1. Study Session April 21, 2009
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
 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 35
D C
D C
µ µ
σ σ
= =
= =

8. 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 35
D C
D C
µ µ
σ σ
= =
= =

9. 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 35
D C
D C
µ µ
σ σ
= =
= =

10. 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 35
D C
D C
µ µ
σ σ
= =
= =

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

12. 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)

13. 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?

14. 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)

15. 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.

16. 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)

17. 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?

18. 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

19. 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?

20. 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

21. 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.

22. 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

23. 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.

24. 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

25. 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?

26. 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

27. 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?

28. 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

29. 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

30. 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

31. 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

32. 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 IndependenceSeverity of attack
Severe Medium Mild
Antibody Positive test 85 125 150
test Negative test 40 95 145

33. 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

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