Study Session May 3, 2007

1. Study Session May 3, 2007 Design Probability Inference

2. Design • Eight overweight females have agreed to participate in a study of the effectiveness of two reducing regimens, A or B. The researcher first calculates how overweight each subject is by comparing the subject’s actual weight with her “ideal” weight. The subjects and their excess weights are as follows:

3. Subjects are numbered with their excess weights noted. Copy this list. 1. 34 2. 34 3. 24 4. 25 5. 33 6. 22 7. 25 8. 32

4. Blocking The response variable is the weight lost after eight weeks of treatment. Because the initial amount overweight will influence the response variable, a block design is appropriate. Form 2 blocks according to the subjects excess weight. Describe your method.

5. Treatment Groups • Describe a procedure for using the random digit table to assign the subjects to the two reducing regimens. • 19223 95024 05756 28713 • 73676 47150 99400 01927

6. Treatment Groups • Block 1: 1, 2, 5, 8 • Block 2: 3, 4, 6, 7 • Read the table from the left one digit at a time. The first 2 digits that appear in the RDT from Block I will receive Treatment A, the rest Treatment B. • Block 1: 1, 2, 5, 8 19223 • Subjects 1 & 2 will receive A, while 5 & 8 will receive B.

7. Probability • Two stores sell watermelons. At the first store the melons weigh an average of 22 pounds, with a standard deviation of 2.5 pounds. At the second store, the melons are smaller with an average of 18 pounds and a standard deviation of 2 pounds. You select a melon at random at each store.

8. Two stores sell watermelons. At the first store the melons weigh an average of 22 pounds, with a standard deviation of 2.5 pounds. At the second store, the melons are smaller with an average of 18 pounds and a standard deviation of 2 pounds. You select a melon at random at each store. What is the mean difference in weights of melons? What is the standard deviation of the difference in weights?

9. Two stores sell watermelons. At the first store the melons weigh an average of 22 pounds, with a standard deviation of 2.5 pounds. At the second store, the melons are smaller with an average of 18 pounds and a standard deviation of 2 pounds. You select a melon at random at each store. What is the mean difference in weights of melons? 4 What is the standard deviation of the difference in weights? 3.2016

10. Two stores sell watermelons. At the first store the melons weigh an average of 22 pounds, with a standard deviation of 2.5 pounds. At the second store, the melons are smaller with an average of 18 pounds and a standard deviation of 2 pounds. You select a melon at random at each store. If a Normal model can be used to describe the difference in weights, what is the probability that the melon you got at the first store is heavier?

11. Two stores sell watermelons. At the first store the melons weigh an average of 22 pounds, with a standard deviation of 2.5 pounds. At the second store, the melons are smaller with an average of 18 pounds and a standard deviation of 2 pounds. You select a melon at random at each store. If a Normal model can be used to describe the difference in weights, what is the probability that the melon you got at the first store is heavier? .8942

12. Buying Melons • The first store sells watermelons for 32 cents a pound. The second store is having a sale on watermelons for 25 cents a pound. Find the mean and standard deviation of the difference in the price you may pay for the melons randomly selected at each store.

13. Buying Melons • The first store sells watermelons for 32 cents a pound. The second store is having a sale on watermelons for 25 cents a pound. Find the mean and standard deviation of the difference in the price you may pay for the melons randomly selected at each store. • Mean difference: 2.54 • Standard deviation of the difference is .94

14. Blood • Only 4% of people have Type AB blood. • On average, how many donors must be checked to find someone with Type AB blood?

15. Blood • Only 4% of people have Type AB blood. • On average, how many donors must be checked to find someone with Type AB blood? • Mean 1/p = 1/.04 =25 (Geometric)

16. Blood • Only 4% of people have Type AB blood. • What is the probability that a Type AB donor will not be found until the 5th person checked?

17. Blood • Only 4% of people have Type AB blood. • What is the probability that a Type AB donor will not be found until the 5th person checked? • (.96)^4(.04) = .0340 (Geometric)

18. Blood • Only 4% of people have Type AB blood. • Ten donors arrive to give blood. What is the probability that exactly one of them will have Type AB.

19. Blood • Only 4% of people have Type AB blood. • Ten donors arrive to give blood. What is the probability that exactly one of them will have Type AB. • 10 C 1 (.04)^1 (.96)^9 = .2770 (Binomial)

20. Which Significance Test? • A random sample of 10 one – bedroom apartments from your local newspaper has these monthly rents (dollars): • 500, 650, 600, 505, 450, 550, 515, 495, 650, 395 • Do these data give good reason to believe that the mean rent is greater than $50 per month?

21. Which Significance Test? • A random sample of 10 one – bedroom apartments from your local newspaper has these monthly rents (dollars): • 500, 650, 600, 505, 450, 550, 515, 495, 650, 395 • Do these data give good reason to believe that the mean rent is greater than $50 per month? • Answer: 1 Sample Mean T

22. Which Significance Test? • A factory hiring people to work on an assembly line gives job applicants a test of manual agility. This test counts how many strangely shaped pegs the applicant can fit into matching holes in a one-minute period. Fifty males were tested with a mean of 19.39 and a standard deviation of 2.52. Fifty females were tested with a mean of 17.91 and a standard deviation of 3.39. Is there significant evidence to suggest that men can fit more pegs during the allowed time than women?

