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Homework review

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My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z Please click in Set your clicker to channel 41

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Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, SOC200 Lecture Section 001, Fall, 2011 Room 201 Physics-Atmospheric Sciences (PAS) 10:00 - 10:50 Mondays & Wednesdays + Lab Session http://www.youtube.com/watch?v=oSQJP40PcGI

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By the end of lecture today 10/3/11 Use this as your study guide Measures of variability Standard deviation and Variance Estimating standard deviation Exploring relationship between mean and variability Empirical, classical and subjective approaches Probability of an event Complement of an event; Union of two events Intersection of two events; Mutually exclusive events Collectively exhaustive events Conditional probability

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Please double check – All cell phones other electronic devices are turned off and stowed away Homework due - (October 5 rd ) On class website: please print and complete homework worksheet #7

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Please read: Chapters 5 - 9 in Lind book & Chapters 10, 11, 12 & 14 in Plous book: Lind Chapter 5: Survey of Probability Concepts Chapter 6: Discrete Probability Distributions Chapter 7: Continuous Probability Distributions Chapter 8: Sampling Methods and CLT Chapter 9: Estimation and Confidence Interval Plous Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability and Risk Chapter 14: The Perception of Randomness

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ApproachExample EmpiricalThere is a 2 percent chance of twins in a randomly- chosen birth. ClassicalThere is a 50 % probability of heads on a coin flip. SubjectiveThere is a 75 % chance that England will adopt the Euro currency by 2010.

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Two mutually exclusive characteristics: if the occurrence of any one of them automatically implies the non-occurrence of the remaining characteristic Two mutually exclusive characteristics: if the occurrence of any one of them automatically implies the non-occurrence of the remaining characteristic Two events are mutually exclusive if they cannot occur at the same time (i.e. they have no outcomes in common). Two propositions that logically cannot both be true. http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-manWarranty No Warranty For example, a car repair is either covered by the warranty (A) or not (B).

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Events are collectively exhaustive if their union is the entire sample space S. Events are collectively exhaustive if their union is the entire sample space S. Two mutually exclusive, collectively exhaustive events are dichotomous (or binary) events. Two mutually exclusive, collectively exhaustive events are dichotomous (or binary) events. For example, a car repair is either covered by the warranty (A) or not (B). Warranty No Warranty Collectively Exhaustive Events

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Satirical take on being mutually exclusive Recently a public figure in the heat of the moment inadvertently made a statement that reflected extreme stereotyping that many would find highly offensive. It is within this context that comical satirists have used the concept of being mutually exclusive to have fun with the statement. http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man Transcript: Speaker 1: Hes an Arab Speaker 2: No maam, no maam. Hes a decent, family man, citizen… Arab Decent, family man Warranty No Warranty

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Lets estimate some standard deviation values Standard deviation is a spread score Were estimating the typical distance score (distance of each score from the mean)

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Movie Packages We sampled 100 movie theaters (Two tickets, large popcorn and 2 drinks)

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Mean = $37 Range = $27 - $47 Whats the largest possible deviation? Whats the typical or standard deviation? Standard Deviation = 4.3 $47 – $37 = $10 $27 – $37 = -$10

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Waiting time for service at bank We sampled 100 banks (From time entering line to time reaching teller) Mean = 3 minutes Range = 2.2- 3.6 Whats the largest possible deviation? Whats the typical or standard deviation? Standard Deviation = 0.31 3.6 – 3.0=.6 2.2 – 3.0= -.8

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Mean = 1700 pounds Range = 1240 – 2110 Whats the typical or standard deviation? Standard Deviation = 200 Pounds of pressure to break casing on an insulator We sampled 100 insulators (applied pressure until the insulator broke) Whats the largest possible deviation? 1240 – 1700 = -460 2110 – 1700 = 410

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Mean = 2.5 kids Range = 1 - 8 Whats the typical or standard deviation? Standard Deviation = 1.7 Number of kids in family We sampled 100 families (counted number of kids) Whats the largest possible deviation? 1 - 2.5= -1.5 8 – 2.5= 5.5

