Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2018 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays. Welcome 2/23/18 http://www.youtube.com/watch?v=oSQJP40PcGI http://www.youtube.com/watch?v=oSQJP40PcGI http://www.youtube.com/watch?v=oSQJP40PcGI http://www.youtube.com/watch?v=oSQJP40PcGI

Lecturer’s desk Projection Booth Screen Screen Harvill 150 renumbered Row A 15 14 Row A 13 12 11 10 9 8 7 6 5 4 3 2 1 Row A Row B 23 22 21 20 Row B 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row B Row C 25 24 23 22 21 Row C 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row C Row D 29 28 27 26 25 24 23 Row D 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row D Row E 31 30 29 28 27 26 25 24 23 Row E 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row E Row F 35 34 33 32 31 30 29 28 27 26 Row F 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row F Row G 35 34 33 32 31 30 29 28 27 26 Row G 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row G Row H 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 Row H 12 11 10 9 8 7 6 5 4 3 2 1 Row H 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 Row J 13 12 11 10 9 8 7 6 5 4 3 2 1 Row J 41 40 39 38 37 36 35 34 33 32 31 30 29 Row K 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row K Row L 33 32 31 30 29 28 27 26 25 Row L 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row L Row M 21 20 19 Row M 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row M Row N 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row P 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Harvill 150 renumbered table 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Projection Booth Left handed desk

Kristina Lecturer’s desk Attila Sezen Hannah Michelle Projection Booth Screen Screen Kristina Lecturer’s desk Row A 15 14 Row A 13 12 11 10 9 8 7 6 5 4 3 2 1 Row A Attila Row B 23 22 21 20 Row B 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row B Row C 25 24 23 22 21 Row C 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row C Row D 29 28 27 26 25 24 23 Row D 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row D Row E 31 30 29 28 27 26 25 24 23 Row E 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row E Michelle Row F 35 34 33 32 31 30 29 28 27 26 Row F 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row F Row G 35 34 33 32 31 30 29 28 27 26 Row G 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row G Row H 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 Row H 12 11 10 9 8 7 6 5 4 3 2 1 Row H 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 1 Row J Row J 13 12 11 10 9 8 7 6 5 4 3 2 41 40 39 38 37 36 35 34 33 32 31 30 29 Row K 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row K Row L 33 32 31 30 29 28 27 26 25 Row L 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row L Row M 21 20 19 Row M 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row M Row N 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row P 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Sezen Hannah table 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Projection Booth Left handed desk Harvill 150 renumbered

Before next exam (March 2nd) Schedule of readings Before next exam (March 2nd) 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

Labs continue next week Lab sessions Everyone will want to be enrolled in one of the lab sessions Labs continue next week Prep for Exam 2

66% chance of getting admitted What is probability 1. Empirical probability: relative frequency approach Number of observed outcomes Number of observations Probability of getting into an educational program Number of people they let in 400 66% chance of getting admitted Number of applicants 600 Probability of getting a rotten apple Number of rotten apples 5 5% chance of getting a rotten apple Number of apples 100 Review

Review What is probability 1. Empirical probability: relative frequency approach “There is a 20% chance that a new stock offered in an initial public offering (IPO) will reach or exceed its target price on the first day.” “More than 30% of the results from major search engines for the keyword phrase “ring tone” are fake pages created by spammers.” 10% of people who buy a house with no pool build one. What is the likelihood that Bob will? Number of observed outcomes Number of observations Probability of hitting the corvette Number of carts that hit corvette Number of carts rolled 182 = .91 200 91% chance of hitting a corvette Review

= = 2. Classic probability: a priori probabilities based on logic rather than on data or experience. All options are equally likely (deductive rather than inductive). Likelihood get question right on multiple choice test Chosen at random to be team captain Lottery Number of outcomes of specific event Number of all possible events In throwing a die what is the probability of getting a “2” Number of sides with a 2 1 16% chance of getting a two = Number of sides 6 In tossing a coin what is probability of getting a tail Number of sides with a 1 1 50% chance of getting a tail = Number of sides 2

3. Subjective probability: based on someone’s personal judgment (often an expert), and often used when empirical and classic approaches are not available. Likelihood that company will invent new type of battery Likelihood get a ”B” in the class 60% chance that Patriots will play at Super Bowl There is a 5% chance that Verizon will merge with Sprint Bob says he is 90% sure he could swim across the river

