Download Math109 homework 1soln

3a. Descriptive statistics involve the statement “76% of women and 60% of men had a physical
examination within the previous year.”
b. An inference drawn from the study is that a higher percentage of women had a physical
examination within the previous year.
Section 1.1
EXERCISE
SOLUTIONS
o1.1—1-10,
11, 13, 14,
17, 19, 21, 29, 30, 32, 33, 36, 38, 40, 41, 46, 47
1. A sample is a subset of a population.
2. It is usually impractical (too expensive and time consuming) to obtain all the population data.
3. A parameter is a numerical description of a population characteristic. A statistic is a numerical
description of a sample characteristic.
4. Descriptive statistics and inferential statistics
5. False. A statistic is a numerical measure that describes a sample characteristic.
CHAPTER 1
6.2 True
2
CHAPTER 1
INTRODUCTION TO STATISTICS
INTRODUCTION TO STATISTICS
2 The
CHAPTER
INTRODUCTION
TOitSTATISTICS
data set1is a population
because
is a collection of the heights of all the players on a school’s
7.11. True
11. basketball
The data set
is a population because it is a collection of the heights of all the players on a school’s
team.
The data
set
is astatistics
population
because
it is
a collection
of the
heights of
all the
players on a school’s
basketball
team.
8.11.False.
Inferential
involves
using
a sample
to draw
conclusions
about
a population.
12. The
data set team.
is a population because it is a collection of the energy collected from all the wind
basketball
turbines
on
The data
setthe
is awind
population
because of
it isalla outcomes,
collection of
the energy
collected fromorallcounts
the wind
9.12.False.
A population
isfarm.
the collection
responses,
measurements,
that are
on
the
wind
farm.
12.ofturbines
The
data
set
is
a
population
because
it
is
a
collection
of
the
energy
collected
from
all the wind
interest. 1 INTRODUCTION TO STATISTICS
213. CHAPTER
The
data set
a sample
because the collection of the 500 spectators is a subset within the
turbines
onisthe
wind farm.
stadium’s
42,000
13. population
The data setofisthe
a sample
because
thespectators.
collection of the 500 spectators is a subset within the
10.
A statistic
differ
from
sample
11. False.
The
data
setofisthe
a can
population
because
it istoa sample.
collection of the heights of all the players on a school’s
population
stadium’s
42,000
spectators.
213.CHAPTER
TO STATISTICS
The data 1set isINTRODUCTION
a sample because
the collection of the 500 spectators is a subset within the
team.
14. basketball
The data set
is a population because it is a collection of the annual salaries of all pharmacists at a
population of the stadium’s 42,000 spectators.
14. pharmacy.
The data set is a population because it is a collection of the annual salaries of all pharmacists at a
11.
The
data
of all the from
players
school’s
12. The
data set
set is
is aa population
population because
because itit is
is aa collection
collection of
of the
the heights
energy collected
all on
theawind
pharmacy.
14.basketball
The data
set
athe
population
is a collection
of1within
the annual
salaries of
pharmacists13at a
team.
CHAPTER
INTRODUCTION
TOall
STATISTICS
15.
Sample,
because
collection
of the 20itpatients
is a subset
the population
turbines
on
theiswind
farm. because
pharmacy.
Copyright
© 2012 because
Pearson Education,
Inc. Publishing
as Prentice
Hall. is a subset within the population
15. Sample,
the collection
of the
20 patients
12.
The
is
because
itcollection
iscollection
a U.S.
collection
of
thespectators
energy
collected
from
all
the
16. The
Thedata
data set
population
it isin
a the
number
of televisions
in all
U.S.
13.
data
set Collection
is aa population
sampleofbecause
the
ofofthethe
500
is a subset
within
thewind
27.
Population:
allsince
adults
turbines
on
the
wind
farm.
15.
Sample,
because
the
collection
of
the
20
patients
is
a
subset
within
the
population
households.
stadium’s since
42,000
spectators.
16. population
The data setofisthe
a population
it is
a collection of the number of televisions in all U.S.
households.
Sample:
Collection of 1442 adults surveyed
17.
Population,
because
it is because
a collection
allaagolfers’
scores
inspectators
the
tournament
13.
is
the itof
collection
of the
500
is atelevisions
subset
theU.S. at a
16.The
Thedata
dataset
set
apopulation
population
since
collection
of
number
of
in all
14.
The
data
set
isisaa sample
because
it isis
collection
the
annual
salaries
of allwithin
pharmacists
ofbecause
the stadium’s
42,000
households.
pharmacy.
17.population
Population,
it isofa all
collection
of all golfers’
scores
in
the
tournament
28.
Population:
Collection
peoplespectators.
CHAPTER 1
INTRODUCTION TO STATISTICS 3
18. Sample, because only the age of every third person entering the clothing store is recorded
14.
data because
set
isbecause
a population
it20
is
collection
the the
annual
ofisallrecorded
pharmacists at a
18.
Sample,
because
only
the
age
ofofevery
third
person
store
15.
Sample,
the
collection
the
isentering
a of
subset
within
the
population
17.The
Population,
it1600
isall
abecause
collection
ofapatients
all
golfers’
scores
inclothing
thesalaries
tournament
Sample:
Collection
of
people
27.
of
adults
insurveyed
19.Population:
Population,Collection
because it is
a collection
ofthe
allU.S.
the U.S. presidents’ political parties
pharmacy.
19.
Population,
because
it1442
isof
a all
collection
the U.S.
presidents’
political
partiesstore
16.
The
dataCollection
set
is a population
since
isofa all
collection
of
the
number
of clothing
televisions
in all
U.S.
29.
Population:
Collection
registered
voters
18.Sample:
Sample,
because
the
age
ofitsurveyed
every
third
person
entering
the
is recorded
ofcollection
adults
20.
Sample,
because
theonly
contamination
is athe
subset
in the population
15.
Sample,
because
the
collection of
of the
the10
20soil
patients
is a subsetlevels
within
population
households.
20.
Sample,
because
theofcollection
of the 10
soil
contamination
levels ispolitical
a subset parties
in the population
Sample:
Collection
voters
19.Population:
Population,
because
it800
isallaregistered
collection
of
allsurveyed
theCounty
U.S. presidents’
28.
Collection
of
people
21.
Population:
Party
of registered
voters in
Warren
16.
data set because
is a population
since it isofa collection
the number
of televisions in all U.S.
17. The
Population,
it is a collection
all golfers’ofscores
in the tournament
21.
Population:
Party of
registered
voters
in
Warren
County
households.
30.
Population:
Collection
ofCounty
allpeople
students
atresponding
a college
20.Sample:
Sample,
because
the
collection
ofsurveyed
the
10
soil contamination
levels is a subset in the population
Collection
of 1600
Sample:
Party
of Warren
voters
to online survey
18. Sample, because only the age of every third person entering the clothing store is recorded
Sample: Collection
Party
of Warren
County
voters
responding
to online
survey
17.
Population,
because
it of
is
aall
collection
all
Sample:
of
496
students
surveyed
22.
Population:
All
students
who
donate
atofavoters
blood
drivescores
29.
Collection
registered
21.Population:
Population:
Party
of
registered
voters
in golfers’
Warren
Countyin the tournament
19. Population, because it is a collection of all the U.S. presidents’ political parties
22.Sample,
Population:
All
students
donate
atin
athe
blood
drive
18.
because
only
the
age
of every
third
person
entering
the clothing
31.
Population:
Collection
ofwho
all
women
U.S.
Sample:
The
students
who
donate
and
have
type
O+ blood
Sample:
Collection
of
800
registered
voters
surveyed
Sample:
Party
of
Warren
County
voters
responding
to online
survey store is recorded
20. Sample, because the collection of the 10 soil contamination
levels
is a subset in the population
+
blood
Sample:
The
students
who
donate
and
have
type
O
19.
Population,
because
it of
is
collection
of
the
U.S.own
presidents’ political parties
Sample:
Collection
theaall546
U.S.
women
surveyed
23.Population:
Population:
Ages of of
adults
instudents
the
United
States
who
30.
Collection
at at
aall
college
22.Population:
Population:
All students
who
donate
a blood
drive cellular phones
21.
Party
of registered
voters
in Warren
County
23.Sample,
Population:
Ages
of adults
in U.S.
the
who
cellular
phones
Sample:
Ages
of the
adults
in the
United
States
who
ownown
Samsung
cellular
32.
Population:
Collection
of
all
vacationers
20.
because
ofUnited
the
10 States
soil
contamination
levels
is aphones
subset in the population
+
Sample:
Collection
ofcollection
496
students
surveyed
blood
Sample:
The
students
who
donate
and
have
type
O
Sample: Party of Warren County voters responding to online survey
Sample: Ages
of adults
inhomeowners
the United States
who own Samsung cellular phones
24. Population:
Population:
Income
all
Texas
Sample:
Collection
of
theall
791
vacationers
surveyed
21.
Party
of of
registered
votersininin
Warren
County
31.
