Study Session April 21, 2009

DesignProbabilityInference

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:

Subjects are numbered with their excess weights noted. Copy this list.

1. 34 2. 34 3. 244. 25 5. 33 6. 227. 25 8. 32

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.

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

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.

Probability The American Veterinary Association

claims that the annual cost of medical care for dogs averages $100 with a standard deviation of $30, and for cats averages $120, with a standard deviation of $35.

A) What’s the expected difference in the cost of medical care for dogs and cats?

B) What’s the standard deviation of that difference?

100 120

30 35D C

D C

Probability The American Veterinary Association

claims that the annual cost of medical care for dogs averages $100 with a standard deviation of $30, and for cats averages $120, with a standard deviation of $35.

C) If the difference in costs can be described by a Normal model, what’s the probability that medical expenses are higher for someone’s dog than for her cat?

100 120

30 35D C

D C

Probability You are thinking about getting two dogs

and a cat. Assume that annual veterinary expenses are independent and have a Normal model with the means and standard deviations described above.

A) Define appropriate variables and express the total annual veterinary costs you may have.

100 120

30 35D C

D C

Probability You are thinking about getting two dogs

and a cat. Assume that annual veterinary expenses are independent and have a Normal model with the means and standard deviations described previously.

B) Describe the model for this total cost. Be sure to specify its name, expected value, and standard deviation.

C) What’s the probability that your total expenses will exceed $400?

100 120

30 35D C

D C

Blood Only 4% of people have Type AB

blood. On average, how many donors must

be checked to find someone with Type AB blood?

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)

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?

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)

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.

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)

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?

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

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?

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

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.

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

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.

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

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?

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

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?

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

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

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

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.    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    Severity of attack  

    Severe Medium Mild

Antibody

Positive test 85 125 150

test Negative test

40 95 145

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

Scoring a Significance Test 1 pt Mechanics; the value of the test

statistic & p-value 1 pt for decision referencing alpha &

conclusion in context.