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MGMT 276: Statistical Inference in Management Fall, 2013

MGMT 276: Statistical Inference in Management Fall, 2013. Welcome. Use this as your study guide. By the end of lecture today 9/24/13. Characteristics of a distribution Standard Deviation Variance Empirical Rule (areas under the curve) Review for Exam 1.

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MGMT 276: Statistical Inference in Management Fall, 2013

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  1. MGMT 276: Statistical Inference in ManagementFall, 2013 Welcome

  2. Use this as your study guide By the end of lecture today9/24/13 • Characteristics of a distribution • Standard Deviation • Variance • Empirical Rule (areas under the curve) • Review for Exam 1

  3. Exam 1 – This Thursday September 26th 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

  4. Please read: Chapters 1 - 4 in Lind book & Chapters 1, 5, 6 and 13 in Plous book: Lind Chapter 1: Overview of Statistics Chapter 2: Describing Data with Graphs Chapter 3: Describing Data with Numbers Chapter 4: Describing Data with Plots Plus 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

  5. No Homework Just study for exam Please double check – Allcell phones other electronic devices are turned off and stowed away

  6. Review of Homework Worksheet

  7. Review of Homework Worksheet 3 – 5 = -2 -22= 4 6 – 5 = +1 -2 1 3 -1 0 4 1 9 1 0 12= 1 3 -3 -1 1 -1 9 9 1 1 1 50 0 36 36 2 = 2 10 - 1 Mode = 4 5 4.5 6 2 8

  8. Review of Homework Worksheet -12= 1 5 – 6 = -1 -1 2 -1 -1 3 1 4 1 1 9 22= 4 8 – 6 = +2 0 -1 3 1 -5 0 1 9 1 25 60 0 52 52 2.4 = 2.4 10 - 1 Mode = 5 6 5.5 8 1 9

  9. Review of Homework Worksheet Must be complete and must be stapled

  10. Please click in My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z Must be complete and must be stapled Hand in Homework

  11. 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

  12. “Sum of Squares” “Sum of Squares” “Sum of Squares” “Sum of Squares” Deviation scores Standard deviation: The average amount by which observations deviate on either side of their mean Diallo is 0” Preston is 2” Mike is -4” Hunter is -2 Shea is 4 David 0” 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

  13. 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)

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

  15. 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

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

  17. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) 12 10 Frequency 8 6 4 2 0 • 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

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

  19. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 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 0 • 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

  20. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 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 0 • 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

  21. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 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 Deviation = 3 8 6 4 2 0 • 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

  22. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 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 0 • 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

  23. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 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 0 • 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

  24. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 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 What is the deviation score for $43? 12 10 Frequency 8 6 Deviation = 6 4 2 0 • 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

  25. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 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 What is the deviation score for $44? 12 10 Frequency 8 6 Deviation = 7 4 2 0 • 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

  26. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 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 0 • 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

  27. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 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 0 • 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

  28. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 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 0 • 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

  29. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 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 0 • 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

  30. 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 1200 – 1700 = -500 Mean = 1700 pounds Range = 1200 – 2100 What’s the ‘typical’ or standard deviation? Standard Deviation = 200

  31. Amount of Bonuses (based on commission)We sampled 100 retail workers 68% 95% 99.7% $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

  32. Waiting time for service at bankWe 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

  33. Number correct on examWe 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

  34. 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

  35. 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 2 – 2.109 = -0.109 Mean = 2.0 Range = 1.894 – 2.109 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

  36. 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

  37. Scores, standard deviations, and probabilities 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

  38. Scores, standard deviations, and probabilities 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

  39. Scores, standard deviations, and probabilities 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

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

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

  42. 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?

  43. 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)

  44. 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

  45. 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

  46. 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

  47. 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”

  48. Exam 1 Review

  49. Thank you! See you next time!!

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