Collection
women
the
U.S.
23.Population:
Population:
Ages
of of
adults
the United
States
who own cellular phones
22.
Population:
All
students
who in
donate
at a blood
drive
24. Sample:
Population:
Income
of
all
homeowners
in
Texas
Income
homeowners
invoters
Texas
with mortgages
33.Sample:
Population:
Collection
ofCounty
all Fortune
magazine’s
topto100
companies
Sample:
Party
of of
Warren
responding
online
survey to work for
Collection
of the
546
U.S.
women
surveyed
Sample:
Ages
of adults
the
United
States
who
bloodSamsung cellular phones
Sample:
The
students
whoindonate
and have
type
O+ own
Sample: Income
of homeowners
in in
Texas
with mortgages
25. Sample:
Population:
Collection
of all
adults
the United
States to the questionnaire
Collection
of of
the
companies
22.
Population:
All
students
who
donate
at
a who
bloodresponded
drive
32.
Population:
Collection
all85U.S.
vacationers
24.Population:
Population:Ages
Income
of allinhomeowners
in Texas
23.
of adults
the United States
who own cellular phones
25. Sample:
Population:
Collection
of alladults
adultssurveyed
in the United States
Collection
of 1000
+
34.Sample:
Population:
of791
all
light
bulbs
from
theOday’s
production
blood
Sample:
TheCollection
students
who
donate
and
have
type
Collection
of the
vacationers
surveyed
Sample:
of adults
in the United
Samsung cellular phones
Sample:Ages
Income
of homeowners
in States
Texas who
withown
mortgages
Sample: Collection
of 1000
26. Population:
Collection
of all adults
infantssurveyed
in Italy
Sample: Collection
theall20
lightUnited
bulbs
selected
from
thecompanies
day’s production
23. Population:
Population:
Ages of of
adults
inFortune
the
States
who
own
cellular
phones
33.
Collection
of
magazine’s
top
100
to work for
24.
Population:
Income
of
all
homeowners
inthe
Texas
25.
Population:
Collection
of
all
adults
in
United
States
26. Sample:
Population:
Collection
of all infants
Collection
of 33,043
infantsin
inItaly
the study
35.Sample:
Statistic.Collection
The value
isUnited
a numerical
of
sample
of annual
salaries.
Sample:
Ages
of adults
thecompanies
States
who
own Samsung
cellular
phones
of$68,000
thein85
whodescription
responded
toathe
questionnaire
Sample:
of homeowners
in Texas
with mortgages
Sample:Income
Collection
1000 infants
adults
surveyed
Sample:
Collection
ofof33,043
in the study
Sample: Collection of the 20 light bulbs selected from the day’s production
Collection
all20light
bulbs
from
thebasketball
day’s
Sample:
Collection
ofof
the
light
selected
fromproduction
theteams.
day’s production
2a.34.
(1)Population:
The final
standings
represent
a bulbs
ranking
of
35. Statistic. TheINTRODUCTION
value $68,000TO
is STATISTICS
a numerical description of a sample of annual salaries.
4 CHAPTER 1
Collection
of$68,000
the 20 light
bulbs selected
from theofday’s
production
35.
Statistic.
The value
is a numerical
description
a sample
of annual
salaries.
(2)Sample:
The collection
phone
numbers
represents
labels.
computations
can be
36.
Statistic.
43%
is aof
numerical
description
of
atheir
sample
ofNo
highmathematical
school
students.
43.
The
statement
“56%
are
the
primary
investors
in
household”
is
an
application
of descriptive
made.
35.
Statistic.
$68,000 is description
a numericalof
description
sample
of annual
salaries.
36.statistics.
Statistic.The
43%value
is a numerical
a sample of
of ahigh
school
students.
37. Parameter. The 62 surviving passengers out of 97 total passengers is a numerical description of
b.36.(1)
Ordinal,
because
the
data
can be
putofan
in
order
allinference
of the43%
passengers
ofthe
thesample
Hindenburg
that
survived.
Statistic.
is a62numerical
description
aassociation
sample
of high
school
students.
drawn
from
is that
exists
between
women and
being of
37.An
Parameter.
The
surviving
passengers
out
of
97 total
passengers
is U.S.
a numerical
description
theallprimary
investor in their
of the passengers
of thehousehold.
Hindenburg that survived.
(2)Parameter.
Nominal,
because
you cannot
makeout
calculations
onnumber
the dataof
37.
The
62issurviving
passengers
ofof97the
total
passengers
is governors.
a numerical description of
38.
Parameter.
52%
a numerical
description
total
all of
the passengers
of the
Hindenburg
survived.
44. The
statement
“spending
at least
$2000 forthat
their
next vacation” is an example of descriptive
38. Parameter. 52% is a numerical description of the total number of governors.
statistics.
3a.39.
(1)
The data8%
setisisa the
collection
of bodyoftemperatures.
Statistic.
numerical
description
a sample of computer users.
38. Parameter. 52% is a numerical description of the total number of governors.
39.AnStatistic.
8% is a numerical
description
a sample
of computer users.
inference
from
the sample
that of
United
States
40.
12%is isthe
a numerical
description
of all
newvacationers
magazines.are associated with
(2)Parameter.
The data drawn
set
collection
ofis heart
rates.
39.spending
Statistic.more
8% isthan
a numerical
of a sample of computer users.
$2000 fordescription
their next vacation.
40. Parameter. 12% is a numerical description of all new magazines.
is a numerical
description
of aand
sample
of all people.
b.41.
(1)Statistic.
Interval,44%
because
the data can
be ordered
meaningful
differences can be calculated, but it
45.
will12%
vary.is a numerical description of all new magazines.
40.Answers
Parameter.
does
not
make
sense
writing
a
ratio
using
the
temperatures
41. Statistic. 44% is a numerical description of a sample of all people.
42. Parameter. 21.0 is a numerical description of ACT scores for all graduates.
46.
The volunteers
the studydescription
represent the
41.(a)
Statistic.
44% is a in
numerical
of sample.
a sample of all people.
(2)Parameter.
Ratio, because
data can description
be ordered,ofcan
be written
as all
a ratio,
you can calculate
42.
21.0 isthe
a numerical
ACT
scores for
graduates.
meaningful
and
the
data
set
contains
inherent
zero
The population
the collection
of all
individuals
who an
completed
the
math test.
42.(b)
Parameter.
21.0differences,
is is
a numerical
description
of ACT
scores
for
all graduates.
The statement “three times more likely to answer correctly” is an application of descriptive
1.2 (c)
EXERCISE
SOLUTIONS
statistics.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
1. Nominal
and ordinal
(d) An inference
drawn from the sample is that individuals who are not sleep deprived will be
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
more
likely
answer asmath
questions
Copyrightthree
© 2012times
Pearson
Education,
Inc.toPublishing
Prentice
Hall.
2. Ordinal,
interval, and ratio
deprived.
correctly than individuals who are sleep
(a) AnData
inference
from
the can
sample
that senioror
citizens
who live in Florida have better
3.47.False.
at thedrawn
ordinal
level
be is
qualitative
quantitative.
memory than senior citizens who do not live in Florida.
4. False. For data at the interval level, you can calculate meaningful differences between data
(b) It implies that if you live in Florida, you will have better memory.
entries. You cannot calculate meaningful differences at the nominal or ordinal level.
48. (a) An inference drawn from the sample is that the obesity rate among boys ages 2 to 19 is
5. False.
More types of calculations can be performed with data at the interval level than with data at
increasing.
Section
1.2
6 the
CHAPTER
INTRODUCTION TO STATISTICS
nominal1 level.
(b) It implies the same trend will continue in future years.
o15.False.
—7-14,
21,at22,
28,
30 can
6.
Data
the25,
ratio
level
be placed
a meaningful
order.
Quantitative,
because
weights
of infants
are in
a numerical
measure
49. Answers will vary.
Qualitative, because
because telephone
species of trees
are merely
labelslabels
7.16.Qualitative,
numbers
are merely
6 Quantitative,
CHAPTER 1 because
INTRODUCTION
TO STATISTICS
1.2
DATA
CLASSIFICATION
Qualitative,
the
results
merely
responses
8.17.
because
thepoll
heights
ofare
hot
air balloons
are a numerical measure
15.Quantitative,
Quantitative,
because
of temperatures
infants
are a numerical
Quantitative,
because weights
wait
times
at a grocery
store
are ameasure
numerical
measure
9.18.
because
the body
of patients
is a numerical
measure.
1.2
Try It Yourself
Solutions
16. Qualitative.
Qualitative, because
of trees
are merely
labels but differences between data entries make no
19.
Ordinal.species
Dataeye
can
be arranged
in order,
1a.Qualitative,
One data set because
contains
names
ofcolors
cities
and
other
contains city populations.
10.
the
arethe
merely
labels
sense.
