AP Stats Cumulative AP Practice Test 2
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The University of Sydney *
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Course
100
Subject
Statistics
Date
Nov 24, 2024
Type
Pages
12
Uploaded by studies212121
Cumulative
AP®
Practice
Test
2
Section
I:
Multiple
Choice
Choose
the
best
answer
for
each
question.
AP2.1
The
five-number
summary
for
a
data
set
is
given
by
min
=5,
Q;
=18,
median
=
20,
O3
=40,
max
=
75.
If
you
wanted
to
construct
a
boxplot
for
the
data
set
that
would
show
outliers,
if
any
existed,
what
would
be
the
maximum
possible
length
of
the
right-side
“whisker”?
a.33
b.
35
c.45
d.53
e.
55
AP2.2
The
probability
distribution
for
the
number
of
heads
in
four
tosses
of
a
coin
is
given
by
Number
of
heads
0
1
2
3
4
Probability
0.0625
0.2500
0.3750
0.2500
0.0625
The
probability
of
getting
at
least
one
fail
in
four
tosses
of
a
coin
is
a.
0.2500.
b.0.3125.
c.0.6875.
d.
0.9375.
e.0.0625.
AP2.3
In
a
certain
large
population
of
adults,
the
distribution
of
IQ
scores
is
strongly
left-skewed
with
a
mean
of
122
and
a
standard
deviation
of
5.
Suppose
200
adults
are
randomly
selected
from
this
population
for
a
market
research
study.
For
SRSs
of
size
200,
the
distribution
of
sample
mean
1Q
score
is
a.
left-skewed
with
mean
122
and
standard
deviation
0.35.
b.
exactly
Normal
with
mean
122
and
standard
deviation
5.
c.
exactly
Normal
with
mean
122
and
standard
deviation
0.35.
d.
approximately
Normal
with
mean
122
and
standard
deviation
5.
e.
approximately
Normal
with
mean
122
and
standard
deviation
0.35.
AP2.4
A
10-question
multiple-choice
exam
offers
5
choices
for
each question.
Jason
just
guesses
the
answers,
so
he
has
probability
1/5
of
getting
any
one
answer
correct.
You
want
to
perform
a
simulation
to
determine
the
number
of
correct
answers
that
Jason
gets.
What
would
be
a
proper
way
to
use
a
table
of
random
digits
to
do
this?
a.
One
digit
from
the
random
digit
table
simulates
one
answer,
with
5
=
correct
and
all
other
digits
=
incorrect.
Ten
digits
from
the
table
simulate
10
answers.
b.
One
digit
from
the
random
digit
table
simulates
one
answer,
with
O
or
1
=
correct
and
all
other
digits
=
incorrect.
Ten
digits
from
the
table
simulate
10
answers.
c.
One
digit
from
the
random
digit
table
simulates
one
answer,
with
odd
=
correct
and
even
=
incorrect.
Ten
digits
from
the
table
simulate
10
answers.
d.
One
digit
from
the
random
digit
table
simulates
one
answer,
with
O
or
1
=
correct
and
all
other
digits
=
incorrect,
ignoring
repeats.
Ten
digits
from
the
table
simulate
10
answers.
e.
Two
digits
from
the
random
digit
table
simulate
one
answer,
with
00
to
20
=
correct
and
21
to
99
=
incorrect.
Ten
pairs
of
digits
from
the
table
simulate
10
answers.
AP2.5
Suppose
we
roll
a
fair
die
four
times.
What
is
the
probability
that
a
6
occurs
on
exactly
one
of
the
rolls?
()
()
(1)
()
AP2.6
On
one
episode
of
his
show,
a
radio
show
host
encouraged
his
listeners
to
visit
his
website
and
vote
in
a
poll
about
proposed
tax
increases.
Of
the
4821
people
who
vote,
4277
are
against
the
proposed
increases.
To
which
of
the
following
populations
should
the
results
of
this
poll
be
generalized?
a.
All
people
who
have
ever
listened
to
this
show
b.
All
people
who
listened
to
this
episode
of
the
show
c.
All
people
who
visited
the
show
host’s
website
d.
All
people
who
voted
in
the
poll
e.
