2. Stage Screen Row B 13 121110 20191817 14 13 121110 19181716 1514 Gallagher Theater 16 65879 Row R 6 58 7 9 Lecturer’s desk Row A Row B Row C 4 3 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 3 21 3 2 43 21 Row A 17 16 15 Row A Row C 131211 10 1514 6 58 7 9 Row D 13121110 1514 16 6 58 7 9 20191817 Row D Row E 131211 10 1514 6 58 7 9 19181716 Row E Row F 13121110 1514 16 6 58 7 9 20191817 Row F Row G 13121110 1514 6 58 7 9 19181716 Row G Row H 13121110 1514 16 6 58 7 9 20191817 Row H Row I 13121110 1514 6 58 7 9 19181716 Row I Row J 13121110 1514 16 6 58 7 9 20191817 Row J Row K 13121110 1514 6 58 7 9 19181716 Row K Row L 13121110 1514 16 6 58 7 9 20 191817 Row L Row M 13121110 1514 6 58 7 9 19181716 Row M Row N 13121110 1514 16 6 5879 20191817 Row N Row O 13121110 1514 6 58 7 9 19181716 Row O Row P 13121110 1514 16 6 5879 20191817 Row P Row Q 13121110 6 5879 161514 Row Q 4 4 Row R 10 879 Row S Row B Row C Row D Row E Row F Row G Row H Row I Row J Row K Row L Row M Row N Row O Row P Row Q 26Left-Handed Desks A14, B16, B20, C19, D16, D20, E15, E19, F16, F20, G19, H16, H20, I15, J16, J20, K19, L16, L20, M15, M19, N16, P20, Q13, Q16, S4 5 Broken Desks B9, E12, G9, H3, M17 Need Labels B5, E1, I16, J17, K8, M4, O1, P16 Left handed

3. Stage Screen 2213 121110 Row A Row B Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 17 Row C Row D Row E Projection Booth 65 4 table Row C Row D Row E 30 27 26252423 282726 2524 23 3127262524 23 R/L handed broken desk 16 1514 13 12 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 Social Sciences 100 Row N Row O Row P Row Q Row R 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 8 7 9 65 4 8 7 9 3 2 6 5 48793 2 1 6 5 48793 2 1 Row F Row G Row H Row J Row K Row L Row M Row N Row O Row P Row Q Row R 6 5 48793 2 1 6 5 48793 2 1 Row I 2213 121110 2019181716151421 Row I 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 Lecturer’s desk 6 5 48793 2 1 262524 23 302928 Row F Row G Row H Row J Row K Row L Row M Row N Row O Row P Row Q Row R Row I 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 Row B 2928 27

4. MGMT 276: Statistical Inference in Management Fall, 2014 Green sheets

5. Reminder Talking or whispering to your neighbor can be a problem for us – please consider writing short notes. A note on doodling

7. Before our next exam (October 21 st ) Lind (5 – 11) 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 (10, 11, 12 & 14) Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability and Risk Chapter 14: The Perception of Randomness Schedule of readings We’ll be jumping around some…we will start with chapter 7

8. Homework due – Tuesday (October 13 th ) On class website: Please print and complete homework worksheet #10 Approaches to probabilities and more z scores / probability transformations

9. By the end of lecture today 10/9/14 Use this as your study guide Connecting probability, proportion and area of curve Percentiles Probability of an event Complement of the probability of an event Mutually exclusive characteristics Collectively Exhaustive Events Union and Intersection of two events Special Law of Addition Conditional Probabilities Central Limit Theorem

10. Mean = 100 Standard deviation = 5 If we go up one standard deviation z score = +1.0 and raw score = 105 If we go down one standard deviation z score = -1.0 and raw score = 95 If we go up two standard deviations z score = +2.0 and raw score = 110 If we go down two standard deviations z score = -2.0 and raw score = 90 If we go up three standard deviations z score = +3.0 and raw score = 115 If we go down three standard deviations z score = -3.0 and raw score = 85 z score: A score that indicates how many standard deviations an observation is above or below the mean of the distribution z score = raw score - mean standard deviation 85 90 95 100 105 110 115 z = -1 z = +1 z = -2 z = +2 z = -3 z = +3 68% 95% 99.7%

11. Raw scores, z scores & probabilities Raw Scores Area & Probability Z Scores Formula z table Have raw score Find z Have z Find raw score Have area Find z Have z Find area

12. Hint: Always draw a picture! Homework worksheet

13. .

14. .

15. .

16. .

