Chapter 12
Notes
Chapter 11 Part I
Answers
Chapter 11 Part II
Answers
Chapter 12
Sampling
Surveys
How do we gather data?
•
•
•
•
Surveys
Opinion polls
Interviews
Studies
– Observational
• Retrospective (past)
• Prospective (future)
• Experiments
1.
Population
• the entire group of
individuals that we
want information about
2.
Census
• Gathering data
involving the entire
population
3.
Why would we not use
a census all the time?
1)
2)
3)
4)
•
•
•
Not accurate
Very expensive
Look at the U.S. census – it
Perhaps impossible
has a huge
amount you
of error
If using destructive
sampling,
wouldin
Since
census
ofknow
any
Suppose
you
it; taking
plus
it awanted
takes
a to
long
to
destroypopulation
thethe
population
takesweight
time, censuses
average
of the
compile the data making the
Breaking strength
of soda bottles
are
VERY
costly
to do!
white-tail
deer
population
data obsolete
by
the
timeinwe
Lifetime
of flashlight
batteries
Texas
– would
it be
get
it! feasible to
Safety ratings for cars
do a census?
4.
Sample
• A part of the population that
we actually examine in
order to gather information
• Use sample to generalize
the population
Why Do We Sample Anyway?
HOW GOOD ARE CURRENT INSPECTION SYSTEMS
Printed below is a story which can be used to
demonstrate the effectiveness of 100% inspection.
Assume that the letter “G” or “g” is a defective
product caused by the Gremlin, and that you are the
inspector. Allow yourself about 3 minutes to count all
the G’s or g’s. Place your total in the box at the bottom
of the story.
3
Minutes
Total number
found:
2
Minutes
Total number
found:
1
Minutes
Total number
found:
15
Seconds
Total number
found:
TIME!
Total number
found:
Why do we sample?
Take a Census of all the “G” or
“g” which appear in the story.
The actual count is…
83
5.
Sampling design
• refers to the method
used to choose the
sample from the
population
6.
Sampling frame
• a list of every
individual in the
population
7.
Simple Random
Sample (SRS)
• consist of n individuals from the
population chosen in such a way
that
–every individual has an equal
chance of being selected
7.
Simple
Random
Suppose we were to take an SRS of
50 SHS
students – put
each students’
Sample
(SRS)
name in a hat. Then randomly select
• consist
of n individuals
from
the
50 names
from the hat.
Each
student has
the same
chancea to
be
population
chosen
in such
way
selected!
that
–every individual has an equal
chance of being selected
7.
Simple Random
Sample (SRS)
• consist of n individuals from the
population chosen in such a way
that
–every individual has an equal
chance of being selected
–every set of n individuals has an
equal chance of being selected
7.
Simple Random
Sample
(SRS)
Not only does each student have the
• same
consist
of ntoindividuals
the
chance
be selected –from
but every
possible groupchosen
of 50 students
the
population
in such has
a way
same chance to be selected!
that
Therefore,
it has to be possible for all
50 students to be seniors in order for
–every individual
has
an
equal
it to be an SRS!
chance of being selected
–every set of n individuals has an
equal chance of being selected
Jelly Blubber Activity
• Marine biologist have just
discovered a new variety of
jellyfish called the Jelly Blubber
• We are to study a colony of Jelly
Blubbers and determine their
average length (measured
horizontally in centimeters)
Jelly Blubber Activity
• You will have 5 seconds to choose a
Jelly Blubber that you think is of
average length and then measure its
length and report your results
• Why is this not an appropriate
sampling method?
Jelly Blubber Activity
• This time you are to choose 5 Jelly
Blubbers which are a representative
sample of the colony. Measure each
blubber and calculate the mean
length.
• Why is this not an appropriate
sampling method?
Jelly Blubber Activity
• Now take a Simple Random Sample
(SRS) of 5 blubblers by generating
5 random numbers of 1 – 100.
• Measure each of the 5 random
blubbers and find the mean length
for your SRS.
What are the results of a census of
the JellyBlubbers colony?
Average size of all
100 members of the
colony is 18.64cm.
Mean 18.64cm; Standard Deviation 13.08cm;
Median 13cm; IQR = 23.5cm
Jelly Blubber Activity
• Now take a Simple Random Sample
(SRS) of 5 blubblers by generating
5 random numbers of 1 – 100.
• Measure each of the 5 random
blubbers and find the mean length
for your SRS.