All
people
who
voted
against
the
proposed
increases
AP2.7
The
number
of
unbroken
charcoal
briquets
in
a
20-pound
bag
filled
at
the
factory
follows
a
Normal
distribution
with
a
mean
of
450
briquets
and
a
standard
deviation
of
20
briquets.
The
company
expects
that
a
certain
number
of
the
bags
will
be
underfilled,
so
the
company
will
replace
for
free
the
5%
of
bags
that
have
too
few
briquets.
What
is
the
minimum
number
of
unbroken
briquets
the
bag
would
have
to
contain
for
the
company
to
avoid
having
to
replace
the
bag
for
free?
a.
404
b.
411
c.418
d.
425
e.
448
AP2.8
You
work
for
an
advertising
agency
that
is
preparing
a
new
television
commercial
to
appeal
to
women.
You
have been
asked
to
design
an
experiment
to
compare
the
effectiveness
of
three
versions
of
the
commercial.
Each
subject
will
be
shown
one
of
the
three
versions
and
then
asked
to
reveal
her
attitude
toward
the
product.
You
think
there
may
be
large
differences
in
the
responses
of
women
who
are
employed
and
those
who
are
not.
Because
of
these
differences,
you
should
use
a.
a
block
design,
but
not
a
matched
pairs
design.
b.
a
completely
randomized
design.
c.
a
matched
pairs
design.
d.
a
simple
random
sample.
e.
a
stratified
random
sample.
AP2.9
Suppose
that
you
have
torn
a
tendon
and
are
facing
surgery
to
repair
it.
The
orthopedic
surgeon
explains
the
risks
to
you.
Infection
occurs
in
3%
of
such
operations,
the
repair
fails
in
14%,
and
both
infection
and
failure
occur
together
1%
of
the
time.
What
is
the
probability
that
the
operation
is
successful
for
someone
who
has
an
operation
that
is
free
from
infection?
a.0.8342
b.
0.8400
c.0.8600
d.
0.8660
e.
0.9900
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AP2.10
Social
scientists
are
interested
in
the
association
between
high
school
graduation
rate
(HSGR,
measured
as
a
percent)
and
the
percent
of
U.S.
families
living
in
poverty
(POV).
Data
were
collected
from
all
50
states
and
the
District
of
Columbia,
and
a
regression
analysis
was
conducted.
The
resulting
least-squares
regression
line
is
given
by
POV
=
59.2
—
0.620
(HSGR)
with
>
=
0.802.
Based
on
the
information,
which
of
the
following
is
the
best
interpretation
for
the
slope
of
the
least-
squares
regression
line?
a.
For
each
1%
increase
in
the
graduation
rate,
the
percent
of
families
living
in
poverty
is
predicted
to
decrease
by
approximately
0.896.
b.
For
each
1%
increase
in
the
graduation
rate,
the
percent
of
families
living
in
poverty
is
predicted
to
decrease
by
approximately
0.802.
c.
For
each
1%
increase
in
the
graduation
rate,
the
percent
of
families
living
in
poverty
is
predicted
to
decrease
by
approximately
0.620.
d.
For
each
1%
increase
in
the
percent
of
families
living
in
poverty,
the
graduation
rate
is
predicted
to
decrease
by
approximately
0.802.
e.
For
each
1%
increase
in
the
percent
of
families
living
in
poverty,
the
graduation
rate
is
predicted
to
decrease
by
approximately
0.620.
Questions
AP2.11-AP2.13
refer
to
the
following
graph.
Here
is
a
dotplot
of
the
adult
literacy
rates
in
177
countries
in
a
recent
year,
according
to
the
United
Nations.
For
example,
the
lowest
literacy
rate
was
23.6%,
in
the
African
country
of
Burkina
Faso.
Mali
had
the
next
lowest
literacy
rate
at
24.0%.
oot
°
eoe
°
o
o0
aoo
°
e
o
®
o
sccscee
°
°
o0
o
000
sooseee
a
o
o
e
e
o
o
000
e0e
seccesee
0
00
oo
0000
0
00000
0
0
000000000000
L
T
20
40
60
80
100
Literacy
rate
(%)
Starnes
&
Tabor,
The
Practice
of
Statistics,
6e,
©
2018
Bedford,
Freeman
&
Worth
High
School
Publishers
AP2.11
The
overall
shape
of
this
distribution
is
a.
clearly
skewed
to
the
right.
b.
clearly
skewed
to
the
left.
c.
roughly
symmetric.
d.
approximately
uniform.
e.