17. City:
Qualitative,
because the poll results are merely responses
Nonnumerical
11.b.Quantitative,
because the lengths of songs on an MP3 player are numerical measures
20. Population:
Qualitative.Numerical
Nominal. No mathematical computations can be made and data are categorized using
18. Quantitative, because wait times at a grocery store are a numerical measure
names.
12. Quantitative,
because the carrying capacities of pickups are numerical measures
c. City: Qualitative
19. Population:
Qualitative. Ordinal. Data can be arranged in order, but differences between data entries make no
21. Qualitative.Quantitative
Nominal. No mathematical computations can be made and data are categorized using
sense.
13. Qualitative,
because the player numbers are merely labels
names.
20.Qualitative,
Qualitative. because
Nominal.student
No mathematical
computations
be made and data are categorized using
14.
ID numbers
are merelycan
labels
22. Quantitative.
Ratio. A ratio of two data values can be formed so one data value can be expressed
names.
Copyright
2012 Pearson
Inc. Publishing as Prentice Hall.
as a©multiple
ofEducation,
another.
21. Qualitative. Nominal. No mathematical computations can be made and data are categorized using
23. Qualitative.
Ordinal. The data can be arranged in order, but differences between data entries are
names.
Copyright
© 2012 Pearson Education, Inc. Publishing as Prentice Hall.
not meaningful.
22. Quantitative. Ratio. A ratio of two data values can be formed so one data value can be expressed
24. Quantitative.
Ratio.
The ratio of two data values can be formed so one data value can be
as a multiple of
another.
expressed as a multiple of another.
23. Qualitative. Ordinal. The data can be arranged in order, but differences between data entries are
not meaningful.
25. Ordinal
24. Ratio
Quantitative. Ratio. The ratio of two data values can be formed so one data value can be
26.
expressed as a multiple of another.
27. Nominal
25. Ordinal
28. Ratio
26. Ratio
c. 63, 7, 40, 19, 26
expressed as a multiple of another.
26.
Ratio
63 07 82 40 19 26
b. 92
4a. (1) The sample was selected by only using the students in a randomly chosen class. Cluster
25. Ordinal
c. 63,
7,sampling
40, 19, 26
27.
Nominal
26. Ratio
(2) The
Thesample
samplewas
wasselected
selectedby
byonly
numbering
each
studentinina the
school,chosen
randomly
choosing
4a.
using the
students
randomly
class.
Clustera
28. (1)
Ratio
starting
number,
and
selecting
students
at
regular
intervals
from
the
starting
number.
27. Nominal
sampling
Systematic sampling
29. (2)
(a) The
Interval
(b) Nominal
(c) Ratio
(d) choosing
Ordinal a
28.
Ratio
sample was selected
by numbering each student
in the school, randomly
b. (1) starting
The sample
may
be
biased
because
some
classes
may
be
more
familiar
with
stem
cell
number, and selecting students at regular intervals from the starting number.
research
than
other
classes
and
have
stronger
opinions.
29.
(b) (b)
Nominal
(c) Ratio
30. (a)
(a) Interval
Interval sampling
Nominal
(c) Interval (d) Ordinal(d) Ratio
Systematic
(2) Interval
Thesample
sample
may
be
biased
if there
is
any
regularly
occurring
in with
the data.
30.
(a)
(b)
(c)
Interval
(d)
Ratio
31.
An
inherent
zero
isbe
aNominal
zero
that
implies
“none.”
Answers
willpattern
vary.
b. (1)
The
may
biased
because
some
classes
may
be more
familiar
stem cell
research than other classes and have stronger opinions.
31.
inherent zero is SOLUTIONS
a zero that implies “none.” Answers will vary.
1.3AnEXERCISE
32. Answers will vary.
(2) 1.3
The sample may be biased if there is any regularly occurring pattern in the data.
Section
32. Answers
will vary.
1.
In
an
experiment,
treatment
is applied
of a population and responses are observed. In an
o 1, 2, 4-10,
11,DATA
13, a15,
17-22,
32,
33, 35to part AND
1.3
COLLECTION
EXPERIMENTAL
DESIGN
observational
study,
a
researcher
measures
characteristics
of interest of part of a population
but
1.3 EXERCISE
SOLUTIONS
1.3
DATA
COLLECTION
does not
change
existing
conditions. AND EXPERIMENTAL DESIGN
1.
In Try
an experiment,
a treatment
is applied to part of a population and responses are observed. In an
1.3
Itincludes
Yourself
Solutions
2. observational
A
census
entire population;
a sample
includesofonly
a portion
ofof
thea population.
1.3
Try
It Yourself
study,the
a Solutions
researcher
measures
characteristics
interest
of part
population but
does not change existing conditions.
1a.
(1)
Focus:
Effect
ofevery
exercise
on relieving
depression
3. (1)
In aFocus:
random
sample,
member
of the
population
has an equal chance of being selected. In a
1a.
Effect
of exercise
on relieving
depression
simple random sample, every possible sample of the same size has an equal chance of being
2. A census includes the entire population; a sample includes only a portion of the population.
selected.
(2)
Focus:
Success
of graduates
(2)
Focus:
Success
of graduates
3. In a random sample, every member of the population has an equal chance of being selected. In a
4. Replication is the repetition of an experiment using a large group of subjects. It is important
simple random sample, every possible sample of the same size has an equal chance of being
because it gives validity to the results.
selected.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright
5. True© 2012 Pearson Education, Inc. Publishing as Prentice Hall.
4.8 Replication
repetition of an
using a large group of subjects. It is important
CHAPTER 1is the
INTRODUCTION
TOexperiment
STATISTICS
because
it
gives
validity
to
the
results.
6. False. A double-blind experiment is used to decrease the placebo effect.
7.
False. Using
sampling
guarantees that members of each group within a population will
8 CHAPTER
1 stratified
INTRODUCTION
TO STATISTICS
5. True
be sampled.
7. False. Using stratified sampling guarantees that members of each group within a population will
6.8. False.
AAdouble-blind
experiment
is used
to decrease the placebo effect.
False.
census is a count
of an entire
population.
be
sampled.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
8. False.
count of ansample,
entire population.
9.
False.ATocensus
selectisaasystematic
a population is ordered in some way and then members of
the population are selected at regular intervals.
9. False. To select a systematic sample, a population is ordered in some way and then members of
population
selected
regular intervals.
Copyright
©
2012 Pearsonare
Education,
Inc.atPublishing
as Prentice Hall.
10. the
True
10. True
11.
Use a census because all the patients are accessible and the number of patients is not too large.
11. Use a census because all the patients are accessible and the number of patients is not too large.
12. Perform an observational study because you want to observe and record motorcycle helmet usage.
12. Perform an observational study because you want to observe and record motorcycle helmet usage.
13. In this study, you want to measure the effect of a treatment (using a fat substitute) on the human
digestive
system.
So, you
would the
want
to perform
an experiment.
13. In
this study,
you want
to measure
effect
of a treatment
(using a fat substitute) on the human
digestive system. So, you would want to perform an experiment.
14. It would be nearly impossible to ask every customer whether he or she would still buy a product
14. It
would
be nearly
impossible
ask every
he or
she data.
would still buy a product
with
a warning
label.
So, youtoshould
usecustomer
a surveywhether
to collect
these
with a warning label. So, you should use a survey to collect these data.
15. Because it is impractical to create this situation, you would want to use a simulation.
15. Because it is impractical to create this situation, you would want to use a simulation.
16. Perform an observational study because you want to observe and record how often people wash
16. Perform
an observational
study because you want to observe and record how often people wash
their hands
in public restrooms.
their hands in public restrooms.
17.
(a) The
Theexperimental
experimentalunits
units
30–35
females
the treatment.
17. (a)
areare
thethe
30–35
yearyear
old old
females
beingbeing
givengiven
the treatment.
One One
treatment
is
used.
treatment is used.
(b) A
Aproblem
problemwith
withthe
thedesign
design
is that
there
be some
onpart
theof
part
the researchers
(b)
is that
there
maymay
be some
bias bias
on the
theof
researchers
if he if he
orshe
sheknows
knowswhich
whichpatients
patients
were
given
A way
to eliminate
this problem
or
were
given
the the
realreal
drug.drug.
A way
to eliminate
this problem
would would
betotomake
makethe
thestudy
study
into
a double-blind
experiment.
be
into
a double-blind
experiment.
(c)
study
if the
researcher
did not
whichwhich
patients
(c) The
Thestudy
studywould
wouldbebea double-blind
a double-blind
study
if the
researcher
didknow
not know
patients
received
oror
thethe
placebo.
receivedthe
thereal
realdrug
drug
placebo.
18. (a)
areare
thethe
80 80
people
withwith
earlyearly
signssigns
of arthritis.
One treatment
is used.is used.
18.
(a) The
Theexperimental
experimentalunits
units
people
of arthritis.
One treatment
(b) A problem with the design is that the sample size is small. The experiment could be
with a warning label. So, you should use a survey to collect these data.
15. Because it is impractical to create this situation, you would want to use a simulation.
16. Perform an observational study because you want to observe and record how often people wash
their hands in public restrooms.