17. . z = 33-30 2 z = 1.5 Go to table.4332

18. . z = 33-30 2 z = 1.5 Go to table.4332

19. z = 33-30 2 z = 1.5 Go to table.4332.5000 -.4332 =.0668 z = 29-30 2 z =-.5 Go to table.1915.5000 +.1915 =.6915 z = 25-30 2 z = -2.5.4938.4938 +.1915 =.6853 z = 31-30 2 z =.5 Go to table.1915 z = 27-30 2 z = -1.5.4332.5000 -.4332 =.0668

20. Problem 12:.5000 -.3413 =.1587 Problem 13: 30 Problem 14: 28 and 32 Problem 11:.5000 +.4938 =.9938

21. . 77 th percentile Go to table.2700 nearest z =.74 x = mean + z σ = 30 + (.74)(2) = 31.48

22. . 13 th percentile Go to table.3700 nearest z = 1.13 x = mean + z σ = 30 + (-1.13)(2) = 27.74 Note:.13 +.37 =.50

23. Problem 17: 68% or.68 or 68.26% or.6826 Problem 18: 95% or.95 or 95.44% or.9544 Problem 19: 99.70% or.9970 Problem 20: 27.34% or.2734

24. z = 230-200 40 z =.75 Go to table.2734 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)

25. Problem 21: 40.13% or.4013 Problem 22: 69.15% or.6915 Problem 23: 18.41% or.1841 Problem 24: 28.81% or.2881 Problem 25: 96.93% or.9693 or 96.93% or.9693 Problem 26:.89% or.0089 Problem 27: 95.99% or.9599 Problem 28: 4.01% or.0401 Problem 29: 293.2 Problem 30: 182.4 Problem 31: 190 x = mean + z σ = 200 + (2.33)(40) = 293.2 x = mean + z σ = 200 + (-.44)(40) = 182.4 Problem 32: 217.6

26. 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 Number of applicants Probability of getting a rotten apple Number of rotten apples Number of apples 5 100 5% chance of getting a rotten apple 400 600 66% chance of getting admitted

27. 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 182 200 91% chance of hitting a corvette =.91 10% of people who buy a house with no pool build one. What is the likelihood that Bob will? “There is a 20% chance that a new stock offered in an initial public offering (IPO) will reach or exceed its target price on the first day.” “More than 30% of the results from major search engines for the keyword phrase “ring tone” are fake pages created by spammers.”

28. 2. Classic probability: a priori probabilities based on logic rather than on data or experience. All options are equally likely (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 Number of sides In tossing a coin what is probability of getting a tail Number of sides with a 1 Number of sides 1 2 50% chance of getting a tail 1 6 16% chance of getting a two = = Lottery Likelihood get question right on multiple choice test Chosen at random to be team captain

29. 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 Likelihood that company will invent new type of battery Likelihood get a ”B” in the class 60% chance that Patriots will play at Super Bowl

30. Approach Example Empirical There is a 2 percent chance of twins in a randomly-chosen birth Classical There is a 50 % probability of heads on a coin flip. Subjective There is a 5% chance that Verizon will merge with Sprint

31. 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 If P(A) = 0, then the event cannot occur. If P(A) = 1, then the event is certain to occur.

32. The probabilities of all simple events must sum to 1 For example, if the following number of purchases were made by P(S) = P(E 1 ) + P(E 2 ) + … + P(E n ) = 1 credit card: 32% debit card: 20% cash: 35% check: 13% Sum =100% P(credit card) =.32 P(debit card) =.20 P(cash) =.35 P(check) =.13 Sum =1.0 Probability

33. 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 into an educational program 66% chance of “admitted” 34% chance of “not admitted” 100% chance of admitted or not 5% chance of “rotten apple” Probability of getting a rotten apple 95% chance of “not rotten apple” 100% chance of rotten or not

34. Two mutually exclusive characteristics: if the occurrence of any one of them automatically implies the non-occurrence of the remaining characteristic Two mutually exclusive characteristics: if the occurrence of any one of them automatically implies the non-occurrence of the remaining characteristic Two events are mutually exclusive if they cannot occur at the same time (i.e. they have no outcomes in common). Two propositions that logically cannot both be true. http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-manWarranty No Warranty For example, a car repair is either covered by the warranty (A) or not (B).