• Why is this sampling method better
than just selecting 5 on your own?
7.
Simple Random
Sample (SRS)
• consist of n individuals from the
population chosen in such a way
that
–every individual has an equal
chance of being selected
–every set of n individuals has an
equal chance of being selected
8.
Stratified
random sample
• population is divided
into homogeneous
groups called strata
8.
Stratified
random sample
Homogeneous groups are groups
that are alike based upon some
characteristic of the group
members.
• population is divided
into homogeneous
groups called strata
• SRS’s are pulled from
each strata
8.
Stratified
random sample
Suppose we were to take a stratified random
sample of 50 SHS students. Since students
are already divided by grade level, grade level
can be our strata. Then randomly select a
some seniors, juniors, sophomores, and
freshman. How many depends of the proportion
of the population.
• population is divided
into homogeneous
groups called strata
• SRS’s are pulled from
each strata
8.
Stratified
random sample
If a high school is 20% Senior, 20% Junior,
30% Sophomore, & 30% Freshman, then a
50 student sample should include...
10 Seniors, 10 Juniors, 15 Sophomores, and
15 Freshman. (Use SRS for each strata.)
8.
Stratified
random sample
ON YOUR OWN: If a high school is 10%
Senior, 20% Junior, 40% Sophomore, &
30% Freshman, then a 30 student sample
should include...
9.
Systematic
random sample
• select sample by
following a systematic
approach
• randomly select where to
begin
Systematic
random sample
Suppose we want to do a systematic random
sample of SHS students - number a list of
students
(There are approximately 2000 students – if we
want a sample of 50, 2000/50 = 40)
• select
sample
by
Select a number between 1 and 40 at
random. That student
will be the first
following
a systematic
student chosen, then choose every 40
approach
student from there.
• randomly select where to
begin
th
9. Suppose we want to do a systematic
random sample of SHS students
- NUMBER a list of students
(sampling frame)
- CALCULATE grouping size:
2000 students – need sample of 50,
so 2000/50 = 40
9. Suppose we want to do a systematic
random sample of SHS students
- CALCULATE grouping size:
2000 students – need sample of 50,
so 2000/50 = 40
- USE the grouping size:
Select a number between 1 and 40 at random.
That student will be the first student chosen,
then choose every 40th student from there.
Systematic random sample
What if it doesn’t work evenly?
Say there are 2011 students.
2011/50 = 40 r. 11
Your starting place will be chosen by
randomly selecting a number between 1 &
51 instead of 1 & 40.
From there choose every 40th student from
your sample frame.
9.
Systematic random sample
ON YOUR OWN: You want to gather a
sample from 1505 students
systematically. Your sample size needs to
be 30. What do you do?
9.
10.
Cluster Sample
• based upon heterogeneous groups
which are representative of the
population
• randomly pick a cluster or clusters
• Take an SRS of that cluster(s)
10.
•
Cluster Sample
Suppose we want to do a cluster sample of
SHS students. One way to do this would
be to randomly
select classrooms during
based
upon heterogeneous
group2nd
period. Perform a SRS of the students in
which is representative
those rooms! of the
population
• randomly pick a cluster or clusters
• Take an SRS of that cluster(s)
11.
Multistage
sample
• select successively
smaller groups within
the population in stages
• SRS used at each stage
11.
Multistage
sample
To use a multistage approach to sampling
SHS students, we could first divide 2nd
period classes by level (AP, Honors,
Regular, etc.) and randomly select 4 second
period classes from each group. Then we
could randomly select 5 students from each
of those classes. The selection process is
done in stages!
• select successively
smaller groups within
the population in stages
• SRS used at each stage
12.
Identify the sampling design
a)The Educational Testing Service
(ETS) needed a sample of colleges.
ETS first divided all colleges into
groups of similar types (small
public, small private, etc.) Then
they randomly selected 3 colleges
from each group.
Stratified random sample
12.
Identify the sampling design
b) A county commissioner wants to
survey people in her district to
determine their opinions on a
particular law up for adoption. She
decides to randomly select blocks in
her district and then survey all who
live on those blocks.
Cluster sampling
12.
Identify the sampling design
c) A local restaurant manager wants
to survey customers about the
service they receive. Each night
the manager randomly chooses a
number between 1 & 10. He then
gives a survey to that customer,
and to every 10th customer after
them, to fill it out before they
leave.
Systematic random sampling
13.