There
is
no
clear
shape.
AP2.12
The
mean
of
this
distribution
(don*
try
to
find
it)
will
be
a.
very
close
to
the
median.
b.
greater
than
the
median.
c.
less
than
the
median.
d.
You
can’t
say,
because
the
distribution
isn’t
symmetric.
e.
You
can’t
say,
because
the
distribution
isn’t
Normal.
AP2.13
The
country
with
a
literacy
rate
of
49%
is
closest
to
which
of
the
following
percentiles?
a.
6th
b.
11th
c.28th
d.
49th
e.
There
is
not
enough
information
to
calculate
the
percentile.
AP2.14
The
correlation
between
the
age
and
height
of
children
under
the
age
of
12
is
found
to
be
»
=
0.60.
Suppose
we
use
the
age
x
of
a
child
to
predict
the
height
y
of
the
child.
What
can
we
conclude?
a.
The
height
is
generally
60%
of
a
child’s
age.
b.
About
60%
of
the
time,
age
will
accurately
predict
height.
c.
Thirty-six
percent
of
the
variation
in
height
is
accounted
for
by
the
linear
model
relating
height
to
age.
d.
For
every
1
year
older
a
child
is,
the
regression
line
predicts
an
increase
of
0.6
foot
in
height.
e.
Thirty-six
percent
of
the
time,
the
least-squares
regression
line
accurately
predicts
height
from
age.
AP2.15
An
agronomist
wants
to
test
three
different
types
of
fertilizer
(A,
B,
and
C)
on
the
yield
of
a
new
variety
of
wheat.
The
yield
will
be
measured
in
bushels
per
acre.
Six
1-acre
plots
of
land
were
randomly
assigned
to
each
of
the
three
fertilizers.
The
treatment,
experimental
unit,
and
response
variable
are,
respectively,
a.
a
specific
fertilizer,
bushels
per
acre,
a
plot
of
land.
b.
variety
of
wheat,
bushels
per
acre,
a
specific
fertilizer.
c.
variety
of
wheat,
a
plot
of
land,
wheat
yield.
d.
a
specific
fertilizer,
a
plot
of
land,
wheat
yield.
e.
a
specific
fertilizer,
the
agronomist,
wheat
yield.
AP2.16
According
to
the
U.S.
Census,
the
proportion
of
adults
in
a
certain
county
who
owned
their
own
home
was
0.71.
An
SRS
of
100
adults
in
a
certain
section
of
the
county
found
that
65
owned
their
home.
Which
one
of
the
following
represents
the
approximate
probability
of
obtaining
a
sample
of
100
adults
in
which
65
or
fewer
own
their
home,
assuming
that
this
section
of
the
county
has
the
same
overall
proportion
of
adults
who
own
their
home
as
does
the
entire
county?
a.
(16050)
(0.71)%(0.29)*
b.
(1605O>
(0.29)%(0.71)*
.
p
(z
0.65
—
0.71
'
~
[(0.71)
(0.29)
\
100
i
P
(z
0.65
—
0.71
'
~
/(0.65)
(0.35)
\
100
(
\
.
065071
=
(0.71)
(0.29)
\
Vo
AP2.17
Which
one
of
the
following
would
be
a
correct
interpretation
if
you
have
a
z-
score
of
+2.0
on
an
exam?
a.
It
means
that
you
missed
two
questions
on
the
exam.
b.
It
means
that
you
got
twice
as
many
questions
correct
as
the
average
student.
c.
It
means
that
your
grade
was
2
points
higher
than
the
mean
grade
on
this
exam.
d.
It
means
that
your
grade
was
in
the
upper
2%
of
all
grades
on
this
exam.
e.
It
means
that
your
grade
is
2
standard
deviations
above
the
mean
for
this
exam.
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AP2.18
Records
from
a
dairy
farm
yielded
the
following
information
on
the
number
of
male
and
female
calves
born
at
various
times
of
the
day.