CHAPTER 1
INTRODUCTION TO STATISTICS
9
17. (a) The experimental units are the 30–35 year old females being given the treatment. One
treatment
used. are divided into strata (rural and urban), and a sample is selected from each
20. Because
theispersons
stratum, this is a stratified sample.
(b) A problem with the design is that there may be some bias on the part of the researchers if he
or she knows
which were
patients
weredue
given
theCHAPTER
real
drug.
to eliminate
problem
would
21. Because
the students
chosen
to their
convenience
of location
(leaving
the
library),
1 A way
INTRODUCTION
TOthis
STATISTICS
9this is
to make thesample.
study into
double-blind
abe
convenience
Biasamay
enter intoexperiment.
the sample because the students sampled may not be
representative
of the
ofstrata
students.
there
may beisanselected
association
20. Because
the persons
arepopulation
divided into
(ruralFor
andexample,
urban), and
a sample
from between
each
(c)stratum,
The spent
study
would
be a double-blind
this at
is
a stratified
sample.
time
the
library
and drinkingstudy
habits.if the researcher did not know which patients
received the real drug or the placebo.
21.
due to into
theirgrids
convenience
of location
(leaving
the library),
this isthis
22.Because
Becausethe
thestudents
disasterwere
areachosen
was divided
and thirty
grids were
then entirely
selected,
sample.units
Biasare
may
into
thewith
sample
because
studentsdamaged
sampled
may others,
not
18. (a)a isconvenience
The
experimental
theenter
80
people
early
signs
ofseverely
arthritis.
One treatment
is be
used.
a cluster
sample.
Certain
grids
may
have
been
much
morethe
than
so this
representative
the population
is a possible of
source
of bias. of students. For example, there may be an association between
spent at the
library
and drinking
(b)time
A problem
with
the design
is that habits.
the sample size is small. The experiment could be
replicated
to increase
validity.
23. Simple
random
sampling
is used because each customer has an equal chance of being contacted,
22. Because the disaster area was divided into grids and thirty grids were then entirely selected, this
and all samples of 580 customers have an equal chance of being selected.
a cluster sample. Certain grids may have been much more severely damaged than others, so this
(c)is In
a placebo-controlled double-blind experiment, neither the subject nor the experimenter
is a possible source of bias.
knows whether
the subject
receiving
a treatment
or aentering
placebo.the
The
experimenter
24. Systematic
sampling
is used is
because
every
tenth person
shopping
mall isissampled. It
informed
after
all
the
data
have
been
collected.
is
possible
for
bias
to
enter
the
sample
if,
for
some
reason,
there
is
a
regular
pattern
to people
23. Simple random sampling is used because each customer has an equal chance of being contacted,
entering
the
shopping
mall.
and all samples of 580 customers have an equal chance of being selected.
(d) The group could be randomly split into 20 males or 20 females in each treatment group.
25.Systematic
Because asampling
sample isistaken
from each
one-acre
subplotentering
(stratum),
this is a stratified
sample. It
24.
used because
every
tenth person
the shopping
mall is sampled.
19. Each
U.S. telephone
hassample
an equal
chance
beingthere
dialed
all samples
ofpeople
1400 phone
is possible
for bias tonumber
enter the
if, for
some of
reason,
is aand
regular
pattern to
numbers
have
an equal
chance
beingofselected,
so thisand
is aallsimple
random
sample.
26.
Each telephone
has an
equalof
chance
being dialed
samples
of 1012
phoneTelephone
numbers have
entering
the shopping
mall.
sampling
only
samples
thoseselected,
individuals
whoishave
telephones,
available,
and are
willing only
to
an equal
chance
of being
so this
a simple
random are
sample.
Telephone
sampling
soa those
this
isindividuals
aispossible
source
ofone-acre
bias.
25.respond,
Because
sample
taken from
subplot
thistoisrespond,
a stratified
sample.
samples
whoeach
have
telephones
and(stratum),
are willing
so this
is a possible
source of bias.
CHAPTER 1
INTRODUCTION TO STATISTICS 9
26. Each telephone has an equal chance of being dialed and all samples of 1012 phone numbers have
equal chance
of being selected, so this is a simple random sample. Telephone sampling only
27.anAnswers
will vary.
20. Because
the
persons
are divided
into telephones
strata (ruraland
andare
urban),
a sample so
is selected
from each
samples
those
individuals
who have
willingand
to respond,
this is a possible
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
stratum,
this
is a stratified sample.
source of
bias.
28. Answers will vary.
21.
students
27.Because
Answersthe
will
vary. were chosen due to their convenience of location (leaving the library), this is
29.a convenience
Answers willsample.
vary. Bias may enter into the sample because the students sampled may not be
of the population of students. For example, there may be an association between
28.representative
Answers will vary.
30.time
Answers
spent atwill
thevary.
library and drinking habits.
29. Answers will vary.
Census,
is relatively
easyinto
to obtain
the thirty
ages of
the were
115 residents
22.31.Because
thebecause
disasteritarea
was divided
grids and
grids
then entirely selected, this
30.isAnswers
vary. Certain grids may have been much more severely damaged than others, so this
a clusterwill
sample.
32.is Sampling,
because
population of subscribers is too large to easily record their favorite movie
a possible source
ofthe
bias.
type. Random
would
beto
advised
it would
easy to randomly select
31. Census,
because sampling
it is relatively
easy
obtain since
the ages
of the be
115too
residents
subscribers
recordistheir
type.
23. Simple
randomthen
sampling
usedfavorite
becausemovie
each customer
has an equal chance of being contacted,
32.and
Sampling,
because
the customers
populationhave
of subscribers
is too large
to easily
record their favorite movie
all samples
of 580
an equal chance
of being
selected.
Random
sampling
woulditbe
advised
since it that
would
be too
easy to randomly
33.type.
Question
is biased
because
already
suggests
eating
whole-grain
foods isselect
good for you. The
subscribers
then record
their because
favorite
movie
type.
24. Systematic
sampling
is used
every
tenth
person
entering the
shopping
mall health?”
is sampled. It
question might
be rewritten
as “How
does
eating
whole-grain
foods
affect your
is possible for bias to enter the sample if, for some reason, there is a regular pattern to people
33.
Question
isis
biased
because
suggests
thatthat
eating
good for
you. The
the
shopping
mall. it already
34.entering
Question
biased
because
it already
suggests
textwhole-grain
messaging foods
while isdriving
increases
the risk
question
might
be
rewritten
as
“How
does
eating
whole-grain
foods
affect
your
health?”
of a crash. The question might be rewritten as “Does text messaging while driving increase the
25. Because
risk of aa sample
crash?”is taken from each one-acre subplot (stratum), this is a stratified sample.
34. Question is biased because it already suggests that text messaging while driving increases the risk
of a crash.
The has
question
might
be rewritten
asdialed
“Doesand
textall
messaging
while
driving
increase
26.35.Each
telephone
an equal
chance
of being
samples
of
1012
phone
numbersthehave
Question
is unbiased
because
it does
not imply
how much
exercise
is good
or bad.
risk
of
a
crash?”
an equal chance of being selected, so this is a simple random sample. Telephone sampling only
samples those individuals who have telephones and are willing to respond, so this is a possible
35. Question is unbiased because it does not imply how much exercise is good or bad.
source of bias.
27. Answers will vary.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
28. Answers will vary.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
29. Answers will vary.
30. Answers will vary.
31. Census, because it is relatively easy to obtain the ages of the 115 residents
32. Sampling, because the population of subscribers is too large to easily record their favorite movie
The graph shows that most of the pungencies of the peppers were between 36 and 43 Scoville
(Answers
will vary.)
e.units.
Answers
will vary.
Range
514 291
=
= 27.875
28
Number of classes
8
Class
Frequency, f
Midpoint
Relative
Cumulative
frequency
frequency
Section 2.1—
291-318
5
304.5
0.1667
5
319-346
4
332.5
0.1333
9
o20 1,CHAPTER
2, 3, 21, 25,
37
2 34,
DESCRIPTIVE
STATISTICS
347-374
3
360.5
0.1000
12
2.1 EXERCISE
SOLUTIONS
375-402
5
388.5
0.1667
17
19a. Number
of classes = 76
b. Least
frequency 0.2000
10
403-430
416.5
23
c. Greatest
frequency
300
d. Class
widthmay
= 10make
1.
Organizing
the data into
distribution
patterns within the
431-458
4a frequency
444.5
0.1333
27 data more evident.
Sometimes
it
is
easier
to
identify
patterns
of
a
data
set
by
looking
at
a
graph
of the frequency
459-486
1
472.5
0.0333
28
20a. Number
of classes = 7
b. Least frequency 100
distribution.
487-514
2
500.5
0.0667
30
900 STATISTICS
d. Class width = 5
Greatest frequency
20c. CHAPTER
2
DESCRIPTIVE
f
2. If there are too few or too
f many
30 classes, it may be difficult to detect
1 patterns because the data are
n
too
condensed
or
too
spread
out.