Suppose your population consisted of these 20 people:
1)
6) Fred
11) Kathy
1) Aidan
Aidan
2) Bob
7) Gloria
12) Lori
3) Chico
Hannah
13)
13) Matthew
Matthew
We will8)need
to use
double
4) Dougdigit9)random
Israel numbers,
14) Nan
15) Opus
5) Edward 10) Jung
16) Paul
17) Shawnie
18) Tracy
19) Uncle Sam
20) Vernon
ignoring any number greater
than
20. Start
with
Rowa sample
1
Use
the following
random digits
to select
ofIgnore.
five from these people.
Ignore.
Ignore.Repeat.
and read
across.
Row
Stop when five people are selected. So
1 4 5 1 8 0 5 1 3 7 1
my sample would consist of :
2 0 1 5 5 1 8 1 5 7 0
3 8 9 9 3 4 3 5 0 6 3
Aidan, Edward, Matthew, Opus, and
Tracy
14.
Bias
• ERROR
Anything that causes the
• favorsdata
certain
outcomes
to be wrong! It
might be attributed to
the researchers, the
respondent, or to the
sampling method!
15.
Sources of
Bias
• things that can cause
bias in your sample
• cannot do anything
with bad data
16.
Voluntary
response
An example would be the surveys in
magazines that ask readers to mail in
the survey. Other examples are callin shows, American Idol, etc.
• People chose to respond
Remember – the way to
• Usually only
people
with
determine
Remember, the
respondentvoluntary
selects
very
strong
opinions
themselves
to participate
in the
response
is:
survey!
respond
• Produces Self-selection
bias results
17.
Convenience
sampling
•Ask
people
who
are
example
would
stopping
TheAn
data
obtained
by be
a convenience
friendly-looking
people– in
the mall
to
easy
ask
sample
willto
be biased
however
this
survey.
Another
example
is the&
method
is often
used
for surveys
surveys
left
on tables
at restaurants
results
reported
in
newspapers
and
•Produces
bias
- a convenient
magazines!method!
results
18.
Undercoverage
People with unlisted
phone numbers – usually
high-income families
•some
groups
of
People without
Suppose you take a
phone numbers –
sample by randomly
population
are
left
usually
lowselecting names from
income families
the phone book –
out
of
the
sampling
some groups will not
have the opportunity
process
People with ONLY cell
of being selected!
phones – usually young
adults
19.
Nonresponse
•People
occurs
when
an
are chosen
the individual
researchers,
Because
of
hugebytelemarketing
BUT refuse
to participate.
efforts
in
the
past
few
years,
chosen
for
the
sample
One surveys
way to help
the problem
telephone
have with
a MAJOR
self-selected!
ofNOT
nonresponse
is to make
can’t
be
contacted
or follow
problem
with
nonresponse!
up contact with the people who
refuses
This
is often
confused
are to
not cooperate
home with
whenvoluntary
you first
response!
contact them.
• telephone surveys 70%
nonresponse
20.
Response bias
Suppose we wanted to survey high
school students on drug abuse and
we used a uniformed police officer
to interview each student in our
sample – would we get honest
answers?
• occurs when the anything in
the survey design influences
the response
–The interviewer can be cause
–The survey’s wording
•Wording must be nuetral
21.
Source of Bias?
a) Before the presidential election of
1936, FDR against Republican ALF
Landon, the magazine Literary Digest
predicting Landon winning the election in
a 3-to-2 victory. A survey of 10 million
people. George Gallup surveyed only
50,000 people and
predicted
that survey
Undercoverage
– since
the Digest’s
Roosevelt
win. Theetc.,
Digest’s
comes
fromwould
car owners,
the survey
people
came from
magazine
car
selected
were
mostly subscribers,
from high-income
owners, and
telephone
directories,
etc.
families
thus mostly
Republican!
(other
answers are possible)
21.
b) Suppose that you want to
estimate the total amount of
money spent by students on
textbooks each semester at
Rice.
You
collect
register
Convenience sampling – easy way to
collect
data
receipts for
students
as they
or
leave
the
bookstore
during
Undercoverage – students who buy
lunch
booksone
fromday.
on-line bookstores are
included.
21.
c) To find the average
value of a home in
Friendswood, one averages
the price of homes that
are listed for sale with a
Undercoverage – leaves out homes
realtor.
that are not for sale or homes that
are listed with different realtors.
(other answers are possible)
22.
Page 289 #2
A question posted on the Lycos Web
site on 18 June 2000 asked visitors
to the site to say whether they
thought that marijuana should be
legally available for medicinal
purposes.
