Screen Stage Lecturer’s desk Gallagher Theater Row A Row A Row A Row B 17 16 15 14 13 12 11 10 9 8 7 6 5 4 Row A 3 2 1 Row A Left handed Row B 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row B 4 3 2 1 Row B Row C 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row C 4 3 2 1 Row C Row D 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row D 4 3 2 1 Row D Row E 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row E 4 3 2 1 Row E Row F 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row F 4 3 2 1 Row F Row G 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row G 4 3 2 1 Row G Row H 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row H 4 3 2 1 Row H Row I 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row I 4 3 2 1 Row I Row J 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row J 4 3 2 1 Row J Row K 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row K 4 3 2 1 Row K Row L 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row L 4 3 2 1 Row L Row M 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row M 4 3 2 1 Row M Row N 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row N 4 3 2 1 Row N Row O 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row O 4 3 2 1 Row O Need Labels B5, E1, I16, J17, K8, M4, O1, P16 Row P 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 Row P 4 3 2 1 Row P Row Q 16 15 14 13 12 11 10 9 8 7 6 5 4 Row Q 3 2 1 Row Q Row R Gallagher Theater 4 3 2 Row R 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 Row S 10 9 8 7 4 3 2 1 Row S

Screen Stage Social Sciences 100 Lecturer’s desk broken desk R/L handed Row A 17 16 15 14 13 12 Row B 27 26 25 24 23 Row B 22 21 20 19 18 17 16 15 14 13 12 11 10 Row C 28 27 26 25 24 23 Row C 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 Row C Row D 30 29 28 27 26 25 24 23 Row D 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 Row D Row E 31 30 29 28 27 26 25 24 23 Row E 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row E Row F 31 30 29 28 27 26 25 24 23 Row F 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row F Row G 31 30 29 28 27 26 25 24 23 Row G 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row G Row H 31 30 29 28 27 26 25 24 23 Row H 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row H Row I 31 30 29 28 27 26 25 24 23 Row I 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row I Row J 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row J Row J 31 30 29 28 27 26 25 24 23 23 Row K 22 13 12 11 10 9 8 7 6 5 2 1 Row K 31 30 29 28 27 26 25 24 21 20 19 18 17 16 15 14 4 3 Row K Row L 31 30 29 28 27 26 25 24 23 Row L 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row L Row M 31 30 29 28 27 26 25 24 23 Row M 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row M Row N 31 30 29 28 27 26 25 24 23 Row N 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row N Row O 31 30 29 28 27 26 25 24 23 Row O 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row O 23 Row P 9 8 7 6 5 4 3 2 1 Row P 31 30 29 28 27 26 25 24 22 21 20 19 18 17 16 15 14 13 12 11 10 Row P Row Q 31 30 29 28 27 26 25 24 23 Row Q 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row Q Row R 31 30 29 28 27 26 25 24 23 Row R 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row R table broken desk 9 8 7 6 5 4 3 2 1 Projection Booth

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

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

Schedule of readings Before next exam: September 25th Please read chapters 1 - 4 & Appendix D & E in Lind Please read Chapters 1, 5, 6 and 13 in Plous Chapter 1: Selective Perception Chapter 5: Plasticity Chapter 6: Effects of Question Wording and Framing Chapter 13: Anchoring and Adjustment

No Homework Just study for exam Exam 1 – This Thursday September 25th Study guide is online Bring 2 calculators (remember only simple calculators, we can’t use calculators with programming functions) Bring 2 pencils (with good erasers) Bring ID

By the end of lecture today 9/23/14 Use this as your study guide By the end of lecture today 9/23/14 Characteristics of a distribution Standard Deviation Variance Empirical Rule (areas under the curve) Common and unusual scores, outliers and extreme outliers Review for Exam 1

Review of Homework Worksheet

Review of Homework Worksheet 3 – 5 = -2 -22= 4 6 – 5 = +1 -2 1 3 -1 4 1 9 12= 1 3 -3 -1 1 9 1 50 36 36 2 = 2 10 - 1 5 4.5 Mode = 4 2 8 6

Review of Homework Worksheet -12= 1 5 – 6 = -1 -1 2 3 1 4 9 22= 4 8 – 6 = +2 -1 3 1 -5 1 9 25 60 52 2.4 52 = 2.4 10 - 1 6 5.5 Mode = 5 1 9 8

Review of Homework Worksheet Must be complete and must be stapled Hand in Homework

Overview Frequency distributions The normal curve Mean, Median, Mode, Trimmed Mean Standard deviation, Variance, Range Mean Absolute Deviation Skewed right, skewed left unimodal, bimodal, symmetric Review