21a.
50
b.
22.5-23.5
pounds
19a. Number of classes = 7
b. Least frequency 10
33.7ab.
Class width =
c. Greatest frequency 300
d. Class width = 10
3. 50
Class limits determine which numbers
can belong
22a.
b. 64-66
inchesto that class.
Class boundaries are the numbers that separate classes without forming gaps between them.
20a. Number of classes = 7
b. Least frequency 100
23a.
b.
d. 29.5
Classpounds
width = 5
c. 42
Greatest frequency 900
c. 35
d. 2
24a.
b.
inches pounds
21a. 48
50
b. 66
22.5-23.5
c. 20
d. 6
22a. 50
b. 64-66 inches
25a.
Class
with
greatest
frequency:
8-9Hall.
inches
The
graph
shows
thatrelative
theInc.most
frequent
reaction
times were between 403 and 430 milliseconds.
Copyright
© 2012
Pearson
Education,
Publishing
as Prentice
Class
with
least
relative
frequency:
17-18
inches
(Answers
will
vary.)
23a. 42
b. 29.5 pounds
c. 35
d. 2
0.195
b. Greatest
relative frequency
Range
2888
24a.
48
b. 66
inches2456
= 86.4 87
34. Class
width = frequency 0.005 =
c. Least
20 relativeNumber
d.
6
of classes
5
Class
Frequency, f
Midpoint
Relative
Cumulative
c. Approximately
0.015
25a.
Class with greatest
relative frequency: 8-9 inches frequency
frequency
Class
with least relative
frequency: 17-18
inches
2456-2542
7
2499
0.28
7
26a. Class with greatest relative frequency: 19-20 minutes
2543-2629
3
2586
0.12
10
with
least relative
frequency:
minutes
0.195 21-22
b. Class
Greatest
relative
frequency
2630-2716
2
2673
0.08
12
0.005
Least
relative frequency
2717-2803
4
2760
0.16
16
b. Greatest relative frequency 40%
2804-2890
9
2847
0.36
25
relative frequency
2%
c. Least
Approximately
0.015
f
f 25
1
c. Approximately
33%relative frequency: 19-20 minutes n
26a.
Class with greatest
Class with least relative frequency: 21-22 minutes
27. Class with greatest frequency: 29.5-32.5
CHAPTER 2
DESCRIPTIVE STATISTICS 23
with
least frequency:
40% and 38.5-41.5
b.Classes
Greatest
relative
frequency 11.5-14.5
Least relative frequency 2%
28. Class with greatest frequency: 7.75-8.25
with least frequency:
c. Class
Approximately
33% Inc. 6.25-6.75
Copyright
© 2012 Pearson Education,
Publishing as Prentice Hall.
Range 29.5-32.5
39 0
27. Class
Class width
with greatest
frequency:
=
= 7.8
8
29.
=
Number
of classes
Classes with least
frequency:
11.5-14.5 5and 38.5-41.5
Class
Frequency, f
Midpoint
Relative
Cumulative
frequency
frequency
28. Class with greatest frequency: 7.75-8.25
The graph shows that the most common pressures at fracture time were between 2804 and 2890
0-7 least frequency:
8 6.25-6.75 3.5
0.32
8
Class with
pounds per square inch. (Answers will vary.)
8-15
8
11.5
0.32
16
16-23
3
19.50
0.12
19
Range
39
Range
55 24
= =27.5
= 7.8
80.12
29. Class
width
= =
=
6.2
7
35. Class
width
24-31
3
22
Number
of classes
5
Number
32-39
3 of classes
35.55
0.12
25
Class
Frequency,
f
Midpoint
Relative
Cumulative
Class
Frequency, f
Midpoint
Relative
Cumulative
f
frequency
frequency
frequency
frequency
f 25
1
n
0-724-30
8 9
3.527
0.32
0.30
98
Classes
with
greatest frequency:
0-7, 8-15
8-15
8 8
11.5
0.32
16
31-37
34
0.27
17
Classes
with
least frequency:
38-44
4132-39
0.33
27
16-23
3 10 16-23, 24-31,
19.5
0.12
19
45-51
48
0.07
29
24-31
3 2
27.5
0.12
22
52-58
55
0.03
30
32-39
3 1
35.5
0.12
25
f
f 1
Copyright © 2012 Pearson Education,f Inc.f Publishing
25 30 as Prentice Hall.
1
nn
Classes with greatest frequency: 0-7, 8-15
Classes with least frequency: 16-23, 24-31, 32-39
Class with greatest relative frequency: 10-24
Class with least relative frequency: 55-69
Range
462 138
=
= 64.8
65
37. Class width =
Number of classes
5
c. It appears that the auto industry (dealers and repair shops) account for the largest portion of
Class
Frequency, f
Midpoint
Relative
Cumulative
complaints filed at the BBB. (Answers will very.)
frequency
frequency
CHAPTER
STATISTICS 33
138-202
12
170
0.46 2 DESCRIPTIVE
12
6a, b.
203-267
6
235
0.23
18
3. Both
the stem-and-leaf 4plot and the dot300
plot allow you to
see how data are
268-332
0.15
22distributed, determine
specific
data entries, and
333-397
1 identify unusual
365data values. 0.04
23
398-462
3
430
0.12
26
4. In a Pareto chart, the height of each bar represents frequency
f or relative frequency and the bars
26
1
are positioned in order fof decreasing
height with the tallest
n bar positioned at the left.
5. b
6. d
7. a
8. c
27, 32, 41,
44, 47,
48, 50, is
51,with
51, 52,
53, 53, the
54, larger
54, 54,the
54,employee’s
55, 56, 56, 58,
59, will
68,
c.9.It appears
that43,
the43,
longer
an 47,
employee
the 53,
company,
salary
68,
68,
73,
78,
78,
85
be.
Max: 85
Min: 27
7a, b.
10. 12.9, 13.3, 13.6, 13.7, 13.7, 14.1, 14.1, 14.1, 14.1, 14.3, 14.4, 14.4, 14.6, 14.9, 14.9, 15.0, 15.0,
15.0, 15.1, 15.2, 15.4, 15.6, 15.7, 15.8, 15.8, 15.8, 15.9, 16.1, 16.6, 16.7
Class
with greatest relative frequency: 138-202
Max: 16.7 Min: 12.9
Class with least relative frequency: 333-397
11. 13, 13, 14, 14, 14, 15, 15, 15, 15, 15, 16, 17, 17, 18, 19
14 6
Max:width
19 =Min: 13 Range
38. Class
=
= 1.6
2
classes
12. 214, 214, 214,Number
216, 216,of217,
218, 218, 5220, 221, 223, 224, 225, 225, 227, 228, 228, 228, 228,
Frequency,
Midpoint
Relative
Cumulative
230, Class
230, 231, 235,
237, 239 f
Max: 239 Min: 214
frequency
c. The average bill increased from 1998 to 2004, then it hovered aroundfrequency
$50.00 from 2004 to 2008.
3
6.5
0.12
3
CHAPTER 2
DESCRIPTIVE
STATISTICS 33
Section 2.2 6-7
13. Sample
spend the most amount
of time on
MySpace and the
8-9answer: Users 10
8.5
0.38
13 least amount of time
on Twitter.
Answers will
vary.
10-11
6 plot
10.5plot allow you
0.23to see how data
19 are distributed, determine
3.1, EXERCISE
Both
the23,
stem-and-leaf
and the dot
o2.2
5-8,
17,
30,SOLUTIONS
34, 35-38
12-13
6
12.5
0.23
25
specific data entries, and identify unusual data values.
14. Sample
answer: Motor vehicle
thefts decreased
between0.04
2003 and 2008. 26
Answers will vary.
14-15
1
14.5
1. Quantitative: stem-and-leaf plot, dot plot, histogram, timef series chart, scatter plot.
4.15.
In
a Pareto
chart,
height
of each
bar represents
frequency
relative
frequency
and the
f 26
Answers
will
vary.
Sample
answer:
Tailgaters
irk drivers
the 1most,orwhile
too cautious
drivers
irk bars
Qualitative:
pie
chart,the
Pareto
chart
ntallest bar positioned at the left.
are
positioned
in
order
of
decreasing
height
with
the
drivers the least.
2. Unlike the histogram, the stem-and-leaf plot still contains the original data values. However,
5.16.
bAnswers
6.vary.
d Sample
7. in
a aThe
8. cplot.
willdifficult
answer:
most frequent
incident occurring while driving and using
some
data are
to organize
stem-and-leaf
a cell phone is swerving. Twice as many people “sped up” than “cut off a car.”