22.
Page 289 #2
A question posted on the Lycos Web site on 18 June 2000 asked
visitors to the site to say whether they thought that marijuana
should be legally available for medicinal purposes.
Identify the following items (if possible).
If you can’t tell, then say so – this
often happens when we read about a
survey.
a) The population
all U.S. adults
22.
Page 289 #2
A question posted on the Lycos Web site on 18 June 2000 asked
visitors to the site to say whether they thought that marijuana
should be legally available for medicinal purposes.
Identify the following items (if possible). If you
can’t tell, then say so – this often happens
when we read about a survey.
b) The population parameter of interest
proportion that feels marijuana
should be legalized for
medicinal purposes
22.
Page 289 #2
A question posted on the Lycos Web site on 18 June 2000 asked
visitors to the site to say whether they thought that marijuana
should be legally available for medicinal purposes.
Identify the following items (if possible). If you
can’t tell, then say so – this often happens
when we read about a survey.
c) The sampling frame
none given –potentially all
people with access to web site
22.
Page 289 #2
A question posted on the Lycos Web site on 18 June 2000 asked
visitors to the site to say whether they thought that marijuana
should be legally available for medicinal purposes.
Identify the following items (if possible). If you
can’t tell, then say so – this often happens
when we read about a survey.
d) The sample
those visiting the web site who
responded
22.
Page 289 #2
A question posted on the Lycos Web site on 18 June 2000 asked
visitors to the site to say whether they thought that marijuana
should be legally available for medicinal purposes.
Identify the following items (if possible). If you
can’t tell, then say so – this often happens
when we read about a survey.
e) The sampling method, including whether
or not randomization was employed
voluntary response (no
randomization employed)
22.
Page 289 #2
A question posted on the Lycos Web site on 18 June 2000 asked
visitors to the site to say whether they thought that marijuana
should be legally available for medicinal purposes.
Identify the following items (if possible). If you
can’t tell, then say so – this often happens
when we read about a survey.
f) Any potential sources of bias you can
detect and any problems you see in
generalizing to the population of interest
voluntary response (no
randomization employed)
Random
Rectangles
Random
Rectangles
Population Parameter
𝝁 = 7.5
Chapter 11 Part I
5&6. Explain why each of the following simulations fails to model
the real situation properly.
a) Use a random integer 0 through 9 to represent the number of heads
that appear when 9 coins are tossed.
Chapter 11 Part I
5&6. Explain why each of the following simulations fails to model
the real situation properly.
b) A basketball player takes a foul shot. Look at a random digit, using
an odd digit to represent a good shot and an even digit to represent a
miss.
Chapter 11 Part I
5&6. Explain why each of the following simulations fails to model
the real situation properly.
c) Use five random digits from 1 through 13 to represent the
denominations of the cards in a poker hand.
Chapter 11 Part I
5&6. Explain why each of the following simulations fails to model
the real situation properly.
d) Use random numbers 2 through 12 to represent the sum of the faces
when two dice are rolled
Chapter 11 Part I
5&6. Explain why each of the following simulations fails to model
the real situation properly.
e) Use a random integer 0 through 5 to represent the number of boys in a
family of 5 children.
Chapter 11 Part I
5&6. Explain why each of the following simulations fails to model
the real situation properly.
f) Simulate a baseball player’s performance at bat by letting 0 = an out,
1 = a single, 2 = a double, 3 = a triple, and 4 = a home run.
Chapter 11 Part I
9. You’re pretty sure that your candidate for class president has about
55% of the votes in the entire school. But you’re worried that only 100
students will show up to vote. How often will the underdog (the one
with 45% support) win? To find out you set up a simulation.
a)Describe how you will simulate a component and its outcomes.
Chapter 11 Part I
9. You’re pretty sure that your candidate for class president has about
55% of the votes in the entire school. But you’re worried that only 100
students will show up to vote. How often will the underdog (the one
with 45% support) win? To find out you set up a simulation.
b)Describe how you will simulate a trial.
Chapter 11 Part I
9. You’re pretty sure that your candidate for class president has about
55% of the votes in the entire school. But you’re worried that only 100
students will show up to vote. How often will the underdog (the one
with 45% support) win? To find out you set up a simulation.
c)Describe the response variable.