Time
of
day
Day
Evening
Night
Total
Males
129
15
117
261
Gender
Females
118
18
116
252
Total
247
33
233
513
What
is
the
probability
that
a
randomly
selected
calf
was
born
in
the
night
or
was
a
female?
369
513
485
513
116
513
116
|
252
116
'
233
AP2.19
When
people
order
books
from
a
popular
online source,
they
are
shipped
in
boxes.
Suppose
that the
mean
weight
of
the
boxes
is
1.5
pounds
with
a
standard
deviation
of
0.3
pound,
the
mean
weight
of
the
packing
material
is
0.5
pound
with
a
standard
deviation
of
0.1
pound,
and
the
mean
weight
of
the
books
shipped
is
12
pounds
with
a
standard
deviation
of
3
pounds.
Assuming
that
the
weights
are
independent,
what
is
the
standard
deviation
of
the
total
weight
of
the
boxes
that
are
shipped
from
this
source?
a.1.84
b.2.60
c.3.02
d.3.40
e.9.10
a.
b.
€
AP2.20
A
grocery
chain
runs
a
prize
game
by
giving
each
customer
a
ticket
that
may
win
a
prize
when
the
box
is
scratched
off.
Printed
on
the
ticket
is
a
dollar
value
($500,
$100,
$25)
or
the
statement
“This
ticket
is
not
a
winner.”
Monetary
prizes
can
be
redeemed
for
groceries
at
the
store.
Here
is
the
probability
distribution
of
the
amount
won
on
a
randomly
selected
ticket:
Amount
won
$500
$100
$25
$0
Probability
0.01
0.05
0.20
0.74
Which
of
the
following
are
the
mean
and
standard
deviation,
respectively,
of
the
winnings?
a.
$15.00,
$2900.00
b.
$15.00,
$53.85
c.
$15.00,
$26.93
d.
$156.25,
$53.85
e.
$156.25,
$26.93
AP2.21
A
large
company
is
interested
in
improving
the
efficiency
of
its
customer
service
and
decides
to
examine
the
length
of
the
business
phone
calls
made
to
clients
by
its
sales
staff.
Here
is
a
cumulative
relative
frequency
graph
from
data
collected
over
the
past
year.
According
to
the
graph,
the
shortest
80%
of
calls
will
take
how
long
to
complete?
a.
Less
than
10
minutes
b.
At
least
10
minutes
c.
Exactly
10
minutes
d.
At
least
5.5
minutes
e.
Less
than
5.5
minutes
100
80
—
&
40
20
0
-
Length
of
phone
call
(min)
Starnes
&
Tabor,
The
Practice
of
Statistics,
6e,
©
2018
Bedford,
Freeman
&
Worth
High
School
Publishers
Section
lI:
Free
Response
Show
all
your
work.
Indicate
clearly
the
methods
you
use,
because
you
will be
graded
on
the
correctness
of
your
methods
as
well
as
on
the
accuracy
and
completeness
of
your
results
and
explanations.
AP2.22
A
health
worker
is
interested
in
determining
if
omega-3
fish
oil
can
help
reduce
cholesterol
in
adults.
She
obtains
permission
to
examine
the
health
records
of
200
people
in
a
large
medical
clinic
and
classifies
them
according
to
whether
or
not
they
take
omega-3
fish
oil.
She
also
obtains
their
latest
cholesterol
readings
and
finds
that
the
mean
cholesterol
reading
for
those
who
are
taking
omega-3
fish
oil
is
18
points
less
than
the
mean
for
the
group
not
taking
omega-3
fish
oil.
a.
Is
this
an
observational
study
or
an
experiment?
Justify
your
answer.
b.
Explain
the
concept
of
confounding
in
the
context
of
this
study and
give
one
example
of
a
variable
that
could
be
confounded
with
whether
or
not
people
take
omega-3
fish
oil.
c.
Researchers
find
that
the
18-point
difference
in
the
mean
cholesterol
readings
of
the
two
groups
is
statistically
significant.
Can
they
conclude
that
omega-3
fish
oil
is
the
cause?
Why
or
why
not?