9. 27, 32, 41, 43, 43, 44, 47, 47, 48, 50, 51, 51, 52, 53, 53, 53, 54, 54, 54, 54, 55, 56, 56, 58, 59, 68,
68,6 73,
7 78,
67 78, 85
17. 68,
Key:
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Max:
85
Min: 27
67 8
7 3 13.3,
5 5 13.6,
6 913.7, 13.7, 14.1, 14.1, 14.1, 14.1, 14.3, 14.4, 14.4, 14.6, 14.9, 14.9, 15.0, 15.0,
10. 12.9,
8 0 15.1,
0 2 15.2,
3 515.4,
5 715.6,
7 15.7,
8
15.0,
15.8, 15.8, 15.8, 15.9, 16.1, 16.6, 16.7
Max:
1 2 12.9
4 5 5
9 0 116.71 Min:
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
It appears that most grades for the biology midterm were in the 80s or 90s. (Answers will vary.)
11. 13, 13, 14, 14, 14, 15, 15, 15, 15, 15, 16, 17, 17, 18, 19
Max: 19
Min: 13
12. 214, 214, 214, 216, 216, 217, 218, 218, 220, 221, 223, 224, 225, 225, 227, 228, 228, 228, 228,
230, 230, 231, 235, 237, 239
Max: 239 Min: 214
13. Sample answer: Users spend the most amount of time on MySpace and the least amount of time
on Twitter. Answers will vary.
14. Sample answer: Motor vehicle thefts decreased between 2003 and 2008. Answers will vary.
15. Answers will vary. Sample answer: Tailgaters irk drivers the most, while too cautious drivers irk
Copyright
© 2012
Education, Inc. Publishing as Prentice Hall.
drivers
thePearson
least.
16. Answers will vary. Sample answer: The most frequent incident occurring while driving and using
a cell phone is swerving. Twice as many people “sped up” than “cut off a car.”
CHAPTER 2
DESCRIPTIVE STATISTICS
35
23.
Category
United States
Italy
Ethiopia
South Africa
Tanzania
Kenya
Mexico
Morocco
Great Britain
Brazil
New Zealand
Frequency, f
15
4
1
2
1
8
4
1
1
2
1
f
40
Relative Frequency
0.375
0.100
0.025
0.050
0.025
0.200
0.100
0.025
0.025
0.050
0.025
f
1
N
CHAPTER 2
Angle
135
36
9
18
9
72
36
9
9
18
9
360
DESCRIPTIVE STATISTICS
37
29.
Most of the New York City Marathon winners are from the United States and Kenya. (Answers
will vary.)
It appears that it was hottest from May 7 to May 11. (Answers will vary.)
24.
30.
Category
Science, aeronautics, exploration
Space operations
Education
Cross-agency support
Inspector general
Frequency, f
8947
6176
126
3401
36
Relative Frequency
Angle
0.479
172.4
0.331
119.2
0.007
2.5
0.182
65.5
0.002
0.7
f
f 18,686
360
1
N
It appears that the largest decrease in manufacturing as a percent of GDP was from 2000 to 2001.
(Answers will vary.)
31. Variable: Scores
Key: 5 5 5.5
5 5
6 2
It
that most of NASA’s budget was spent on science, aeronautics, and exploration.
6 appears
8
(Answers will vary.)
7 0 1
7 5 6
8 0 2 3
8 5 6 7 8 8 9
Copyright
Education, Inc. Publishing as Prentice Hall.
3 Pearson
3
9 0© 2012
9 5 5 8 9
10 0
It appears that most scores on the final exam in economics were in the 80’s and 90’s. (Answers
will vary.)
CHAPTER 2
DESCRIPTIVE STATISTICS
34a.
It appears that the number of registrations is increasing over time. (Answers will vary.)
b.
It appears that the number of crashes is decreasing over time. (Answers will vary.)
c.
It appears that the number of registrations is increasing over time. (Answers will vary.)
d.
It appears that the number of crashes is decreasing over time. (Answers will vary.)
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
39
40
CHAPTER 2
DESCRIPTIVE STATISTICS
35a. The graph is misleading because the large gap from 0 to 90 makes it appear that the sales for the
3rd quarter are disproportionately larger than the other quarters. (Answers will vary.)
b.
36a. The graph is misleading because the vertical axis has no break. The percent of middle schoolers
that responded “yes” appears three times larger than either of the others when the difference is
only 10%. (Answers will vary.)
b.
37a. The graph is misleading because the angle makes it appear as though the 3rd quarter had a
larger percent of sales than the others, when the 1st and 3rd quarters have the same percent.
b.
38a. The graph is misleading because the “OPEC countries” bar is wider than the “non-OPEC
countries” bar.
b.
39a. At Law Firm A, the lowest salary was $90,000 and the highest salary was $203,000. At Law
Firm B, the lowest salary was $90,000 and the highest salary was $190,000.
b. There are 30 lawyers at Law Firm A and 32 lawyers at Law Firm B.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
63-69
66
70-76
73
77-83
80
84-90
5. 1, 2, 2, 2, 3 (Answers87will vary.)
10
5
8
6
N = 50
660
CHAPTER 2
365
640
552
x f
3265
DESCRIPTIVE STATISTICS
43
6. 2, 4, 5, 5,x 6,f 8 (Answers
will vary.)
3265
d.
65.3
N
50
7. 2,
5, mean
7, 9, 35
will vary.)
The
age(Answers
of the 50 richest
people is 65.3
Section
2.3
o
1-8, 9-16, 19, 20, 23, 42, 45, 49, 56, 58
8.2.3
1, EXERCISE
2, 3, 3, 3, 4, 5SOLUTIONS
(Answers will vary.)
True
9.1. Skewed
right because the “tail” of the distribution extends to the right.
2. Symmetric
False. All quantitative
dataleft
setsand
have
a median.
10.
because the
right
halves of the distribution are approximately mirror images.
3. True
11. Uniform because the bars are approximately the same height.
4. True
CHAPTER 2
DESCRIPTIVE STATISTICS
12. Skewed left because the “tail” of the distribution
extends to the
left.
43
5. 1, 2, 2, 2, 3 (Answers will vary.)
13. (11), because the distribution values range from 1 to 12 and has (approximately) equal
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
6. frequencies.
2, 4, 5, 5, 6, 8 (Answers will vary.)
14.
the distribution
has values in the thousands of dollars and is skewed right due to the
7. (9),
2, 5,because
7, 9, 35 (Answers
will vary.)
few executives that make a much higher salary than the majority of the employees.
8. 1, 2, 3, 3, 3, 4, 5 (Answers will vary.)
15. (12), because the distribution has a maximum value of 90 and is skewed left due to a few students
9. scoring
Skewed much
right because
the “tail”
of the distribution
extends to the right.
lower than
the majority
of the students.
10. Symmetric because the left and right halves of the distribution are approximately mirror images.
16. (10), because the distribution is rather symmetric due to the nature of the weights of seventh
boys.
11. grade
Uniform
because the bars are approximately the same height.
12. Skewedxleft 64
because the “tail” of the distribution extends to the left.
17. x
n
13
4.9
13. (11), because the distribution values range from 1 to 12 and has (approximately) equal
frequencies.
= 4 (occurs
3 times) has values in the thousands of dollars and is skewed right due to the
14. mode
(9), because
the distribution
few executives that make a much higher salary than the majority of the employees.
x 396
39.6
18.
15. x(12), because
the distribution
has a maximum value of 90 and is skewed left due to a few students
10
n
scoring much lower than the majority of the students.
16. (10), because the distribution is rather symmetric due to the nature of the weights of seventh
grade boys.
mode = 39 (occurs 3 times)
17. x
19. x
x
x
n
n
64
76.8 4.9
13
11.0
7
mode = 4 (occurs 3 times)
396
mode =x11.7
(occurs 3 times)
18. x
10
n
39.6
mode = 39 (occurs 3 times)
x
76.8
7
Copyright
19. x © 2012 Pearson Education,
11.0 Inc. Publishing as Prentice Hall.
n
mode = 11.7 (occurs 3 times)
21. x
44
x
n
686.8
32
CHAPTER 2
21.46
DESCRIPTIVE STATISTICS
mode = 20.4 (occurs 2 times)
CHAPTER 2
DESCRIPTIVE STATISTICS
x 2004
20. x
200.4
x 1223
22. x
10 61.2
n
41.
20
n
Source
Score, x Weight, w
x·w
Homework
85
0.05
4.25
Quiz
80
0.35
28
mode==80,
none
mode
125
Project
100
0.20
20
Themodes
modedo
cannot
be found
points
are they
repeated.
The
not represent
the because
center of no
the data
data set
because
are large values compared to
Speech
90
0.15
13.5
the
rest of the data.
Final exam
0.25
23.25
x 686.8 93
21.46
21.
x
w 1
x w 89
23. x notnpossible32(nominal data)
47
median = not possible (nominal data)
x w
89
xmode = “Eyeglasses” 89
The meanwand median
1 cannot be found because the data are at the nominal level of measurement.
24. x not possible (nominal data)
42.
mode = 20.4 (occurs(nominal
2 times)
median
data)
Source= not possible
Score, x
Weight,
w
x·w
mode = “Money needed”
MBAs
92,500
8 because the data740,000
The
meanx and1223
median
cannot be found
are at the nominal level of measurement.
