2. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall 2015 Room 150 Harvill Building 10:00 - 10:50 Mondays, Wednesdays & Fridays. http://courses.eller.arizona.edu/mgmt/delaney/d15s_database_weekone_screenshot.xlsx

3. z tables

4. Everyone will want to be enrolled in one of the lab sessions Labs continue this week, Project 1

7. Please re-register your clicker http://student.turningtechnologies.com/

8. By the end of lecture today 10/7/15 Connecting raw scores, and z scores to probability, proportion and area of curve Percentiles Approaches to probability: Empirical, Subjective and Classical

9. Before next exam (October 16th) Please read chapters 1 - 8 in OpenStax textbook 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 Schedule of readings

10. Homework Assignment Assignment 9 - Extension Please complete this homework worksheet Finding z scores and areas under the curve Due: Monday, October 5th Extended deadline to Wednesday, October 7 th Homework Assignment Assignment 10 Please complete this homework worksheet Approaches to Probability and Dispersion Due: Wednesday, October 7 th

11. Raw Scores (actual data) Distance from the mean (z scores) Proportion of curve (area from mean) convert We care about this! “percentiles” “percent of people” “proportion of curve” “relative position” We care about this! What is the actual number on this scale? “height” vs “weight” “pounds” vs “test score” Raw Scores (actual data) Distance from the mean (z scores) Proportion of curve (area from mean) convert Raw scores, z scores & probabilities z = -1z = 1 68% z = -1z = 1 68%

12. 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 Normal distribution Raw scores z-scores probabilities

13. Notice: 3 types of numbers raw scores z scores probabilities Mean = 50 Standard deviation = 10 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 z = -2 z = +2

14. Always draw a picture! Homework worksheet

15. 1.6800 z =-1 z = 1

16. Homework worksheet 2.9500 z =-2 z = 2

17. Homework worksheet 3.9970 z =-3 z = 3

18. Homework worksheet 4.5000 z = 0

19. Homework worksheet 5 2 z = 33-30 z = 1.5 Go to table.4332 z = 1.5

20. 6 z = 33-30 2 z = 1.5 Go to table.4332 Add area Lower half.4332 +.5000 =.9332 z = 1.5

21. Homework worksheet 7 2 z = 33-30 = 1.5 Go to table.4332 Subtract from.5000.5000 -.4332 =.0668 z = 1.5

22. 8 z = 29-30 2 = -.5 Go to table.1915 Add to upper Half of curve.5000 +.1915 =.6915 z = -.5

23. 9.4938 +.1915 =.6853 = 25-30 2 = -2.5.4938 Go to table = 31-30 2 =.5.1915 Go to table z =.5 z =-2.5

24. 10 z = 27-30 2 = -1.5 Go to table.4332 Subtract From.5000.5000 -.4332 =.0668 z =-1.5

25. 11 z = 25-30 2 = -2.5 Go to table.4938 Add lower Half of curve.5000 +.4938 =.9938 z =-2.5

26. 12 z = 32-30 2 = 1.0 Go to table.3413 Subtract from.5000.5000 -.3413 =.1587 z =1

27. 13 50 th percentile = median 30 z =0

28. 14 28 32 z =-1 z = 1

29. 15 x = mean + z σ = 30 + (.74)(2) = 31.48 77 th percentile Find area of interest.7700 -.5000 =.2700 Find nearest z =.74 z =.74

30. 16 13 th percentile Find area of interest.5000 -.1300 =.3700 Find nearest z = -1.13 x = mean + z σ = 30 + (-1.13)(2) = 27.74 z =-1.13

31. Please use the following distribution with a mean of 200 and a standard deviation of 40.

32. 17.6800 z =-1 z = 1

33. .9500 18 z =-2 z = 2

34. .9970 19 z =-3 z = 3

35. 20 = 230-200 40 =.75 Go to table.2734 z =.75

36. 22 Go to table Add to upper Half of curve z = 180-200 40 = -.5.1915.5000 +.1915 =.6915 z =-.5

37. 23 z = 236-200 40 = 0.9 Go to table.3159 Subtract from.5000.5000 -.3159 =.1841 z =.9

38. 24.0793 +.2088 =.2881 z = 192 - 200 40 = -.2.0793 Go to table z = 222 - 200 40 =.55.2088 Go to table z =-.2 z =.55

39. 25 40 z = 275-200 = 1.875 Go to table.4693 or.4699 Add area Lower half.4693 +.5000 =.9693.4699 +.5000 =.9699 z =1.875

40. 26 z = 295-200 40 z = 2.375 Go to table.4911 or.4913 Add area Lower half.5000 -.4911 =.0089.5000 -.4913 =.0087 z =2.375

41. 27 z = 130-200 40 = -1.75.4599 Add to upper Half of curve Go to table.5000 +.4599 =.9599 z =-1.75

42. 28 40 z = 130-200 = -1.75.4599 Subtract from.5000.5000 -.4599 =.0401 Go to table z =-1.75

43. 29 x = mean + z σ = 200 + (2.33)(40) = 293.2 99 th percentile Find area of interest.9900 -.5000 =.4900 Find nearest z = 2.33 z =2.33

44. 30 33 rd percentile Find area of interest.5000 -.3300 =.1700 Find nearest z =.44 x = mean + z σ = 200 + (-.44)(40) = 182.4 z =-.44

45. 31 40 th percentile Find area of interest.5000 -.4000 =.1000 Find nearest z = -.25 x = mean + z σ = 200 + (-.25)(40) = 190 z =-.25

46. 32 67 th percentile Find area of interest.6700 -.5000 =.1700 Find nearest z =.44 x = mean + z σ = 200 + (.44)(40) = 217.6 z =.44

47. . 75 th percentile Go to table.2500 nearest z =.67 x = mean + z σ = 30 + (.67)(2) = 31.34 z =.67 Additional practice

48. . 25 th percentile Go to table.2500 nearest z = -.67 x = mean + z σ = 30 + (-.67)(2) = 28.66 z = -.67 Additional practice

49. . 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 Additional practice

50. . Try this one: Please find the (2) raw scores that border exactly the middle 95% of the curve Mean of 100 and standard deviation of 5 Go to table.4750 nearest z = 1.96 mean + z σ = 100 + (1.96)(5) = 109.80 Go to table.4750 nearest z = -1.96 mean + z σ = 100 + (-1.96)(5) = 90.20 Additional practice

51. . Try this one: Please find the (2) raw scores that border exactly the middle 99% of the curve Mean of 30 and standard deviation of 2 Go to table.4750 nearest z = 1.96 mean + z σ = 30 + (2.58)(2) = 35.16 Go to table.4750 nearest z = -1.96 mean + z σ = 30 + (-2.58)(2) = 24.84 Additional practice