AP2.23
The
scatterplot
shows
the
relationship
between
the
number
of
yards
allowed
by
teams
in
the
National
Football
League
and
the
number
of
wins
for
that
team
in
a
recent
season,
along
with
the
least-squares
regression
line.
Computer
output
is
also
provided.
Term
Coef
SE
Coef
T-Value
P-Value
Constant
25.66
5.37
4.78
0.000
Yards
allowed
-0.003131
0.000948
-3.30
0.002
S
=
2.65358
R-Sq
=
26.65%
R-Sqg(adj)
=
24.21%
I
I
I
I
I
4500
5000
5500
6000
6500
7000
Yards
allowed
Starnes
&
Tabor,
The Practice
of
Statistics,
6e,
©
2018
Bedford,
Freeman
&
Worth
High
School
Publishers
a.
State
the
equation
of
the
least-squares
regression
line.
Define
any
variables
you
use.
b.
Calculate
and
interpret
the
residual
for
the
Seattle
Seahawks,
who
allowed
4668
yards
and
won
10
games.
c.
The
Carolina
Panthers
allowed
5167
yards
and
won
15
games.
What
effect
does
the
point
representing
the
Panthers
have
on
the
equation
of
the
least-
squares
regression
line?
Explain.
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AP2.24
Every
17
years,
swarms
of
cicadas
emerge
from
the
ground
in
the
eastern
United
States,
live
for
about
six
weeks,
and
then
die.
(There
are
several
different
“broods,”
so
we
experience
cicada
eruptions
more
often
than
every
17
years.)
There
are
so
many
cicadas
that
their
dead
bodies
can
serve
as
fertilizer
and
increase
plant
growth.
In
a
study,
a
researcher
added
10
dead
cicadas
under
39
randomly
selected
plants
in
a
natural
plot
of
American
bellflowers
on
the
forest
floor,
leaving
other
plants
undisturbed.
One
of
the
response
variables
measured
was
the
size
of
seeds
produced
by
the
plants.
Here
are
the
boxplots
and
summary
statistics
of
seed
mass
(in
milligrams)
for
39
cicada
plants
and
33
undisturbed
(control)
plants:
n
Minimum
Q¢
Median
Q3
Maximum
Cicada
plants
39
0417
022
025
0.28
0.35
Control
plants
33
0.14
019
025
0.26
0.29
Cicada
_
CD
plants
Control
_|
plants
[
I]
T
T
T
T
T
0.15
0.20
0.25
0.30
0.35
Seed
mass
(mg)
Starnes
&
Tabor,
The
Practice
of
Statistics,
6e,
©
2018
Bedford,
Freeman
&
Worth
High
School
Publishers
a.
Write
a
few
sentences
comparing
the
distributions
of
seed
mass
for
the
two
groups
of
plants.
b.
Based
on
the
graphical
displays,
which
distribution
likely
has
the
larger
mean?
Justify
your
answer.
c.
Explain
the
purpose
of
the
random
assignment
in
this
study.
d.
Name
one
benefit
and one
drawback
of
only
using
American
bellflowers
in
the
study.
AP2.25
In
a
city
library,
the
mean
number
of
pages
in
a
novel
is
525
with
a
standard
deviation
of
200.
Furthermore,
30%
of
the
novels
have
fewer
than
400
pages.
Suppose
that
you
randomly
select
50
novels
from
the
library.
a.
What
is
the
probability
that
the
average
number
of
pages
in
the
sample
is
less
than
5007
b.
What
is
the
probability
that
at
least
20
of
the
novels
have
fewer
than
400
pages?
Answers
to
Cumulative
AP®
Practice
Test
2
AP2.1a
AP2.2d
AP23e
AP24Db
AP25c
AP2.6d
AP2.7
c
AP28
a
AP29d
AP2.10c
AP2.11b
AP2.12c
AP2.13a
AP2.14c
AP2.15d
AP2.16
c
AP2.17
e
AP2.18
a
AP2.19
c
AP2.20Db
AP2.21
a
AP2.22
(a)
This
is
an
observational
study.
Subjects
were
not
assigned
to
take
(or
not
take)
fish
oil.
(b)
Two
variables
are
confounded
when
their
effects
on
the
cholesterol
level
cannot
be
distinguished
from
one
another.