68,000
17
1,156,000
61.2
22. BAs
x
20
n
x 1194.4
w 25
x w 1,896,000
25. x
n
7
170.63
x w
1,896,000
x
75,840
w
25
48 CHAPTER
2 125
DESCRIPTIVE STATISTICS
mode = 80,
The modes
mode
= none do not represent the center of the data set because they are large values compared to
43.
be found because no data points are repeated.
the mode
rest ofcannot
the data.
45. The
Balance, x
Days, w
x·w
Grade
Points,
x Credits, w12,552
x·w
$523
24
26. xx B
not
possible
(nominal
data)data)
3
3
9
not
possible
(nominal
23.
$2415 = not possible 2(nominal data)
4830
median
B
3
3
9
median
=
not
possible
(nominal
data)
$250 = “Mashed” 4
1000
mode
A
4
4
16
mode
=
“Eyeglasses”
The mean and medianwcannot
the data are at the nominal level of measurement.
30 be found xbecause
w 18,382
1
2 found because the2 data are at the nominal level of measurement.
TheDmean and median
cannot be
C x w
2
3
6
18,382
x
$612.73
w
15
x
w 42
24. x not wpossible 30
(nominal data)
median
= not possible (nominal data)
x w
42
Copyright
© 2012
Pearson
Education,
Inc. Publishing as Prentice Hall.
mode
=
“Money
needed”
x
2.8
44.
w
15
The
meanxand median
the data are at the nominal level of measurement.
Balance,
Days, wcannot be found
x · because
w
CHAPTER 2
DESCRIPTIVE STATISTICS 49
$759
15
11,385
46. $1985 x 1194.4 5
9925
x
170.63
25.Source
Score,
x Weight, w7050
x·w
49.$1410n
7 5
Engineering
85
9
$348
6
2088 f 765
Class
Midpoint,
x Frequency,
x·f
Business
81 31
13
1053
29-33
341
w 31
x w11 30, 448
Math
90 36
5
450
34-38
12
432
x none
w
30, 44841
w 27 2
x w 226882
mode
=
39-43
x
$982.19
The
mode
cannot
be
found
because no 5data points are repeated.
w
31
44-48
46
230
x w
2268
x
84
x f
1085
n 30
w
27
26. x not possible (nominal data)
x f
1085 (nominal data)
median
= not possible
x
36.2 miles per gallon
47.
n
30
mode = “Mashed”
Source
x cannot
Weight,
w because the
x·w
The mean andScore,
median
be found
data are at the nominal level of measurement.
Homework
85
0.05
4.25
50.
Quiz
80
Class
Midpoint, x0.35Frequency, f 28
x·f
Project
100
0.20
20
22-27
24.5
16
392
Speech
90 30.5
0.15
13.5
28-33
2
61
Final
exam
85 36.5
0.25
21.25
34-39
2
73
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
w
1
x
w
87
40-45
42.5
3
127.5
46-51
48.5
1
48.5
Copyright © 2012
Pearson87
Education, Inc. Publishing as Prentice Hall.
x w
Range
Number of classes
Class
Frequency, f
1
6
2
5
3
4
4
6
5
4
6
5
f 30
Shape: Uniform
56. Class width =
6 1
6
0.8333
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
1
254
454.5
64,516
206,570.25
3,870,960
14,459,917.5
x
x
d. s
x
2
f
x
2
28,715,797.5
f
28,715,797.5
999
n 1
169.5
Section 2.4
2.4 EXERCISE SOLUTIONS
o
1-10, 11, 13, 19, 21, 22, 23, 31,32, 33, 38
1. The range is the difference between the maximum and minimum values of a data set. The
advantage of the range is that it is easy to calculate. The disadvantage is that it uses only two
entries from the data set.
58
CHAPTER 2
DESCRIPTIVE STATISTICS
Copyright
© 2012 Pearson
Publishing between
as Prentice an
Hall.
2. A deviation
x Education,
is theInc.
difference
entry
x and the mean of the data µ. The sum of
the deviations is always zero.
3. The units of variance are squared. Its units are meaningless. (Example: dollars2)
4. The standard deviation is the positive square root of the variance.
Because squared deviations can never be negative, the standard deviation and variance can never
be negative.
5. {9, 9, 9, 9, 9, 9, 9}
n=7
x 63
9
x
7
n
x
x
9
9
9
9
9
9
9
x
s
x
x
0
0
0
0
0
0
0
63
x
x
x
x
2
0
0
0
0
0
0
0
0
x
x
x
2
0
2
0
6
n 1
0
6. {3, 3, 3, 7, 7, 7}
n=6
x 30
5
n
6
x
x
3
3
3
7
7
7
x 30
x
N
–2
–2
–2
2
2
2
4
4
4
4
4
4
0
x
2
2
x
24
6
x
4
2
24
2
7. When calculating the population standard deviation, you divide the sum of the squared deviations
by N, then take the square root of that value. When calculating the sample standard deviation, you
divide the sum of the squared deviations by n 1 , then take the square root of that value.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
CHAPTER 2
DESCRIPTIVE STATISTICS
59
8. When given a data set one would have to determine if it represented the population or if it was a
sample taken from the population. If the data are a population, then is calculated. If the data
are a sample, then s is calculated.
9. Similarity: Both estimate proportions of the data contained within k standard deviations of the
mean.
Difference: The Empirical Rule assumes the distribution is bell-shaped. Chebychev’s Theorem
makes no such assumption.
10. You must know that the distribution is bell-shaped.
11. Range = Max – Min = 12 – 5 = 7
CHAPTER 2
DESCRIPTIVE STATISTICS
x 90
9
N – 10
12. Range = Max
Min = 25 – 15 = 10
266
x
x
19
x
x
N
14
2 0
9
0
x
x
x
5
–4
16
18
–1
1
0
0
20 9
1
1
19 10
0
0
1
1
21 11
2
4
2
4
19
0
0
12
3
9
17
–2
4
7
–2
4
15
–4
16
17 7
–2 –2
4
4
25 8
6 –1
36
1
22
3
9
12
3
9
19
0
0
20 x 90
1 x
1 x
0
60
16
18
2
x 90
x
N
2
x
2
x
N
N2
x
–3
2
–1
x
48
0 4.8
10
2
86
14
6.1
4.8
86
14
N
2
2
9
1
2
x
48
86
2.2
2.5
13. Range = Max – Min = 19 – 4 = 15
x 108
x
12
n
9
x
x
4
15
9
12
16
8
11
19
14
x
s2
s
x
x
–8
3
–3
0
4
–4
–1
7
2
108
x
n
x
x
x
n
1
2
64
9
9
0
16
16
1
49
4
0
x
x
2
168
2
168
9 1
1
x
x
x
21
2
21
4.6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
15.
Range==Max
Max– Min
– Min
= 96
15. Range
= 96
– 23– =23
73= 73
CHAPTER 2
DESCRIPTIVE STATISTICS
67
= 34
– 24– =24
10= 10
16. Range
Range==Max
Max– Min
– Min
= 34
2
x
x
0.00467689
17. Range
– Min = 98 – 74 = 24
s ==Max
0.02418
17.
Range
Max
n 1– Min = 98 –874 = 24
It appears
data– that
18.b.Range
= Maxform
– Minthe
= 6.7
0.5 =the
6.2batting averages for Team A are more variable than the batting
18. Range
= Max
– MinB.= The
6.7 –batting
0.5 = averages
6.2
averages
for Team
for Team A have a higher mean and a higher
19a. Range
= Max
Min for
= 38.5
– 20.7
median
than –those
Team
B. = 17.8
19a.
Range==Max
Max– Min
– Min
= 38.5
– 20.7
= 17.8
b. Range
= 60.5
– 20.7
= 39.8
b.
Range
=
Max
–
Min
=
60.5
–
20.7
= 39.8
29a. Greatest sample standard deviation: (ii)
20. Changing
of the
greatly
affects
thethe
range.
Data setthe
(ii)maximum
has morevalue
entries
thatdata
are set
farther
away
from
mean.
Least sample
standard deviation:
(iii)data set greatly affects the range.
20. Changing
the maximum
value of the
21. Graph
of 24are
and
graph
a standard deviation of 16 because
Data(a)
sethas
(iii)a standard
has moredeviation
entries that
close
to(b)
thehas
mean.
graph (a) has more variability.
The three
dataa sets
have deviation
the same mean
different
deviations.
21.b.Graph
(a) has
standard
of 24but
andhave
graph
(b) hasstandard
a standard
deviation of 16 because
graph
(a)
has
more
variability.
22. Graph (a) has a standard deviation of 2.4 and graph (b) has a standard deviation of 5 because
30a.graph
Greatest
sample
standard deviation: (i)
(b) has
more variability.
