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Lecturer’s desk

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.

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Lecturer’s desk

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  1. 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

  2. Hand out z tables

  3. Introduction to Statistics for the Social SciencesSBS200, COMM200, GEOG200, PA200, POL200, or SOC200Lecture Section 001, Fall, 2014Room 120 Integrated Learning Center (ILC)10:00 - 10:50 Mondays, Wednesdays & Fridays. Welcome http://www.youtube.com/watch?v=oSQJP40PcGI

  4. A noteon doodling Reminder

  5. Lab sessions Labs continue this week

  6. One positive correlation One negative correlation One t-test

  7. Schedule of readings Before next exam (October 17th) Please read chapters 5, 6, & 8 in Ha & Ha Please read Chapters 10, 11, 12 and 14 in Plous Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability and Risk Chapter 14: The Perception of Randomness

  8. Use this as your study guide By the end of lecture today10/6/14 Counting ‘standard deviationses’ – z scores Connecting raw scores, z scores and probabilityConnecting probability, proportion and area of curve Percentiles

  9. Homework due – Wednesday (October 8th) On class website: Please print and complete homework worksheet #11 Calculating z-score, raw scores and areas under normal curve Deadline extended

  10. Mean = 100 Standard deviation = 5 If we go up one standard deviation z score = +1.0 and raw score = 105 z = +1 z = -1 68% If we go down one standard deviation z score = -1.0 and raw score = 95 85 90 95 100 105 110 115 If we go up two standard deviations z score = +2.0 and raw score = 110 z = +2 z = -2 95% If we go down two standard deviations z score = -2.0 and raw score = 90 85 90 95 100 105 110 115 If we go up three standard deviations z score = +3.0 and raw score = 115 99.7% z = +3 z = -3 If we go down three standard deviations z score = -3.0 and raw score = 85 85 90 95 100 105 110 115 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

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

  12. Ties together z score with Draw picture of what you are looking for... Find z score (using formula)... Look up proportions on table • probability • proportion • percent • area under the curve 68% 34% 34%

  13. Writing AssignmentLet’s do some problems Mean = 50Standard deviation = 10

  14. ? 45 Mean = 50Standard deviation = 10 Find the percentile rank for score of 45 z-table (from z to area) Distance from the mean ( from raw to z scores) Raw Scores (actual data) Proportion of curve (area from mean) 1) Find z score z score = 45 - 50 10 z score = - 5 10 = -0.5 2) Go to z table Problems 1 & 2 were completed in lecture on Friday Problem 3

  15. ? 45 Mean = 50Standard deviation = 10 Find the percentile rank for score of 45 .1915 ? 1) Find z score z score = 45 - 50 10 z score = - 5 10 = -0.5 2) Go to z table Problem 3

  16. ? 45 Mean = 50Standard deviation = 10 Find the percentile rank for score of 45 .1915 z-table (from z to area) Distance from the mean ( from raw to z scores) .3085 Raw Scores (actual data) Proportion of curve (area from mean) 1) Find z score z score = 45 - 50 10 z score = - 5 10 = -0.5 2) Go to z table 3) Look at your picture - subtract .5000 -.1915 = .3085 Problem 3 4) Percentile rank or score of 45 = 30.85%

  17. ? Mean = 50Standard deviation = 10 Find the percentile rank for score of 55 z-table (from z to area) Distance from the mean ( from raw to z scores) 55 Raw Scores (actual data) Proportion of curve (area from mean) 1) Find z score z score = 55 - 50 10 z score = 5 10 = 0.5 2) Go to z table Problem 4

  18. ? Mean = 50Standard deviation = 10 Find the percentile rank for score of 55 .1915 55 1) Find z score z score = 55 - 50 10 z score = 5 10 = 0.5 2) Go to z table Problem 4

  19. ? Mean = 50Standard deviation = 10 Find the percentile rank for score of 55 .1915 z-table (from z to area) Distance from the mean ( from raw to z scores) .5 55 Raw Scores (actual data) Proportion of curve (area from mean) 1) Find z score z score = 55 - 50 10 z score = 5 10 = 0.5 2) Go to z table 3) Look at your picture - add .5000 +.1915 = .6915 4) Percentile rank or score of 55 = 69.15% Problem 4

  20. Find the score for z = -2 ? Mean = 50Standard deviation = 10 30 Hint always draw a picture! Find the score that is associated with a z score of -2 z-table (from z to area) Distance from the mean ( from raw to z scores) raw score = mean + (z score)(standard deviation) Raw Scores (actual data) Proportion of curve (area from mean) Raw score = 50 + (-2)(10) Raw score = 50 + (-20) = 30 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion

  21. ? .7700 ? Mean = 50Standard deviation = 10 Find the score for percentile rank of 77%ile z-table (from z to area) Distance from the mean ( from raw to z scores) Raw Scores (actual data) Proportion of curve (area from mean) Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion Problem 5

  22. ? .7700 ? Mean = 50Standard deviation = 10 .27 Find the score for percentile rank of 77%ile .5 .5 + .27 = .77 .5 .27 1) Go to z table - find z score for for area .2700 (.7700 - .5000) = .27 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion area = .2704 (closest I could find to .2700) z = 0.74 Problem 5

  23. ? .7700 ? Mean = 50Standard deviation = 10 .27 Find the score for percentile rank of 77%ile .5 x = 57.4 .5 .27 2) x = mean + (z)(standard deviation) x = 50 + (0.74)(10) x = 57.4 x = 57.4 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion Problem 5

  24. ? .5500 ? Mean = 50Standard deviation = 10 Find the score for percentile rank of 55%ile z-table (from z to area) Distance from the mean ( from raw to z scores) Raw Scores (actual data) Proportion of curve (area from mean) Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion Problem 6

  25. ? .5500 ? Mean = 50Standard deviation = 10 .05 Find the score for percentile rank of 55%ile .5 .5 + .05 = .55 .5 .05 1) Go to z table - find z score for for area .0500 (.5500 - .5000) = .05 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion area = .0517 (closest I could find to .0500) z = 0.13 Problem 6

  26. ? .5500 ? Mean = 50Standard deviation = 10 .05 Find the score for percentile rank of 55%ile .5 .5 .05 1) Go to z table - find z score for for area .0500 (.5500 - .5000) = .05 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion area = .0517 (closest I could find to .0500) z = 0.13 Problem 6

  27. ? .5500 ? Mean = 50Standard deviation = 10 .05 Find the score for percentile rank of 55%ile .5 x = 51.3 .5 .05 1) Go to z table - find z score for for area .0500 (.5500 - .5000) = .0500 area = .0517 (closest I could find to .0500) z = 0.13 2) x = mean + (z)(standard deviation) x = 50 + (0.13)(10) x = 51.3 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion x = 51.3 Problem 6

  28. Normal Distribution has a mean of 50 and standard deviation of 4. Determine value below which 95% of observations will occur.Note: sounds like a percentile rank problem Go to table .4500 nearest z = 1.64 x = mean + z σ = 50 + (1.64)(4) = 56.56 .9500 .4500 .5000 Problem 7 38 62 54 46 58 ? 42 50 56.60

  29. Normal Distribution has a mean of $2,100 and s.d. of $250. What is the operating cost for the lowest 3% of airplanes.Note: sounds like a percentile rank problem = find score for 3rd percentile Go to table .4700 nearest z = - 1.88 x = mean + z σ = 2100 + (-1.88)(250) = 1,630 .0300 .4700 Problem 8 ? 2100 1,630

  30. Normal Distribution has a mean of 195 and standard deviation of 8.5. Determine value for top 1% of hours listened. Go to table .4900 nearest z = 2.33 x = mean + z σ = 195 + (2.33)(8.5) = 214.805 .4900 .0100 .5000 Problem 9 195 ? 214.8

  31. . Find score associated with the 75th percentile 75th percentile Go to table nearest z = .67 .2500 x = mean + z σ = 30 + (.67)(2) = 31.34 .7500 .25 .5000 24 36 ? 28 34 26 30 31.34 Problem 10 z = .67

  32. . Find the score associated with the 25th percentile 25th percentile Go to table nearest z = -.67 .2500 x = mean + z σ = 30 + (-.67)(2) = 28.66 .2500 .25 .25 28.66 24 ? 36 28 34 26 30 Problem 11 z = -.67

  33. . Try this one: Please find the (2) raw scores that border exactly the middle 95% of the curve Mean of 30 and standard deviation of 2 Go to table .4750 nearest z = 1.96 mean + z σ = 30 + (1.96)(2) = 33.92 Go to table .4750 nearest z = -1.96 mean + z σ = 30 + (-1.96)(2) = 26.08 .9500 .475 .475 Problem 12 26.08 33.92 ? ? 24 32 36 28 30

  34. Raw scores, z scores & probabilities • Notice: • 3 types of numbers • raw scores • z scores • probabilities Mean = 50 Standard deviation = 10 z = -2 z = +2 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

  35. Normal distribution Raw scores z-scores probabilities Z Scores Have z Find raw score Have z Find area z table Formula Have area Find z Area & Probability Raw Scores Have raw score Find z

  36. . Homework Worksheet

  37. Hint: Always draw a picture! Homework worksheet

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

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

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

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

  42. Thank you! See you next time!!

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