Transcript Study Session May 2, 2005

Study Session May 3, 2007
Design
Probability
Inference
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
4. 25
7. 25
2.
5.
8.
34
33
32
3.
6.
24
22
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
 73676 47150

05756
99400
28713
01927
Treatment Groups

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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

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.

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?

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

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?

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
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.
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
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?
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
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 1attached, 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 1attached, 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.
Antibody
test
Severity
of attack
Severe
Medium
Mild
Positive test
85
125
150
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
Antibody
test
Severity
of attack
Severe
Medium
Mild
Positive test
85
125
150
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.
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