23. Which Significance Test? • A factory hiring people to work on an assembly line gives job applicants a test of manual agility. This test counts how many strangely shaped pegs the applicant can fit into matching holes in a one-minute period. Fifty males were tested with a mean of 19.39 and a standard deviation of 2.52. Fifty females were tested with a mean of 17.91 and a standard deviation of 3.39. Is there significant evidence to suggest that men can fit more pegs during the allowed time than women? • Answer: 2 Sample Mean T

24. Which Significance Test? • An education researcher wants to learn whether inserting questions before or after introducing a new concept is more effective. He prepares two text segments that teach the concept, one with motivating questions before and the other with review questions after. Each text segment is used to teach a different group of children, and their scores on a test over the material is compared.

25. Which Significance Test? • An education researcher wants to learn whether inserting questions before or after introducing a new concept is more effective. He prepares two text segments that teach the concept, one with motivating questions before and the other with review questions after. Each text segment is used to teach a different group of children, and their scores on a test over the material is compared. • Answer: 2 Sample Mean T

26. Which Significance Test? • Another researcher approaches the same problem differently. She prepares text segments on two unrelated topics. Each segment comes in two versions, one with questions before and the other with questions after: Each of a group of children is taught both topics, one topic (chosen at random) with questions before and the other with questions after. Each child’s test scores on the two topics are compared to see which topic he or she learned better.

27. Which Significance Test? • Another researcher approaches the same problem differently. She prepares text segments on two unrelated topics. Each segment comes in two versions, one with questions before and the other with questions after: Each of a group of children is taught both topics, one topic (chosen at random) with questions before and the other with questions after. Each child’s test scores on the two topics are compared to see which topic he or she learned better. • Answer: Matched Pairs T

28. Which Significance Test? • The English mathematician John Kerrich tossed a coin 10,000 times and obtained 5067 heads. Is this significant evidence at the 5% level that the probability that Kerrich’s coin comes up heads is not .5?

29. Which Significance Test? • The English mathematician John Kerrich tossed a coin 10,000 times and obtained 5067 heads. Is this significant evidence at the 5% level that the probability that Kerrich’s coin comes up heads is not .5? • Answer: 1 Proportion Z

30. Which Significance Test? • To devise effective marketing strategies it is helpful to know the characteristics of your customers. A study compared demographic characteristics of people who use the Internet for travel arrangements an of people who do not. Of 1132 Internet users, 643 had completed college. Among the 852 nonusers, 349 had completed college. Do users and nonusers differ significantly?

31. Which Significance Test? • To devise effective marketing strategies it is helpful to know the characteristics of your customers. A study compared demographic characteristics of people who use the Internet for travel arrangements an of people who do not. Of 1132 Internet users, 643 had completed college. Among the 852 nonusers, 349 had completed college. Do users and nonusers differ significantly? • 2 Proportion Z

32. Which Significance Test? • Two human traits controlled by a single gene are the ability to roll one’s tongue and whether one’s ear lobes are free or attached to the neck. Genetic theory says that people will have neither, one, or both of these traits in the ratio 1:3:3:9 1-attached, non-curling; 3 – attached, curling; 3 – free, non-curling; 9 – free, curling. A Biology class of 122 students collected data listing the counts in the order of the ratio given: 10, 22, 31, 59

33. Which Significance Test? • Two human traits controlled by a single gene are the ability to roll one’s tongue and whether one’s ear lobes are free or attached to the neck. Genetic theory says that people will have neither, one, or both of these traits in the ratio 1:3:3:9 1-attached, non-curling; 3 – attached, curling; 3 – free, non-curling; 9 – free, curling. A Biology class of 122 students collected data listing the counts in the order of the ratio given: 10, 22, 31, 59 • Chi-Square Goodness of Fit

34. Severity of attack Severe Medium Mild Antibody Positive test 85 125 150 test Negative test 40 95 145 Which Significance Test? • A medical researcher tests 640 heart attack victims for the presence of a certain antibody in their blood and cross-classfies against the severity of the attack. The results are reported in the table below. Is there evidence of a relationship between presence of the antibody and severity of the heart attack? Test at the 5% significance level.

35. Severity of attack Severe Medium Mild Antibody Positive test 85 125 150 test Negative test 40 95 145 Which Significance Test? • A medical researcher tests 640 heart attack victims for the presence of a certain antibody in their blood and cross-classfies against the severity of the attack. The results are reported in the table below. Is there evidence of a relationship between presence of the antibody and severity of the heart attack? Test at the 5% significance level. • Answer: Chi-Square Test of Independence

36. Scoring a Significance Test • 1 pt for the null and alternative hypotheses & defining the parameter. • 1 pt for assumptions & either the test statistic and formula OR name of the test

37. Scoring a Significance Test • 1 pt Mechanics; the value of the test statistic & p-value • 1 pt for decision referencing alpha & conclusion in context.