Chapter 11 Part I
10. When drawing five cards randomly from a deck, which is more
likely, two pairs or three of a kind? A pair is exactly two of the same
denomination. (Don’t count three 8’s as a pair – that’s 3 of a kind. And
don’t count 4 of the same kind as two pair- that’s four of a kind, a very
special hand.) How could you simulate 5-card hands? Be careful; once
you’ve picked the 8 of spades for a hand, you can’t get it again until the
next hand.
a) Describe how you will simulate a component and its outcomes.
Chapter 11 Part I
10. When drawing five cards randomly from a deck, which is more
likely, two pairs or three of a kind? A pair is exactly two of the same
denomination. (Don’t count three 8’s as a pair – that’s 3 of a kind. And
don’t count 4 of the same kind as two pair- that’s four of a kind, a very
special hand.) How could you simulate 5-card hands? Be careful; once
you’ve picked the 8 of spades for a hand, you can’t get it again until the
next hand.
b)Describe how you will simulate a trial.
Chapter 11 Part I
10. When drawing five cards randomly from a deck, which is more
likely, two pairs or three of a kind? A pair is exactly two of the same
denomination. (Don’t count three 8’s as a pair – that’s 3 of a kind. And
don’t count 4 of the same kind as two pair- that’s four of a kind, a very
special hand.) How could you simulate 5-card hands? Be careful; once
you’ve picked the 8 of spades for a hand, you can’t get it again until the
next hand.
c) Describe the response variable.
Chapter 11 Part I
11. Suppose a cereal manufacturer puts pictures of famous athletes on
cards in boxes of cereal in the hope of boosting sales. The manufacturer
announces that 20% of the boxes contain a picture of Tiger Woods, 30%
a picture of Lance Armstrong, and the rest a picture of Serena Williams.
Suppose you buy five boxes of cereal. Estimate the probability that you
end up with a complete set of the pictures. Your simulation should use at
least 10 runs.
A component is… checking one box of
cereal for the picture inside.
Chapter 11 Part I
11. Suppose a cereal manufacturer puts pictures of famous athletes on
cards in boxes of cereal in the hope of boosting sales. The manufacturer
announces that 20% of the boxes contain a picture of Tiger Woods, 30%
a picture of Lance Armstrong, and the rest a picture of Serena Williams.
Suppose you buy five boxes of cereal. Estimate the probability that you
end up with a complete set of the pictures. Your simulation should use at
least 10 runs.
I’ll look at a one-digit random number.
Let 0-1 represent a box with… Tiger Woods
Let 2-4 represent a box with… Lance Armstrong
Let 5-9 represent a box with… Serena Williams
Chapter 11 Part I
11. Suppose a cereal manufacturer puts pictures of famous athletes on
cards in boxes of cereal in the hope of boosting sales. The manufacturer
announces that 20% of the boxes contain a picture of Tiger Woods, 30%
a picture of Lance Armstrong, and the rest a picture of Serena Williams.
Suppose you buy five boxes of cereal. Estimate the probability that you
end up with a complete set of the pictures. Your simulation should use at
least 10 runs.
Each trial consists of…
check 5 boxes which is represented by 5 digits
The response variable is…
whether or not the 5 boxes had at least one of each
athlete (a.k.a. “a complete set”)
Chapter 11 Part I
11. Suppose a cereal manufacturer puts pictures of famous athletes on
cards in boxes of cereal in the hope of boosting sales. The manufacturer
announces that 20% of the boxes contain a picture of Tiger Woods, 30%
a picture of Lance Armstrong, and the rest a picture of Serena Williams.
Suppose you buy five boxes of cereal. Estimate the probability that you
end up with a complete set of the pictures. Your simulation should use at
least 10 runs.
Conclusion:
According to our simulation the probability that
you end up with a complete set of pictures after
checking 5 boxes is _________. However, it
should be noted that only 10 trials were run.
Chapter 11 Part I
#1:
TABLE OF RANDOM NUMBERS
78545 49201 05329 14182 10971 90472 44682 39304 19819 55799
Trial #
1
2
3
4
5
6
7
8
9
10
Complete
Set?