Let’s build it up again… U of A Baseball team Deviation scores Diallo is 0” Let’s build it up again… U of A Baseball team Preston is 2” Mike is -4” Hunter is -2 Shea is 4 David is 0” David Shea 5’8” 5’10” 6’0” 6’2” 6’4”

“Sum of Squares” “Sum of Squares” “Sum of Squares” “Sum of Squares” Standard deviation: The average amount by which observations deviate on either side of their mean “Sum of Squares” “Sum of Squares” “Sum of Squares” “Sum of Squares” Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David 0” Preston is 2” Deviation scores Remember, it’s relative to the mean “n-1” is “Degrees of Freedom” “n-1” is “Degrees of Freedom” Generally, (on average) how far away is each score from the mean? Based on difference from the mean Mean Remember, We are thinking in terms of “deviations” Diallo Please memorize these Preston Shea Mike Review

Let’s estimate some standard deviation values Standard deviation is a ‘spread’ score We’re estimating the typical distance score (distance of each score from the mean)

Price per Movie Package What’s the ‘typical’ or standard deviation? Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) 12 10 Frequency 8 6 4 2 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package What’s the ‘typical’ or standard deviation? Mean = $37 Range = $27 - $47 Standard Deviation = 3.5

Price per Movie Package Deviation scores Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) 0,0,0,0,0,0,0,0,0 What is the most common score? What is the most common “deviation score”? 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package 12 10 8 6 4 2 Frequency Deviation = 0 What is the least common “deviation scores”? $27 – $37 = -$10 $47 – $37 = $10 What’s the largest possible deviation? Mean = $37 Range = $27 - $47

Price per Movie Package Deviation scores Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) 0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 What is the deviation score for $38? 12 Deviation = 1 10 Frequency 8 6 4 2 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package Mean = $37 Range = $27 - $47

Price per Movie Package Deviation scores Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) 0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 What is the deviation score for $39? 12 10 Deviation = 2 Frequency 8 6 4 2 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package Mean = $37 Range = $27 - $47

Price per Movie Package Deviation scores Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 What is the deviation score for $40? 12 10 Frequency 8 Deviation = 3 6 4 2 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package Mean = $37 Range = $27 - $47

Price per Movie Package Deviation scores Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 What is the deviation score for $41? 12 10 Frequency 8 Deviation = 4 6 4 2 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package Mean = $37 Range = $27 - $47

Price per Movie Package Deviation scores Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 What is the deviation score for $42? 12 10 Frequency 8 Deviation = 5 6 4 2 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package Mean = $37 Range = $27 - $47

Price per Movie Package Deviation scores Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 12 What is the deviation score for $43? 10 Frequency 8 6 Deviation = 6 4 2 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package Mean = $37 Range = $27 - $47

Price per Movie Package Deviation scores Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 12 What is the deviation score for $44? 10 Frequency 8 6 Deviation = 7 4 2 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package Mean = $37 Range = $27 - $47

Price per Movie Package Deviation scores Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 8,8,8 12 10 Frequency 8 6 Deviation = 8 4 2 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package What is the deviation score for $45? Mean = $37 Range = $27 - $47

Price per Movie Package Deviation scores Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 8,8,8 9,9 12 10 Frequency 8 6 Deviation = 9 4 2 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package What is the deviation score for $46? Mean = $37 Range = $27 - $47

Price per Movie Package Deviation scores Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 8,8,8 9,9 10 12 10 Frequency 8 6 4 Deviation = 10 2 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package What is the deviation score for $46? Mean = $37 Range = $27 - $47

Price per Movie Package What’s the ‘typical’ or standard deviation? Deviation scores Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks) 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 8,8,8 9,9 10 Estimate Average Deviation Score 12 10 Frequency 8 6 4 2 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package What’s the ‘typical’ or standard deviation? Mean = $37 Range = $27 - $47 Standard Deviation = 3.5

What’s the ‘typical’ or standard deviation? Pounds of pressure to break casing on an insulator (We applied pressure until the insulator casing broke) What’s the largest possible deviation? 2100– 1700 = 400 Mean = 1700 pounds Range = 1200 – 2100 1200 – 1700 = -500 What’s the ‘typical’ or standard deviation? Standard Deviation = 200

Amount of Bonuses (based on commission) We sampled 100 retail workers $75 – $50= $25 What’s the largest possible deviation? $25 – $50= -$25 Mean = $50 Range = $25 - $75 What’s the ‘typical’ or standard deviation? Standard Deviation = 10