Approach Example Empirical Classical Subjective There is a 2 percent chance of twins in a randomly-chosen birth Classical There is a 50 % probability of heads on a coin flip. Subjective There is a 5% chance that Verizon will merge with Sprint

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

Always draw a picture! Homework worksheet

1 .6800 1 sd 1 sd 28 30 32 Homework worksheet .6800 also fine: 68% z =-1 z = 1 28 30 32

2 .9500 2 sd 2 sd 26 28 30 32 34 Homework worksheet .9500 also fine: 95% also fine: .9544 .9500 2 sd 2 sd z =-2 z = 2 26 28 30 32 34

3 .9970 3 sd 3 sd 24 26 28 30 32 34 36 Homework worksheet .9970 also fine: 99.7% also fine: .9974 .9970 3 sd 3 sd z =-3 z = 3 24 26 28 30 32 34 36

4 .5000 24 26 28 30 32 34 36 Homework worksheet .5000 also fine: 50% z = 0 24 26 28 30 32 34 36

5 .4332 24 26 28 30 32 34 36 Homework worksheet z = 33-30 z = 1.5 Go to table .4332 2 5 also fine: 43.32% .4332 z = 1.5 24 26 28 30 32 34 36

z = 33-30 2 z = 1.5 Go to table .4332 Add area Lower half .4332 + .5000 = .9332 6 also fine: 93.32% .9332 .4332 .5000 z = 1.5 24 26 28 30 32 34 36

7 .4332 .0668 24 26 28 30 32 34 36 Homework worksheet z = 33-30 = 1.5 = 1.5 Go to table .4332 Subtract from .5000 .5000 - .4332 = .0668 2 7 also fine: 6.68% .4332 .0668 z = 1.5 24 26 28 30 32 34 36

z = 29-30 2 = -.5 Go to table .1915 Add to upper Half of curve .5000 - .1915 = .6915 8 also fine: 69.15% .6915 .1915 .5000 z = -.5 24 26 28 30 32 34 36

= 25-30 2 = -2.5 .4938 Go to table = 31-30 2 =.5 .1915 Go to table .4938 + .1915 = .6853 9 also fine: 68.53% .6853 .1915 .4938 z =-2.5 z = .5 24 26 28 30 32 34 36

z = 27-30 2 = -1.5 Go to table .4332 Subtract From .5000 .5000 - .4332 = .0668 10 also fine: 6.68% .5000 .0668 .4332 z =-1.5 24 26 28 30 32 34 36

z = 25-30 2 = -2.5 Go to table .4938 Add lower Half of curve .5000 + .4938 = .9938 11 also fine: 99.38% .9938 .5000 .4938 z =-2.5 24 26 28 30 32 34 36

z = 32-30 2 = 1.0 Go to table .3413 Subtract from .5000 .5000 - .3413 = .1587 12 .5000 also fine: 15.87% .1587 .3413 z =1 24 26 28 30 32 34 36

13 24 26 28 30 32 34 36 50th percentile = median 30 In a normal curve Median= Mean = Mode z =0 24 26 28 30 32 34 36

28 32 14 .6800 1 sd 1 sd z =-1 z = 1 24 26 28 30 32 34 36

z table provides area from mean to score x = mean + z σ = 30 + (.74)(2) = 31.48 77th percentile Find area of interest .7700 - .5000 = .2700 Find nearest z = .74 15 .2700 .7700 z table provides area from mean to score .5000 31.48 z =.74 24 ? 30 36

z table provides area from mean to score 13th percentile Find area of interest .5000 - .1300 = .3700 Find nearest z = -1.13 x = mean + z σ = 30 + (-1.13)(2) = 27.74 16 Note: .13 +.37 =.50 z table provides area from mean to score .3700 .1300 z =-1.13 27.74 ? 24 30 36

Please use the following distribution with a mean of 200 and a standard deviation of 40. 80 120 160 200 240 280 320

17 .6800 1 sd 1 sd 160 200 240 .6800 also fine: 68% also fine: .6826 z =-1 z = 1 160 200 240

18 .9500 2 sd 2 sd 120 200 280 .9500 also fine: 95% also fine: .9544 z =-2 z = 2 120 200 280

19 .9970 3 sd 3 sd 80 200 320 .9970 also fine: 99.7% also fine: .9974 z =-3 z = 3 80 200 320