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Mean = 80 Range = 55 - 100 Whats the typical or standard deviation? Standard Deviation = 10 Number correct on exam We tested 100 students (counted number of correct on 100 point test) Whats the largest possible deviation? 100 - 80 = 20 55 - 80= -25

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Lets try one Standard Deviation = 27 Monthly electric bills for 50 apartments (amount of dollars charged for the month) 150 – 213 = - 63 150 – 97 = 53 Mean = $150 Range = 97 - 213 Whats the largest possible deviation? The best estimate of the population standard deviation is a. $150 b. $27 c. $53 d. $63

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Lets try one Standard Deviation = 0.044 Amount of soda in 2-liter containers (measured amount of soda in 2-liter bottles) The best estimate of the population standard deviation is a. 0.106 b. 0.109 c. 0.044 d. 2.0 Mean = 2.0 Range = 1.894 – 2.109 Whats the largest possible deviation? 2 – 1.894 = 0.106 2 – 2.109 = -0.109

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Lets try one Standard Deviation = 10 Scores on an Art History exam (measured number correct out of 100) The best estimate of the population standard deviation is a. 50 b. 25 c. 10 d..5 Mean = 50 Range = 25 - 70 Whats the largest possible deviation? 70 - 80 = 20 25 - 50= - 25

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Lets try one Standard Deviation = 10 Amount of soda in 2-liter containers (measured amount of soda in 2-liter bottles) The best estimate of the population standard deviation is a. 50 b. 25 c. 10 d..5 Mean = 50 Range = 25 - 70 One way to estimate standard deviation* σ range / 6 45 / 6 = 7.5 *See page 142 in text

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Mean = 50 Range = 25 - 70 Standard Deviation = 10 Number correct on exam We tested 100 students (counted number of correct on 100 point test)

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If score is within 2 standard deviations (z < 2) not unusual score If score is beyond 2 standard deviations (z 2) is unusual score If score is beyond 3 standard deviations (z 3) is an outlier If score is beyond 4 standard deviations (z 4) is an extreme outlier

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Variability and means 38 40 44 48 52 56 58 40 44 48 52 56 What might this be an example of? What might the standard deviation be? The variability is different…. The mean is the same …

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Variability and means 38 40 44 48 52 56 58 40 44 48 52 56 What might this be an example of? What might the standard deviation be? Heights of elementary students Heights of 3 rd graders Other examples?

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Variability and means 38 40 44 48 52 56 58 40 44 48 52 56 Remember, there is an implied axis measuring frequency f f

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Variability and means What might this be an example of? What might the standard deviation be? Other examples? 0 4 8 12 16 Hours of homework – (kids K – 12) Hours of homework – (7 grade)

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Variability and means What might this be an example of? What might the standard deviation be? Other examples? 40 50 60 70 80 90 100 Score on driving test Driving ability – (35 year olds) 40 50 60 70 80 90 100 Score on driving test Driving ability – (16 - 90)

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Variability and means Distributions same mean different variability Final exam scores C students versus whole class Birth weight within a typical family versus within the whole community Running speed 30 year olds vs. 20 – 40 year olds Number of violent crimes Milwaukee vs. whole Midwest Social distance (personal space) California vs international community

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Variability and means Distributions different mean same variability Performance on a final exam Before versus after taking the class 40 50 60 70 80 90 100 Score on final (before taking class)

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Variability and means Distributions different mean same variability 62 64 66 68 70 72 74 76 Inches in height (women) Height of men versus women 62 64 66 68 70 72 74 76 Inches in height (men)

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Variability and means Distributions different mean same variability 2 4 6 8 10 12 14 16 Number of errors (not on phone) Driving ability Talking on a cell phone or not 2 4 6 8 10 12 14 16 Number of errors (on phone)

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Variability and means Comparing distributions different mean same variability Performance on a final exam Before versus after taking the class Height of men versus women Driving ability Talking on a cell phone or not

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. Writing Assignment Comparing distributions (mean and variability) Think of examples for these three situations same mean but different variability same variability but different means same mean and same variability (different groups) estimate standard deviation calculate variance for each curve find the raw score for the zs given on worksheet

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