7-W
OUTCOMES
8-W
5-W
4-A
5-W
NO
4-A
0-T
1-T
1-T
9-W
4-A
3-A
1-T
5-W
9-W
5-W
4-A
0-T
0-T
4-A
9-W
9-W
5-W
1-T
9-W
2-A
2-A
2-T
2-A
4-A
9-W
9-W
YES
YES
YES
YES
YES
NO
YES
NO
NO
2-A
3-A
1-T
9-W
4-A
6-W
3-A
8-W
7-W
0-T
2-A
8-W
7-W
7-W
8-W
0-T
1-T
9-W
60% CHANCE OF COMPLETE SET
Chapter 11 Part I
#2:
TABLE OF RANDOM NUMBERS
72749 13347 65030 26128 49067 27904 49953 74674 94617 13317
Trial #
1
2
3
4
5
6
7
8
9
10
7-W
1-T
6-W
2-A
4-A
2-A
4-A
7-W
9-W
1-T
2-A
3-A
5-W
6-W
9-W
7-W
9-W
4-A
4-A
3-A
OUTCOMES
7-W
4-A
3-A
4-A
0-T
3-A
1-T
2-A
0-T
6-W
9-W
0-T
9-W
5-W
6-W
7-W
6-W
1-T
3-A
1-T
9-W
7-W
0-T
8-W
7-W
4-A
3-A
4-A
7-W
7-W
70% CHANCE OF COMPLETE SET
Complete
Set?
NO
YES
YES
YES
YES
YES
NO
NO
YES
YES
Chapter 11 Part I
#3:
TABLE OF RANDOM NUMBERS
11071 44430 94664 91294 35163 05494 32882 23904 41340 61185
Trial #
1
2
3
4
5
6
7
8
9
10
1-T
4-A
9-W
9-W
3-A
0-T
3-A
2-A
4-A
6-W
OUTCOMES
1-T
0-T
4-A
4-A
4-A
6-W
1-T
2-A
5-W
1-T
5-W
4-A
2-A
8-W
3-A
9-W
1-T
3-A
1-T
1-T
7-W
3-A
6-W
9-W
6-W
9-W
8-W
0-T
4-A
8-W
1-T
0-T
4-A
4-A
3-A
4-A
2-A
4-A
0-T
5-W
40% CHANCE OF COMPLETE SET
Complete
Set?
NO
NO
NO
YES
YES
YES
NO
YES
NO
NO
Chapter 11 Part I
#4:
TABLE OF RANDOM NUMBERS
42831 95113 43511 42082 15140 34733 68076 18292 69486 80468
Trial #
1
2
3
4
5
6
7
8
9
10
4-A
9-W
4-A
4-A
1-T
3-A
6-W
1-T
6-W
8-W
2-A
5-W
3-A
2-A
5-W
4-A
8-W
8-W
9-W
0-T
OUTCOMES
8-W
1-T
5-W
0-T
1-T
7-W
0-T
2-A
4-A
4-A
3-A
1-T
1-T
8-W
4-A
3-A
7-W
9-W
8-W
6-W
1-T
3-A
1-T
2-A
0-T
3-A
6-W
2-A
6-W
8-W
70% CHANCE OF COMPLETE SET
Complete
Set?
YES
YES
YES
YES
YES
NO
NO
YES
NO
YES
Chapter 11 Part II
12. Suppose a cereal manufacturer puts pictures of famous athletes on
cards in boxes of cereal in the hope of boosting sales. The manufacturer
announces that 20% of the boxes contain a picture of Tiger Woods, 30%
a picture of Lance Armstrong, and the rest a picture of Serena Williams.
Suppose you really want the Tiger Woods picture. How many boxes of
cereal do you need to buy to be pretty sure of getting at least one? Your
simulation should use at least 10 runs.
Chapter 11 Part II
14. A friend of yours got all 6 questions right on a multiple choice quiz,
but now claims to have guessed blindly on every question. If each
question offered 4 possible answers, do you believe her? Explain, basing
your argument on a simulation involving 10 runs. (Make sure that you
remember to define your simulation first. That means give the
component, outcomes, trial, and response variable first. Then run 10
trials, analyze your response variable, and write your conclusion.) Use
the following table for your simulation.
Chapter 11 Part II
19. You are about to take the road test for your driver’s license. You hear
that only 34% of candidates pass the test the first time, but the percentage
rises to 72% on subsequent retests. Estimate the average number of test
drivers take in order to get a license. Your simulation should use 10 runs.
Chapter 11 Part II
25. Many couples want to have both a boy and a girl. If they decide to
continue to have children until they have one child of each gender, what
would the average family size be? Assume that boys and girls are equally
likely. (Make sure that you remember to define your simulation first.
That means give the component, outcomes, trial, and response variable
first. Then run 10 trials, analyze your response variable, and write your
conclusion.) Use the following table for your simulation.