For
example,
people
who
take
omega-3
fish
oil
might
also
be
more
health
conscious
in
general
and
do
other
things
such
as
eat
more
healthfully
or
exercise
more.
If
eating
more
healthfully
or
exercising
more
lowers
cholesterol,
researchers
would
not
know
whether
it
was
the
omega-3
fish
oil
or
the
more
healthy
food
consumption
or
exercise
that
lowered
cholesterol.
(¢)
No;
this
wasn’t
an
experiment
and
taking
fish
oil
is
possibly
confounded
with
other
good
habits,
such
as
healthful
eating
and
exercise.
AP2.23
(a)
y
=
25.66
—
0.003131z,
where
¢
is
the
predicted
number
of
wins
and
x
is
the
number
of
yards
allowed.
(b)
§
=
25.66
—
0.003131(4668)
=
11.04
wins.
The
residual
=
10
—11.04
=—1.04
wins.
The
actual
number
of
Seattle
Seahawk
wins
was
1.04
less
than
the
number
of
wins
predicted
by
the
regression
line
with
x
=
4668
yards
allowed.
(c)
Because
the
Carolina
Panthers
allowed
fewer
yards
than
average
and
also
had
more
wins
than
average,
this
point
will
increase
the
steepness
of
the
negative
slope
of
the
least-squares
regression
line
(make
it
more
negative)
and
increase
the
y
intercept
of
the
least-squares
regression
line.
AP2.24
(a)
The
distribution
of
seed
mass
for
the
cicada
plants
is
roughly
symmetric,
whereas
that
for
the
control
plants
is
skewed
to
the
left.
Neither
group
had
any
outliers.
The
median
seed
mass
is
the
same
for
both
groups
(median
=
0.25).
The
cicada
plants
had
a
larger
range
in
seed
mass,
but
the
control
plants
had
a
larger
IQR.
(b)
The
distribution
of
seed
mass
for
the
cicada
plants
is
roughly
symmetric,
which
suggests
that the
mean
should
be
about
the
same
as
the
median.
However,
the
distribution
of
seed
mass
for
the
control
plants
is
skewed
to
the
left,
which
will
pull
the
mean
of
this
distribution
below
its
median
toward
the
smaller
values.
Because
the
medians
of
both
distributions
are
equal,
the
mean
for
the
cicada
plants
is
likely
greater
than
the
mean
for
the
control
plants.
(¢)
The
purpose
of
the
random
assignment
is
to
create
two
groups
of
plants
that
are
roughly
equivalent
at
the
beginning
of
the
experiment.
(d)
A
benefit
of
using
only
American
bellflowers
is
that the
researchers
may
then
control
a
source
of
variability.
Different
types
of
flowers
will
have
different
seed
masses,
making
the
response
more
variable
if
other
types
of
plants
were
used.
A
drawback
to
only
using
American
bellflowers
is
that
we
can’t
make
inferences
about
the
effect
of
cicadas
on
other
types
of
plants,
because
other
plants
may
respond
differently
to
cicadas.
AP2.25
(a)
Because
the
sample
size
is
large
(n
=
50 >
30),
the
distribution
of
Z
is
approximately
Normal
with
puz
=
p
=
525
pages.
Because
n
=
50
is
less
than
10%
of
all
&=
=
%
=
28.28
pages.
We
want
to
find
P(Z
<
500).
(i)
z=
—0.88;
P(z
<
—0.88)=0.1894
(ii)
P(z
<
500)
=
normalcdf(lower:
—
1000,
upper:
500,
mean:
525,
SD:
28.28)
=
0.1883.
There
is
a
0.1883
probability
that the
average
number
of
pages
in
the
sample
is
less
than
500.
(b)
X
is
a
binomial
random
variable
with
n»
=
50
and
p
=
0.30.
We
want
to
find
P(X
>
20).
P(X
>
20)
=
1
—
binomcdf(trials:
50,
p:
0.30,
value:
19)
=
1
—
0.9152
=
0.0848. There
is
a
0.0848
probability
of
selecting
at
least
20
novels
that
have
fewer
than
400
pages.
novels
in
the
library,
oz
=
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