What’s the ‘typical’ or standard deviation? Waiting time for service at bank We sampled 100 banks (From time entering line to time reaching teller) 3.8 – 3.0= .8 What’s the largest possible deviation? 2.2 – 3.0= -.8 Mean = 3 minutes Range = 2.2- 3.8 What’s the ‘typical’ or standard deviation? Standard Deviation = 0.30

Scores, standard deviations, and probabilities Actually 68.26 Actually 95.44 To be exactly 95% we will use z = 1.96

What’s the ‘typical’ or standard deviation? Number of kids in family We sampled 100 families (counted number of kids) 8 – 3= 5 What’s the largest possible deviation? Mean = 3 kids Range = 1 - 8 1 - 3= -2 What’s the ‘typical’ or standard deviation? Standard Deviation = 1.7

What’s the ‘typical’ or standard deviation? Number correct on exam We tested 100 students (counted number of correct on 100 point test) 55 - 80= -25 What’s the largest possible deviation? 100 - 80 = 20 Mean = 80 Range = 55 - 100 What’s the ‘typical’ or standard deviation? Standard Deviation = 10

Let’s try one What’s the largest possible deviation? 150 – 97 = 53 Monthly electric bills for 50 apartments (amount of dollars charged for the month) Let’s try one What’s the largest possible deviation? Mean = $150 Range = 97 - 213 150 – 97 = 53 150 – 213 = - 63 The best estimate of the population standard deviation is a. $150 b. $27 c. $53 d. $63 Standard Deviation = 27

Let’s try one What’s the largest possible deviation? 2 – 1.894 = 0.106 Amount of soda in 2-liter containers (measured amount of soda in 2-liter bottles) Let’s try one What’s the largest possible deviation? 2 – 1.894 = 0.106 Mean = 2.0 Range = 1.894 – 2.109 2 – 2.109 = -0.109 The best estimate of the population standard deviation is a. 0.106 b. 0.109 c. 0.044 d. 2.0 Standard Deviation = 0.044

Scores on an Art History exam (measured number correct out of 100) Let’s try one What’s the largest possible deviation? 25 - 50= - 25 Mean = 50 Range = 25 - 70 70 - 80 = 20 The best estimate of the population standard deviation is a. 50 b. 25 c. 10 d. .5 Standard Deviation = 10

Scores on Art History Exam One way to estimate standard deviation* Let’s try one One way to estimate standard deviation* σ≈ range / 6 45 / 6 = 7.5 Mean = 50 Range = 25 - 70 The best estimate of the population standard deviation is a. 50 b. 25 c. 10 d. .5 Standard Deviation = 10

Number correct on exam We tested 100 students (counted number of correct on 100 point test) Mean = 50 Range = 25 - 70 Standard Deviation = 10

Raw scores, z scores & probabilities Please note spatially where 1 standard deviation falls on the curve Review

Raw scores, z scores & probabilities 68% 95% 99.7%

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

Amount of Bonuses (based on commission) We sampled 100 retail workers 68% 95% 99.7% Mean = $50 Range = $25 - $75 Standard Deviation = 10

Scores, standard deviations, and probabilities 68% Mean = 50 S = 10 (Note S = standard deviation) If we go up one standard deviation z score = +1.0 and raw score = 60 If we go down one standard deviation z score = -1.0 and raw score = 40

Scores, standard deviations, and probabilities 95% 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

Scores, standard deviations, and probabilities 99.7% Mean = 50 S = 10 (Note S = standard deviation) If we go up three standard deviations z score = +3.0 and raw score = 80 If we go down three standard deviations z score = -3.0 and raw score = 20

Scores, standard deviations, and probabilities What if we go up 2.0 standard deviations? Then, z score = +2.0

Scores, standard deviations, and probabilities What if we go up 2.5 standard deviations? Then, z score = +2.5

Scores, standard deviations, and probabilities What if we go down 1.26 standard deviations? Then, z score = -1.26 What’s the biggest possible z score?

z scores 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 How are standard deviations (or z scores) related to probability (also known as area under the curve or proportion of curve or percent of curve)

Raw scores, z scores & probabilities 1 sd above and below mean 68% z = +1 z = -1 Mean = 50 S = 10 (Note S = standard deviation) If we go up one standard deviation z score = +1.0 and raw score = 60 If we go down one standard deviation z score = -1.0 and raw score = 40

Raw scores, z scores & probabilities 2 sd above and below mean 95% 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

Raw scores, z scores & probabilities 3 sd above and below mean 99.7% z = +3 z = -3 Mean = 50 S = 10 (Note S = standard deviation) If we go up three standard deviations z score = +3.0 and raw score = 80 If we go down three standard deviations z score = -3.0 and raw score = 20

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”

Exam 1 Review

Thank you! See you next time!!