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Introduction to Statistics for the Social Sciences - Lecture Section 001

Welcome to the Integrated Learning Center (ILC) for the Introduction to Statistics for the Social Sciences lecture. This class covers topics such as probability and risk, perception of randomness, and heuristics. Get ready to explore the world of statistics!

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Introduction to Statistics for the Social Sciences - Lecture Section 001

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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. 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

  3. A noteon doodling Reminder

  4. Lab sessions Labs continue this week

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

  6. 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

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

  8. No homework due Friday (October 10th)

  9. 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

  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. . Homework Worksheet

  13. Hint: Always draw a picture! Homework worksheet

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

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

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

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

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

  19. . 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

  20. .0668 Go to table 33-30 .4332 z = 1.5 z = .4332 2 33 .5000 - .4332 = .0668 Go to table 29-30 z =-.5 z = .1915 .5000 .1915 2 .5000 + .1915 = .6915 29 .4938 .1915 25-30 25 31 z = -2.5 z = .4938 2 .4938 + .1915 = .6853 Go to table 31-30 z =.5 z = .1915 2 .0668 .4332 27-30 z = -1.5 z = .4332 27 .5000 - .4332 = .0668 2

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

  22. . 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

  23. . 13th percentile Go to table nearest z = 1.13 .3700 x = mean + z σ = 30 + (-1.13)(2) = 27.74 Note: .13 + .37 = .50 .37 .50 .13 ? 24 36 32 27.74 34 26 30

  24. Homework Worksheet 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

  25. 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

  26. Homework Worksheet 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 x = mean + z σ = 200 + (2.33)(40) = 293.2 Problem 30: 182.4 x = mean + z σ = 200 + (-.44)(40) = 182.4 Problem 31: 190 Problem 32: 217.6

  27. 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

  28. 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

  29. 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

  30. . 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

  31. . 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

  32. . 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

  33. Thank you! See you next time!!

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