1. + Lab 4: Expert Groups 008 Group 1DavidGuillermoLaurenMallory 2JonathonVivianKristen 3Alexander BBerkleyMelanieEddie 4RichardKeltanHeather Skriba 5ChrisMayaHeather SmallwoodAlexander W 6MollieBradHannah 7ErinHowieAnnaPujiao 8JessicaElliotDominic Please sit with your group and do not log on the computers.

2. + Lab 4: Expert Groups (010) Group 1BradSo YunKrisMolly 2JacobAlexPeter 3DrakeDannyDerekAndrew 4AshleyMichelleEmily R 5Emily FMattMatanGrant 6MadelineReneeTaylor 7KatieMardieChrissyGordon 8Emily JJosephSupriya Please sit with your group and do not log on the computers.

3. + STATS 250 Lab 3 Julie Ghekas September 22, 2014 Please don’t log in. We will not be using the computers, and we will be moving.

4. + Schedule Lab 2 Wrap Up Probability Warm Up Lab 3 Cool Down/iClicker Questions Example Exam Question

5. + Practice Homework Comments Only 80% of you turned in homework As a class, you struggled the most with Q3 Estimating the percent of time over 90 minutes Show work Count frequencies over 90/total (272) *100 Graph Describe the shape In context With values

6. + Time Plots Looks can be misleading Has a time variable on the x-axis Checking for stability to check independently distributed assumption Trend means no trend, no seasonal variation, and no pattern in variation Should make histogram only when the time plot shows stability

7. + Lab 2: Time-Dependent Data

8. +

9. + QQ Plots Is the sample drawn from a normally distributed population? We want a roughly straight line. Remember that we are making inferences about the population. Shows the relationship between quantiles (Q) of observed data and quantiles (Q) of expected of a normal distribution.

10. + Ticket: Warm Up Answers

11. + Ticket: Cool Down Answers

12. +

13. + Probability

14. + Three distributions that you have learned: NormalX~N( μ, σ ) Standard NormalX~N(0, 1) BinomialX~Binom(n, p) Normal Approximation for Binomial Distribution UniformX~Unif(a,b) Two probability definitions that you have learned: Independent events Mutually exclusive events

15. + Probability Rules from Yellow Formula Card To calculate the probability of an observation by hand: Draw distribution curve Shade appropriate area of the curve Calculate the probability using z-table if normal distribution Calculate area under the curve if continuous random variable Add the individual probabilities if discrete random variable

16. + Probability Calculations Empirical rule can answer some probability questions What if empirical rule fails because observation is not exactly on a standard deviation from the mean? Example: random variable IQ scores for Americans IQ~N(100,20) P(IQ>125) Draw the curve, and shade the area Find the z-score, and use Table A1 on your formula card

17. + Probability Calculations: Table A1 Use only with Normal distributions Provides probabilities for a standard normal curve Gives area to the left of a z- score Let’s try using Table A1

18. + Probability Calculations If IQ~N(100, 20), find P(IQ>125)

19. + Probability Calculations Can use R to calculate probability Canvas -> R Tutorials -> Probabilities in R -> Download file under Necessary Files header Open the downloaded prob-calc.rdata Type prob( ) to start the program Type q to quit Calculate P(Z<1.2)

20. + Probability Calculations Can use R to calculate probability Canvas -> R Tutorials -> Probabilities in R -> Download file under Necessary Files header Open the downloaded prob-calc.rdata Type prob( ) to start the program Type q to quit Calculate P(Z<1.2) = 0.8849

21. + Probability Calculations What if the distribution is Uniform instead of Normal? Example: IQ~U(100, 200) Draw curve, and shade desired region Find the area of rectangle(s) Area=length*width

22. + Probability Calculations If IQ~U(100, 200), find P(IQ>125)

23. + Probability Calculations If discrete random variable, then sum up all of the individual probabilities Binomial distribution is a discrete distribution Binomial counts the number of successful trials with equal probability p if you perform n trials Consider flipping a coin 10 times. If X is a random variable for the number of heads, X~Bin(10, 0.5), assuming the coin is fair

