INTEGRATED LEARNING CENTER Screen Lecturer’s desk Cabinet Cabinet Table Computer Storage Cabinet 4 3 Row A 19 18 5 17 16 15 14 13 12 11 10 9 8 7 6 2 1 Row B 3 23 22 6 5 4 21 20 19 7 18 17 16 15 14 13 12 11 10 9 8 2 1 Row C 24 4 3 23 22 5 21 20 6 19 7 18 17 16 15 14 13 12 11 10 9 8 1 Row D 25 2 24 23 4 3 22 21 20 6 5 19 7 18 17 16 15 14 13 12 11 10 9 8 1 Row E 26 25 2 24 4 3 23 22 5 21 20 6 19 18 17 16 15 14 13 12 11 10 9 8 7 27 26 2 1 Row F 25 24 3 23 4 22 5 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 28 27 26 1 Row G 25 24 3 2 23 5 4 22 29 21 20 6 28 19 18 17 16 15 14 13 12 11 10 9 8 7 27 26 2 1 Row H 25 24 3 23 22 6 5 4 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 26 2 1 Row I 25 24 3 23 4 22 5 21 20 6 19 18 17 16 15 14 13 12 11 10 9 8 7 26 1 25 3 2 Row J 24 23 5 4 22 21 20 6 28 19 7 18 17 16 15 14 13 12 11 10 9 8 27 26 25 3 2 1 Row K 24 23 4 22 5 21 20 6 19 7 18 17 16 15 14 13 12 11 10 9 8 Row L 20 19 18 1 17 3 2 16 5 4 15 14 13 12 11 10 9 8 7 6 INTEGRATED LEARNING CENTER ILC 120 broken desk

Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall, 2014 Room 120 Integrated Learning Center (ILC) 10:00 - 10:50 Mondays, Wednesdays & Fridays. Welcome http://www.youtube.com/watch?v=oSQJP40PcGI

A note on doodling Reminder

Labs continue this week Lab sessions Labs continue this week

One positive correlation One negative correlation One t-test

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

By the end of lecture today 10/8/14 Use this as your study guide By the end of lecture today 10/8/14 Counting ‘standard deviationses’ – z scores Connecting raw scores, z scores and probability Connecting probability, proportion and area of curve Percentiles

No homework due Friday (October 10th)

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

z score = raw score - mean standard deviation 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 95% z = +2 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

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

. Homework Worksheet

Hint: Always draw a picture! Homework worksheet

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

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

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

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

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

.9332 .4332 .5000 Homework Worksheet: Problem 6 . 24 26 28 30 32 34 36 33-30 Go to table z = z = 1.5 .4332 2 .9332 .4332 .5000 24 26 28 30 32 34 36

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

Homework Worksheet Problem 11: .5000 + .4938 = .9938 Problem 14: 28 and 32

. 77th percentile Go to table nearest z = .74 .2700 x = mean + z σ = 30 + (.74)(2) = 31.48 .7700 .27 .5000 24 26 28 30 ? 34 36 31.48

. 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 ? 26 27.74 30 32 34 36

Homework Worksheet Problem 17: 68% or .68 or 68.26% or .6826

.2734 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) 230-200 Go to table z = z = .75 .2734 40 .2734 80 120 160 200 240 280 320

Homework Worksheet Problem 21: 40.13% or .4013 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

? .9500 .4500 .5000 x = mean + z σ = 50 + (1.64)(4) = 56.56 Problem 7 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 42 46 50 54 56.60 ? 58 62

? .4700 .0300 x = mean + z σ = 2100 + (-1.88)(250) = 1,630 Problem 8 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 1,630 ? 2100

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 .5000 .0100 Problem 9 195 214.8 ?

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

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

Mean of 30 and standard deviation of 2 . 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 ? 28 30 32 ? 36

Thank you! See you next time!!