35. Events are collectively exhaustive if their union is the entire sample space S. Events are collectively exhaustive if their union is the entire sample space S. Two mutually exclusive, collectively exhaustive events are dichotomous (or binary) events. Two mutually exclusive, collectively exhaustive events are dichotomous (or binary) events. For example, a car repair is either covered by the warranty (A) or not (B). Warranty No Warranty Collectively Exhaustive Events

36. Satirical take on being “mutually exclusive” Recently a public figure in the heat of the moment inadvertently made a statement that reflected extreme stereotyping that many would find highly offensive. It is within this context that comical satirists have used the concept of being “mutually exclusive” to have fun with the statement. http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man Transcript: Speaker 1: “He’s an Arab” Speaker 2: “No ma’am, no ma’am. He’s a decent, family man, citizen…” Arab Decent, family man Warranty No Warranty

37. Union versus Intersection Union of two events means Event A or Event B will happen Intersection of two events means Event A and Event B will happen Also called a “joint probability” ∩ P(A B) P(A ∩ B)

38. 5A-37 union The union of two events: all outcomes in the sample space S that are contained either in event A or in event B or both (denoted A  B or “A or B”).  may be read as “or” since one or the other or both events may occur.

39. What is probability of drawing a red card or a queen? It is the possibility of drawing It is the possibility of drawing either a queen (4 ways) or a red card (26 ways) or both (2 ways). either a queen (4 ways) or a red card (26 ways) or both (2 ways). what is Q  R? union The union of two events: all outcomes contained either in event A or in event B or both (denoted A  B or “A or B”).

40. P(Q) = 4/52 (4 queens in a deck) = 4/52 + 26/52 – 2/52 P(Q  R) = P(Q) + P(R) – P(Q  R) = 28/52 =.5385 or 53.85% P(R) = 26/52 (26 red cards in a deck) P(Q  R) = 2/52 (2 red queens in a deck) Probability of picking a Queen Probability of picking a Red Probability of picking both R and Q 4/52 26/52 2/52 When you add the P(A) and P(B) together, you count the P(A and B) twice. So, you have to subtract P(A  B) to avoid over- stating the probability.

41. Union versus Intersection Union of two events means Event A or Event B will happen Intersection of two events means Event A and Event B will happen Also called a “joint probability” ∩ P(A B) P(A ∩ B)

42. what is Q  R? The intersection of two events: all outcomes contained in both event A and event B (denoted A  B or “A and B”) What is probability of drawing red queen? It is the possibility of drawing both a queen and a red card (2 ways).

43. If two events are mutually exclusive (or disjoint) their intersection is a null set (and we can use the “Special Law of Addition”) Intersection of two events means Event A and Event B will happen Examples: If A = Poodles If B = Labradors P(A ∩ B) = 0 Poodles and Labs: Mutually Exclusive (assuming purebred) mutually exclusive

44. Intersection of two events means Event A and Event B will happen P(A ∩ B) = 0 If two events are mutually exclusive (or disjoint) their intersection is a null set (and we can use the “Special Law of Addition”) Examples: If A = Poodles If B = Labradors ∩ P(A B) = P(A) +P(B) P(poodle or lab) = P(poodle) + P(lab) P(poodle or lab) = (.10) + (.15) = (.25) What’s the probability of picking a poodle or a lab at random from pound? Dog Pound (let’s say 10% of dogs are poodles) (let’s say 15% of dogs are labs) Poodles and Labs: Mutually Exclusive (assuming purebred )

45. Conditional Probabilities Probability that A has occurred given that B has occurred P(A | B) = P(A ∩ B) P(B) Denoted P(A | B): The vertical line “ | ” is read as “given.” The sample space is restricted to B, an event that has occurred. A  B is the part of B that is also in A. The ratio of the relative size of A  B to B is P(A | B).

46. Of the population aged 16 – 21 and not in college: Unemployed13.5% No high school diploma29.05% Unemployed with no high school diploma 5.32% What is the conditional probability that a member of this population is unemployed, given that the person has no diploma? Conditional Probabilities Probability that A has occurred given that B has occurred P(U) =.1350 P(ND) =.2905 P(U  ND) =.0532 P(A | B) = P(A ∩ B) P(B).0532.2905 = =.1831 or 18.31%

47. Of the population aged 16 – 21 and not in college: Unemployed13.5% No high school diploma29.05% Unemployed with no high school diploma 5.32% What is the conditional probability that a member of this population is unemployed, given that the person has no diploma? Conditional Probabilities Probability that A has occurred given that B has occurred P(U) =.1350 P(ND) =.2905 P(U  ND) =.0532 P(A | B) = P(A ∩ B) P(B).0532.2905 = =.1831 or 18.31%