24. + Probability Calculations If X~ Bin(10, 0.25), find P(X<2)

25. + Warm Up

26. + Warm Up/iClicker A. Uniform(10, 20) B. Uniform(15, 5) C. Normal(15, 5) D. Uniform(10, 1/10)

27. + Warm Up/iClicker A. Uniform(10, 20) B. Uniform(15, 5) C. Normal(15, 5) D. Uniform(10, 1/10)

28. + Warm Up/iClicker A. Normal(10,.45) B. Binomial(10,.45) C. Uniform(0, 10) D. Binomial(4.5, 10)

29. + Warm Up/iClicker A. Normal(10,.45) B. Binomial(10,.45) C. Uniform(0, 10) D. Binomial(4.5, 10)

30. + Warm Up/iClicker A. Uniform(12, 84) B. Normal(12, 84) C. Normal(48, 12) D. Uniform(48, 12)

31. + Warm Up/iClicker A. Uniform(12, 84) B. Normal(12, 84) C. Normal(48, 12) D. Uniform(48, 12)

32. + Lab 4: Expert Groups 008 GroupProblemFloat 11DavidGuillermoLaurenMallory 21JonathonVivianKristen 32Alexander BBerkleyMelanieEddie 42RichardKeltanHeather Skriba 53ChrisMayaHeather SmallwoodAlexander W 63MollieBradHannah 74ErinHowieAnnaPujiao 84JessicaElliotDominic Don’t worry about the R-script part of Problem 4 Change Question 3 part c to “Interpret the z-score.”

33. + Lab 4: Expert Groups (010) GroupProblemFloat 11BradSo YunKrisMolly 21JacobAlexPeter 32DrakeDannyDerekAndrew 42AshleyMichelleEmily R 53Emily FMattMatanGrant 63MadelineReneeTaylor 74KatieMardieChrissyGordon 84Emily JJosephSupriya Don’t worry about the R-script part of Problem 4 Change Question 3 part c to “Interpret the z-score.”

34. + Lab 4: Share Groups 008 Problem1234 1DavidAlexander BChrisErin 2GuillermoBerkleyMayaHowie 3LaurenMelanieHeather SmallwoodAnna 4JonathonRichardMolliePujiao 5VivianKeltanBradJessica 6KristenHeather SkribaHannahElliot 7MalloryEddieAlexander WDominic Don’t worry about the R-script part of Problem 4

35. + Lab 4: Share Groups (010) Problem1234 1BradDrakeEmily FKatie 2So YunDannyMattMardie 3KrisDerekMatanChrissy 4MollyAndrewGrantGordon 5JacobAshleyMadelineEmily J 6AlexMichelleReneeJoseph 7PeterEmily RTaylorSupriya Don’t worry about the R-script part of Problem 4

36. + Lab 4: Problem 1 a. What is the probability that a randomly selected person smiled? b. To check if smiling status is independent of gender, (a) should be compared to: P(smiled and male)P(smiled given male) P(male given smiled)P(male) c. Find (b). d. Do smiling status and gender appear to be independent? SmileNo SmileTotal 1=Male326938067075 2=Female447142788749 Total7740808415824

37. + Lab 4: Problem 2 Suppose the probability of 7 days is twice as likely as the probability of 8 days. Complete the probability distribution. What is the expected number of days for the longest trip? Include symbol, value, and units. X45678 Probability0.100.200.25

38. + Lab 4: Problem 3 Which are correct? On average, the number of hours spent studying statistics varied from the mean by about 3.5 hours. The average distance between the number of hours spent studying statistics is roughly 3.5 hours. The average number of hours spent studying statistics is about 3.5 hours away from the mean.

39. + Lab 4: Problem 3 Assume the mean is 10 and the standard deviation is 3.5. Julie studies for about 6 hrs/week. What is her z-score? Male students have a lower mean and larger standard deviation than female students. Jake’s response corresponds to z=2.1. Can we compare scores?

40. + Lab 4: Problem 4 Assume that for Chem, the mean is 12 and the standard deviation is 3. What is the probability that a randomly selected Chemistry student studies between 16 and 20 hours per week?