230-200 Go to table = = .75 .2734 40 20 also fine: 27.34% .2734 z =.75 80 120 160 200 240 280 320

Go to table Add to upper Half of curve z = 180-200 40 = -.5 .1915 .5000 + .1915 = .6915 22 also fine: 69.15% .5000 .1915 .6915 z =-.5 80 120 160 200 240 280 320

z = 236-200 40 = 0.9 Go to table .3159 Subtract from .5000 .5000 - .3159 = .1841 23 .3159 also fine: 18.41% .1841 z =.9 80 120 160 200 240 280 320

z = 192 - 200 40 = -.2 .0793 Go to table .0793 + .2088 = .2881 z = 222 - 200 40 =.55 .2088 Go to table 24 also fine: 28.81% .2881 .2088 .0793 z =-.2 z =.55 80 120 160 200 240 280 320

.4693 + .5000 = .9693 z = 275-200 = 1.875 Go to table Add area Lower half .4693 or .4699 .4699 + .5000 = .9699 40 25 Please note: If z-score rounded to 1.88, then percentile = 96.99% also fine: 96.93% .9693 .4693 .5000 z =1.875 80 120 160 200 240 280 320

Add area Lower half .5000 - .4911 = .0089 .5000 - .4913 = .0087 z = 295-200 40 z = 2.375 Go to table .4911 or .4913 26 Please note: If z-score rounded to 2.38, then area = .0087 also fine: 0.89% .4911 .0089 z =2.375 80 120 160 200 240 280 320

z = 130-200 40 = -1.75 .4599 Add to upper Half of curve Go to table .5000 + .4599 = .9599 27 also fine: 95.99% .9599 .5000 .4599 z =-1.75 80 120 160 200 240 280 320

40 z = 130-200 = -1.75 .4599 Subtract from .5000 .5000 - .4599 = .0401 Go to table 28 .0401 .4599 .5000 also fine: 4.01% z =-1.75 80 120 160 200 240 280 320

z table provides area from mean to score x = mean + z σ = 200 + (2.33)(40) = 293.2 99th percentile Find area of interest .9900 - .5000 = .4900 Find nearest z = 2.33 29 .4900 .9900 z table provides area from mean to score .5000 293.2 z =2.33 80 ? 120 160 200 240

z table provides area from mean to score 33rd percentile Find area of interest .5000 - .3300 = .1700 Find nearest z = .44 x = mean + z σ = 200 + (-.44)(40) = 182.4 30 z table provides area from mean to score Note: .33 +.17 =.50 .3300 .1700 182.4 z =-.44 ? 80 200 240 280 320

z table provides area from mean to score 40th percentile Find area of interest .5000 - .4000 = .1000 Find nearest z = -.25 x = mean + z σ = 200 + (-.25)(40) = 190 31 z table provides area from mean to score Note: .40 +.10 =.50 190 .1000 .4000 z =-.25 ? 80 200 240 280 320

z table provides area from mean to score 67th percentile Find area of interest .6700 - .5000 = .1700 Find nearest z = .44 x = mean + z σ = 200 + (.44)(40) = 217.6 32 z table provides area from mean to score .1700 z =.44 80 200 217.6 ? 320

Please hand in Homework worksheet Kristina Lecturer’s desk Attila Screen Screen Kristina Lecturer’s desk Row A 15 14 Row A 13 12 11 10 9 8 7 6 5 4 3 2 1 Row A Attila Row B 23 22 21 20 Row B 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row B Row C 25 24 23 22 21 Row C Please hand in Homework worksheet 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row C Row D 29 28 27 26 25 24 23 Row D 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row D Row E 31 30 29 28 27 26 25 24 23 Row E 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row E Michelle Row F 35 34 33 32 31 30 29 28 27 26 Row F 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row F Row G 35 34 33 32 31 30 29 28 27 26 Row G 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row G Row H 37 36 35 34 33 32 31 30 29 28 Row H 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row H 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 Row J 13 12 11 10 9 8 7 6 5 4 3 2 1 Row J 41 40 39 38 37 36 35 34 33 32 31 30 29 Row K 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row K Row L 33 32 31 30 29 28 27 26 25 Row L 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row L Row M 21 20 19 Row M 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row M Row N 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Row P 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Sezen Hannah table 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Projection Booth Left handed desk Harvill 150 renumbered

Thank you! See you next time!!