MGMT 276: Statistical Inference in Management.

1. MGMT 276: Statistical Inference in Management. Welcome

2. Please read: Chapters 5 - 9 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 Plous Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability and Risk Chapter 14: The Perception of Randomness We’ll be jumping around some…we will start with chapter 7

3. Use this as your study guide By the end of lecture today2/22/11 Measures of variability Standard deviation and Variance Exploring relationship between mean and variability Empirical, classical and subjective approaches Probability of an event Complement of an event; Union of two events Intersection of two events; Mutually exclusive events Collectively exhaustive events Conditional probability Law of Large Numbers Central Limit Theorem

4. Please click in Homework due next class - (Due February 27th) My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z Complete probability worksheet available on class website Please double check – All cell phones other electronic devices are turned off and stowed away Turn your clicker on

5. Standard deviation: The average amount by which observations deviate on either side of their mean These would be helpful to know by heart – please memorize these formula Fun Fact: Standard deviation squared = variance

6. 2 sd above and below mean 95% 1 sd above and below mean 68% 3 sd above and below mean 99.7% These would be helpful to know by heart – please memorize areas

7. Raw scores, z scores & probabilities 2 sd above and below mean 95% • Notice: • 3 types of numbers • raw scores • z scores • probabilities z = -2 z = +2 Mean = 50 S = 10 (Note S = standard deviation) If we go up two standard deviations z score = +2.0 and raw score = 70 If we go down two standard deviations z score = -2.0 and raw score = 30

8. If score is within 2 standard deviations (z < 2) “not unusual score” If score is beyond 2 standard deviations (z = 2 or up to 3) “is unusual score” If score is beyond 3 standard deviations (z = 3 or up to 4) “is an outlier” If score is beyond 4 standard deviations (z = 4 or beyond) “is an extreme outlier”

9. Homework Worksheet: Problem 1 1 sd 1 sd .68 30 32 28

10. Homework Worksheet: Problem 2 2 sd 2 sd .95 32 28 34 26 30

11. Homework Worksheet: Problem 3 3 sd 3 sd .997 24 36 32 28 34 26 30

12. Homework Worksheet: Problem 4 .50 24 36 32 28 34 26 30

13. Homework Worksheet: Problem 5 Go to table 33-30 z = 1.5 z = .4332 2 .4332 24 36 32 28 34 26 30

14. Homework Worksheet: Problem 6 Go to table 33-30 z = 1.5 z = .4332 2 .9332 .4332 .5000 24 36 32 28 34 26 30

15. 77th percentile Go to table nearest z = .74 .2700 x = mean + z σ = 30 + (.74)(2) = 31.48 .7700 .27 .5000 24 36 ? 28 34 26 30 31.48

16. 13th percentile Go to table nearest z = 1.13 .3700 x = mean + z σ = 30 + (-1.13)(2) = 27.74 .37 .50 .13 ? 24 36 32 27.74 34 26 30

17. Please use the following distribution with a mean of 200 • and a standard deviation of 40. Find the area under the curve between scores of 200 and 230. Start by filling in the desired information on curve 20 (to the right)(Note this one will require you to calculate a z-score for a raw score of 230 and use the z-table) Go to table 230-200 z = .75 z = .2734 40 .2734 80 320 240 160 280 120 200

18. 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

19. 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?

20. 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

21. 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?

22. 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?

23. 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

24. 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)

25. 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)

26. 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)

27. 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

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

29. What is probability 1. Empirical probability: relative frequency approach Number of observed outcomes Number of observations Probability of getting into an educational program Number of people they let in 400 66% chance of getting admitted Number of applicants 600 Probability of getting a rotten apple 5% chance of getting a rotten apple Number of rotten apples 5 Number of apples 100

30. What is probability 1. Empirical probability: relative frequency approach Number of observed outcomes Number of observations Probability of hitting the corvette Number of carts that hit corvette Number of carts rolled 182 = .91 200 91% chance of hitting a corvette

31. 2. Classic probability: a priori probabilities based on logic rather than on data or experience. We assume we know the entire sample space as a collection of equally likely outcomes (deductive rather than inductive). Number of outcomes of specific event Number of all possible events In throwing a die what is the probability of getting a “2” Number of sides with a 2 1 16% chance of getting a two = Number of sides 6 In tossing a coin what is probability of getting a tail 1 Number of sides with a 1 50% chance of getting a tail = 2 Number of sides

32. 3. Subjective probability: based on someone’s personal judgment (often an expert), and often used when empirical and classic approaches are not available. There is a 5% chance that Verizon will merge with Sprint Bob says he is 90% sure he could swim across the river

34. Summary of Types of Probability

35. If P(A) = 0, then the event cannot occur. If P(A) = 1, then the event is certain to occur. The probability of an event is the relative likelihood that the event will occur. The probability of event A [denoted P(A)], must lie within the interval from 0 to 1: 0 <P(A) < 1

36. Probability The probabilities of all simple events must sum to 1 P(S) = P(E1) + P(E2) + … + P(En) = 1 For example, if the following number of purchases were made by

37. What is the complement of the probability of an event • The probability of event A = P(A). • The probability of the complement of the event A’ = P(A’) • A’ is called “A prime” • Complement of A just means probability of “not A” • P(A) + P(A’) = 100% • P(A) = 100% - P(A’) • P(A’) = 100% - P(A) Probability of getting a rotten apple 5% chance of “rotten apple” 95% chance of “not rotten apple” 100% chance of rotten or not Probability of getting into an educational program 66% chance of “admitted” 34% chance of “not admitted” 100% chance of admitted or not

38. Thank you! See you next time!!