation of the true signal (e.g. mean) As the number of observations (n) increases or the number of times the experiment is performed, the signal will become more clear (static cancels out) With only a few people any little error is noticed (becomes exaggerated when we look at whole group) With many people any little error is corrected (becomes minimized when we look at whole group) http://www.youtube.com/watch?v=ne6tB2KiZuk

10. Review of Homework Worksheetjust in case of questions

11. Homework review Based on data (Percent of stocks that meet reach or exceed target price on first day) Based on expert opinion - don’t have previous data for these two companies merging together Based on data (Percent of rockets that successfully launch) Based on apriori probability – not previous experience and not data-driven

12. Homework review Based on expert opinion (experience of experts), but not actual percent of space stations that have actually been critically damaged by debris. Based on actual data (percent of results that are fake pages)

13. . .8276 .1056 .2029 .1915 .3944 .4332 .3944 .3944 55 55 55 52 44 50 50 44 - 50 4 52 - 50 4 -1.5 +.5 = = 55 - 50 4 +1.25 = z of 1.5 = area of .4332 z of 1.5 = area of .1915 1.25 = area of .3944 55 - 50 4 55 - 50 4 +1.25 +1.25 = = .5000 - .3944 = .1056 z of 1.25 = area of .3944 z of 1.25 = area of .3944 .4332 +.3944 = .8276 .3944 -.1915 = .2029

14. .3264 Homework review .2152 .5143 .1255 .3888 .1736 .1736 .3888 3,000 3,500 2,500 3,500 3,000 2500 - 2708 650 3000 - 2708 650 3000 - 2708 650 -.32 = 0.45 0.45 = = z of -0.32 = area of .1255 z of 0.45 = area of .1736 z of 0.45 = area of .1736 3500 - 2708 650 3500 - 2708 650 1.22 = 1.22 = .5000 - .1736 = .3264 z of 1.22 = area of .3888 z of 1.22 = area of .3888 .3888 +.1255= .5143 .3888 - .1736 = .2152

15. .0764 Homework review .9236 .1185 .4236 .4236 .4236 .3051 10 12 20 20 10 - 15 3.5 -1.43 = 20 - 15 3.5 20 - 15 3.5 1.43 1.43 = = z of -1.43 = area of .4236 z of 1.43 = area of .4236 z of 1.43 = area of .4236 12 - 15 3.5 -0.86 = .5000 + .4236 = .9236 .5000 - .4236 = .0764 z of -.86 = area of .3051 .4236 – .3051 = .1185

16. Variability and means x = mean + z σ 50th Percentile 75th Percentile 25th Percentile .25 .25 .25 .25 30 z =.67 z =.67

17. Variability and means Variability and means 38 40 44 48 52 56 58 The variability is different…. The mean is the same … What might the standard deviation be? What might this be an example of? 40 44 48 52 56

18. Variability and means Heights of elementary students 38 40 44 48 52 56 58 Heights of 3rd graders What might the standard deviation be? What might this be an example of? 40 44 48 52 56 Other examples?

19. Variability and means Remember, there is an implied axis measuring frequency f 38 40 44 48 52 56 58 f 40 44 48 52 56

20. Variability and means Hours of homework – (kids K – 12) 0 4 8 12 16 Hours of homework – (7 grade) What might the standard deviation be? What might this be an example of? 0 4 8 12 16 Other examples?

21. Variability and means Driving ability – (16 - 90) 40 50 60 70 80 90 100Score on driving test Driving ability – (35 year olds) What might the standard deviation be? What might this be an example of? 40 50 60 70 80 90 100 Score on driving test Other examples?

22. Variability and means Distributions same mean different variability Final exam scores “C” students versus whole class Birth weight within a typical family versus within the whole community Running speed 30 year olds vs. 20 – 40 year olds Number of violent crimes Milwaukee vs. whole Midwest Social distance (personal space) California vs international community

23. Variability and means Distributions different mean same variability Performance on a final exam Before versus after taking the class 40 50 60 70 80 90 100 Score on final (before taking class) 40 50 60 70 80 90 100 Score on final (before taking class)

24. Variability and means Distributions different mean same variability Height of men versus women 62 64 66 68 70 72 74 76Inches in height (women) 62 64 66 68 70 72 74 76Inches in height (men)

25. Variability and means Distributions different mean same variability Driving ability Talking on a cell phone or not 2 4 6 8 10 12 14 16Number of errors (not on phone) 2 4 6 8 10 12 14 16Number of errors (on phone)

26. Variability and means Comparing distributions different mean same variability Performance on a final exam Before versus after taking the class Height of men versus women Driving ability Talking on a cell phone or not

27. . Writing AssignmentComparing distributions (mean and variability) • Think of examples for these three situations • same mean but different variability • same variability but different means • same mean and same variability (different groups) • estimate standard deviation • calculate variance • for each curve find the raw score for the z’s given

28. Thank you! See you next time!!