41. + Lab 4: Problem 4 Assume that for Chem, the mean is 12 and the standard deviation is 3. Jing learns that she is in the top 30%. This means that Jing must study at least how many hours per week?

42. + Cool Down/iClicker If the time to wait for pharmacy help has a uniform distribution from 0 to 30 minutes, then 33% of the customers are expected to wait for more than 20 minutes. A. True B. False

43. + Cool Down/iClicker If the time to wait for pharmacy help has a uniform distribution from 0 to 30 minutes, then 33% of the customers are expected to wait for more than 20 minutes. A. True B. False

44. + Cool Down/iClicker If X has a Binomial(50, 0.7) distribution, then the criteria to use the normal approximation are met. A. True B. False

45. + Cool Down/iClicker If X has a Binomial(50, 0.7) distribution, then the criteria to use the normal approximation are met. A. True B. False

46. + Cool Down/iClicker 68% of all test scores will fall within one standard deviation of the mean test score. A. True B. False

47. + Cool Down/iClicker 68% of all test scores will fall within one standard deviation of the mean test score. A. True B. False

48. + Cool Down/iClicker Police report that 78% of drivers stopped on suspicion of drunk driving are given a breath test, 36% are given a blood test, and 22% are given both tests. Do the police administer these two tests independently? A. True B. False

49. + Cool Down/iClicker Police report that 78% of drivers stopped on suspicion of drunk driving are given a breath test, 36% are given a blood test, and 22% are given both tests. Do the police administer these two tests independently? A. True B. False

50. + iClicker If the variable X is strongly skewed to the right with a mean of 80 and a standard deviation of 2, then 95% of the values are expected to be between 76 and 84. A. True B. False

51. + iClicker If the variable X is strongly skewed to the right with a mean of 80 and a standard deviation of 2, then 95% of the values are expected to be between 76 and 84. A. True B. False

52. + iClicker Suppose the amount spent by students on materials for summer half term has approx a normal, bell-shaped distribution. Mean amount spent was $300 and standard deviation was $100. About 68% of the students spent between ____. A. $300 and $400 B. $200 and $400 C. $100 and $500 D. $266 and $334

53. + iClicker Suppose the amount spent by students on materials for summer half term has approx a normal, bell-shaped distribution. Mean amount spent was $300 and standard deviation was $100. About 68% of the students spent between ____. A. $300 and $400 B. $200 and $400 C. $100 and $500 D. $266 and $334

54. + iClicker Suppose the amount spent by students on materials for summer half term has approx a normal, bell-shaped distribution. Mean amount spent was $300 and standard deviation was $100. What amount spent on materials has a standardized score of 0.5? A. $150 B. $250 C. $300.50 D. $350

55. + iClicker Suppose the amount spent by students on materials for summer half term has approx a normal, bell-shaped distribution. Mean amount spent was $300 and standard deviation was $100. What amount spent on materials has a standardized score of 0.5? A. $150 B. $250 C. $300.50 D. $350

56. + iClicker Suppose the amount spent by students on materials for summer half term has approx a normal, bell-shaped distribution. Mean amount spent was $300 and standard deviation was $100. Approx what percent of students spent more than $400 on materials? A. 16% B. 32% C. 68% D. 50%

57. + iClicker Suppose the amount spent by students on materials for summer half term has approx a normal, bell-shaped distribution. Mean amount spent was $300 and standard deviation was $100. Approx what percent of students spent more than $400 on materials? A. 16% B. 32% C. 68% D. 50%

58. + Example Exam Question

59. + What is P(A)? What is P(A and B)? What is P(B|A) What is P(A and C)? Are the events A and C mutually exclusive?

60. + iClicker How did you feel about the material covered in today’s lab? A. Completely understood everything B. Understood main ideas, shaky on details C. Good for the first half, lost for the second D. Trouble with some main ideas E. Difficulty following most material

61. + Reminders Homework 1 is open and due Thursday at 8 am No prelab due this week Can do prelab for next week