Data
set
(i)
has
more
entries
that are
from
22. Graph (a) has a standard
deviation
offarther
2.4 andaway
graph
(b)the
hasmean.
a standard deviation of 5 because
Least
sample
standard
deviation:
(iii)
23. Company
Anmore
offer variability.
of $33,000 is two standard deviations from the mean of Company A’s
graph (b)B.has
Data set
(iii) has
more
entries
that areThe
close
to the
starting
salaries,
which
makes
it unlikely.
same
offermean.
is within one standard deviation of the
b.mean
Theofthree
data sets
have
thesalaries,
same mean,
median,
and
mode,
but have different standard
Company
B’s
starting
which
makes
the
offer
likely.
23. Company B. An offer of $33,000 is two standard deviations
from the mean of Company A’s
deviations.
starting salaries, which makes it unlikely. The same offer is within one standard deviation of the
mean of Company B’s starting salaries, which makes the offer likely.
31a. Greatest sample standard deviation: (ii)
Data set (ii) has more entries that are farther away from the mean.
Least sample standard deviation: (iii)
Data set (iii) has more entries that are close to the mean.
b. The three data sets have the same mean, median, and mode, but have different standard
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
deviations.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
32a. Greatest sample standard deviation: (iii)
68 CHAPTER 2
STATISTICS
Data set (iii)DESCRIPTIVE
has more entries
that are farther away from the mean.
Least sample standard deviation: (i)
36a. n 40
Data set (i) has more entries that are close to the mean.
95%(40) = (0.95)(40) 38 farms have values between $1500 and $3300 per acre.
b. nThe20
three data sets have the same mean and median but have different modes and standard
b.
deviations.
95%(20)
= (0.95)(20) 19 farms have values between $1500 and $3300 per acre.
37.
33.
34.
38.
x1300,
15001700
s 1500
200 1 200 , 1500 1 200
x s, x s
{$950, $1000, $2000, $2180} are outliers. They are more than 2 standard deviations from the
68% (1100,
of the 1900).
farms $2180
have values
betweenbecause
$1300itand
$1700
acre. deviations from
mean
is very unusual
is more
thanper
3 standard
the mean.
95% of the data falls between x
xx 2400
450
2s 2400 s2 450
1500
2 s and x
2s .
{$1045, $1490, $3325, $3800} are outliers. They are more than 2 standard deviations from the
x 2(1500,
s 2400
450 and 3300
mean
3300). 2
$1045
$3800 are very unusual because they are more than 3 standard
deviations
from
the
mean.
95% of the farms have values between $1500 and $3300 per acre.
s, x 2 s
1.14,
39.
nx 275
35a.
68%(75)
= (0.68)(75)
1
1
1
1
1
1
2
b. n k 225
4
2
68%(25) = (0.68)(25)
minutes.
5.5 are 2 standard deviations from the mean.
51 farms have values between $1300 and $1700 per acre.
At least 75% of the eruption times lie between 1.14 and 5.5
0.75
17 farms have values between $1300 and $1700 per acre.
If n = 32, at least (0.75)(32) = 24 eruptions will lie between 1.14 and 5.5 minutes.
40.
1
k2
1
1
1
0.75
2
4
2
At least 75% of the 400-meter dash times lie within 2 standard deviations of the mean.
1
1
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
x
2 s, x
2s
54.97, 59.17
At least 75% of the 400-meter dash times lie between 54.97 and 59.17 seconds.
41.
x
f
xf
0
1
2
5
11
7
0
11
14
x
x
–2.1
–1.1
–0.1
x
x
4.41
1.21
0.01
2
x
x
2
22.05
13.31
0.07
f
Best actress:
35.9,
11.4
43.7
0.49
8.7
33 35.9
x
Kate Winslet: x 33: z
0.25
11.4
c. Sean Penn’s age is 0.49 standard deviation above the mean of the best actors. Kate Winslet’s age
is 0.25 standard deviation below the mean of the best actresses. Neither actor’s age is unusual.
b. Sean Penn: x
48 : z
x
48
Section 2.5
o
(odd), 17, SOLUTIONS
25-28, 29, 30, 37, 39, 44, 58, 59
2.51-13
EXERCISE
1. The soccer team scored fewer points per game than 75% of the teams in the league.
2. The salesperson sold more hardware equipment than 80% of the other sales people.
3. The student scored higher than 78% of the students who took the actuarial exam.
4. The child’s IQ is higher than 93% of the other children in the same age group.
5. The interquartile range of a data set can be used to identify outliers because data values that are
greater than Q3 1.5 IQR or less than Q1 1.5 IQR are considered outliers.
6. Quartiles are special cases of percentiles. Q1 is the 25th percentile, Q2 is the 50th percentile, and
Q3 is the 75th percentile.
7. False. The median of a data set is a fractile, but the mean may or may not be fractile depending on
80 CHAPTER 2
the distribution ofDESCRIPTIVE
the data. STATISTICS
8. b.True
9. True
10. False. The five numbers you need to graph a box-and-whisper plot are the minimum, the
maximum, Q1 , Q3 , and the median Q2 .
24a.
11. False. The 50th percentile is equivalent to Q2 .
CHAPTER 2
DESCRIPTIVE STATISTICS
12. False. Any score equal to the mean will have a corresponding z-score of zero.
79
b. Min
IQR==1,Q3Q1 Q13, Q270
– 130
140
5,
Q3 = 8,
Max = 9
unusual.
13. False. A z-score
of 2 2.5 is considered
b.
17a.
Min = 900, Q1 1250, Q2 1500, Q3 1950, Max = 2100
14. True
b. IQR = Q3 Q1 1950 – 1250 = 700
15a. Min = 10, Q1 13, Q2 15, Q3 17, Max = 20
18a.b. Min
Q2– 1365,
Q3 Q1 Q1 50,17
= 4Q3 70, Max = 85
IQR==25,
25.
not– skewed
Q3 Data
Q1 are70
50 = 20 or symmetric.
b. None.
IQR =The
16a. Min = 100, Q1 130, Q2 205, Q3 270, Max = 320
26. Skewed
the,data
to the
in the
box-and-whisker
plot.
19a.
Min = right.
1.9 , Most
Q1 of 0.5
Q2 lie0.1,
Q3 left0.7,
Max
= 2.1
Q
0.7the data
0.5lie to
= 1.2
b. Skewed
IQR = Qleft.
3
1
27.
Most
of
the right in the box-and-whisker plot.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
28. Symmetric.
left
and=to2.1
the right of the median.
, Q1data are
0.3evenly
, Q2 spaced
0.2, Q3to the
0.4,
Max
20a.
Min = 1.3The
0.4
0.3 = 0.7
b. IQR = Q Q1
Q3 C
29. Q1 B, Q3 2 A,
25% of the values are below B, 50% of the values are below A, and 75% of the values are below
21a. C.
30. P10 T, P50 R, P80 S
10% of the values are below T, 50% of the values are below R, and 80% of the values are below
S.
Min = 24, Q1 28, Q2 35, Q3 41, Max = 60
31a.
b. Q1 2, Q2 4, Q3 5
b.
22a.
63 63
0
c. 25% 7
23 23
x
Biology: x 23 z
0
36a. $17.65 b. 50%
c. 50%3.9
b. The student performed equally well on the two tests.
1.43
37. A z
34,000 35,000
x
B z 0
0.44
43a. x 34,000 z
C z 2.14
2, 250
The z-score 2.14 is unusual
because
is so large.
37,000 it 35,000
x
0.89
x 37,000 z
2, 250
38. A z
1.54
30,000 35,000
Bx 30,000
z 0.77 z x
2.22
2, 250
C z 1.54
None
of the
are unusual.
The tire
withz-scores
a life span
of 30,000 miles has an unusually short life span.
30,500 35,000
x
b. x 30,500 z
2 2.5th percentile
75 63
x
2,250
39a. Statistics: x 75 z
1.71
7
37, 250 35,000
x
1 84th percentile
x 37, 250 z
x
2,2525023 0.51
Biology: x 25 z
35,000 3.9
35,000
x
z a better score on the statistics0test.50th percentile
b. xThe35,000
student had
2, 250
x
42a. Statistics: x 63 z
35a. 5
b. 50%
34 33
0.25
4
30 33
x
0.75
x 30 z
4
33
xEducation, 42
Copyright
2012 Pearson
Inc. Publishing
as Prentice Hall.
2.25
x ©42
z
4
The fruit fly with a life span of 42 days has an unusually long life span.
29 33
x
16th percentile
1
b. x 29 z
4
41 33
x
97.5th percentile
2
x 41 z
4
25 33
x
2.5th percentile
2
x 25 z
4
44a. x
34
x
z
CHAPTER 2
Copyright © 2012 Pearson
Education,ofInc.
Publishing
Prentice
Hall.
x
Number
data
valuesas less
than
58. Percentile
Total number of data values
3
100
73
59. Percentile
4th percentile
Number of data values less than x
100
Total number of data values
30
100 41st percentile
73
60a.
Q1 9, Q2 11, Q3 13
IQR Q3 Q1 13 9 4
1.5 IQR 6
Q1
100
1.5 IQR
9
6
3
DESCRIPTIVE STATISTICS
85