?JJ
‘Aj
AP Statistics-Ern 7/8 (C)
Nan”
Period
)
Accordmg to the DuPont 2012 Global Automotive Color
Popularity Report. 23% ofall cars
inifat ired Ln 21i I’ u crc GUL in a random
smpk. ot 100 cars parked in iongterm p irking it
Philadelphia International Airport, 19% of the cars were
white. \Vhich of the following statements
is trne?
(a) I 9% and 23% are parameters, 100 is a statistic.
b) 23% is a parameter, 19% is a statistic.
(c) 23% is a statistic, 19% is a parameter.
(d) 19% and 23% are statistics, 100 is neither a paramete
r nor a statistic.
(e) 19%. 23%, and 100 are all statistics.
2, The best statistic for estimating a parameter has which
of the following characteristics?
(a) Low bias, high variability.
(h) High bias, high variability.
(c) Low bias. Since a statistic should always equal the
parameter it is estimating, there should be
no variability.
Low bias, low variability.
(e) High bias, low variability.
&
————
‘ The chipmunk popu
lation in a certain area is known to have a mean weight
of 84 gm and a
standard deviation of 18 gm. A wildlife biologist weighs
9 chipmunks that have been caught in
live traps before releasing them. Which of the follow
ing best describes what we know about the
sampling distribution of means for the biologist’s sample
? [Assume the 9 chipmunks represent a
simple random sample of chipmunks in the area.]
(a) u = 84; u = IS; distribution approximately Norma
l
= 84;
= 6; shape of distribution unkno
wn
c) p = 84; u = 6: disthbumion approximatcly Norma
l
(d) u = 84; ounknown; distribution approximately
Normal
(d) p = 84; Ur unknowp; shape of distribution
unlcpown
-
—
I
A census of the labor force in a large metr
opolitan area found that the time it takes for
people to
conunute to work has a mean of 20.5 minu
tes and a standard deviation of 15.4 minutes.
Which one
of the following represents the probability that
a random sample of 30 people have a mean
commute tune that is greater than 25 minute
s?
—
20 a
—
2a
(a) Pz>—-—-—
L.3
CO
/
25-2ft5
z>———-—
15.4
1
(
‘
P
(C)
1
—‘0
l.4
/
(c P
20.5—24’
P z>-—————
15.4
A >i
cBF i’.D:hers
fhe tr.tce 1
atis ftr Ai’,
—‘0
15.4
-
_____
5.
(1
to estimate tiC mean SA[ score for 3 population of students u h a 90’ cenfidence
interval Assume Unit the population standard deviation is r 100. If you
ant the Inargin of
error to he no more than 10, you will need a minimum sample size of approximatel
y
(:1) 17
b 38
/
/
f
(o 271
0
IoU Want
‘
.
Ic) 1646
£
U.
/
In order to use the tormul
—
i
—
U
=
—
to calLul ite the standard dc nit ion of the ampl
‘
n
distribution of the sample mean, which of the following
conditions must be met?
I.
n30
II. The population’s distribution is approximately
Normal.
Ill. The sample size is less than 10% of the popula
tion size.
(a) I only
(h) 11 only
ifi
(d) Ill and either I or 11
(e) All three conditions must be meç
/
/
-.
/
I.)
-
—r
1
.‘
A 95% confidence interval forp, the proportion of allioppers
cookies, was found to be (0.236, 0.282).
likf
at a large
7:. 9
grocery store who purchase
7) The point estimate and än or error for this interval are:
(a) Point estimate = 0.236; Margin of error = 0.282
(b) Point estimate = 0,236; Margin or error = 0.046
(c) Point estimate unknown; Margin of error = 0.023
D,Point estimate = 0.259; Margin or error = 0.046
c(9oint estimate 0.259; Margin of error 0.023
/23
1LE
/0Lit ‘
(.dkI
Which of the fillowing is a correct statement?
J
(a) About 95% of the shoppers have between a 23.6% and a 28.2% chance of purcha
sing cookies.
(b) There is a 95% prbilfty that the sample proportion lies between 0.236 and 0.282.
(c) If a second samfe was taken, there is a 95% chance that
its confidence interval would contain
0.25.
(dLFhis confidence interval indicates that more than 25% of shoppers buy cookies.
e)..We are reasonably certain the true proportion ot’shoppcrs who purchase
cookies s between
24% and 28%.
.4’
1)
Which of the foI1o ini would be true about a )s
1 confidence interval constructed usm the same
data?
(a) The interval would he wider, because the standard error would be lareer.
m
(h) ihc interval would he narrower, because the standard error would be smaller.
.Tbe interval would he sidr because the critical z ou1d be Iargr
(d The interval would he narrower, because the critical z would smal!er.
Ic) The interval would be about the same width, because the standard error would
be smaller, hut
the critical ; noud be Lraer.
1
LkJL/t
e
i’
1’
I)
a A friend has offered to play a game with you that involves flipping a coin that he has provided.
Since a flip of heads will be to his advantage, you want to test the coin for fairness before you
begin to play. Your friend is willing to let you flip the coin 50 times to determine if the probab
ility
of getting heads is actually 0.50, as it should be if the coin is Ibir.
(a) Assume for the moment that the coin is fair. If is the proportion of heads in 50 flips
of the
fr
coin, what are the ipeanpnd standard deviation of the sampling distribution oft?
4 tn c—h.-
two
I
(fl
ioCc)
;;m
Irz
‘I
.‘
(b) Explain why you can use the formula for the standard deviation of
ft in this setting.
c?fT 1*1
(34
css.-
a,.i.tt.--,...
/4’
(c) You flip the coin 50 times and get 30 heads. Do you risk insulting your friend
by refusing to
play with his coin? Supped your answer witht appropriate probability calculation.
‘/4g
p.r-5
Step I (s)j w4’t Fo
>
tã
—
4.,
£Mtyzct’.;.w
CP&Qj1
Z”-’ y’
p(z4mj-r1’Ga7fsti)
.5”
¶3Lap3
‘
—,
4/’4
4
rLW
J!r
3
tj
)roL
S
O7($f
t.,1 45)(.&’).>’
II)
—-
.-
.-
.
T’
(1
,
.,
1
.
4
ft?
:
.
-.
CBflV.Pubtkh.u
3,’)
f)4’
I EEO
$
?‘
..
4.244
tcrc4
&_i
/.tt .‘_4
yl) /9
;‘
I
.2
HC
7 ‘.;?
. The ?ncdçe of Stzthdcs toe AP. Sc
0
/
I
12. Political parties rely hcaviv upon polling
to measure their support in the electorate. In
a country
with ftmr major political parties, a poll is cond
ucted and the Coffee Party is supported by
435 of
the 11 <3 randomlvseleced oters ho
were polled
ia) Cunstrut and interprt a
support the Lotlee Pany.
1
7
I
I
contidenee interval to st1mate the
,r
/
,._F(
I
J
J
I
If S
f
/
/
I
d
fr
-i
-
/,J
uho
E
—
—
7,
••i_)
96
‘I
—
—‘
F
F
F
/
/
/
,I
4
4
_
j1
y
IJ
-(
/)—
I
I
IF
J L
0
(
—I-----
J_
A
-
I
—I
-
YE I
)
IS.
) 7
1
a
vi
((
—fS) ),‘)
I! f 3
)
c—
_‘
‘i’-’’?
‘
I
‘
4
7
—
-
ii
7
I
:-
_f
( 3 3/
03 ‘2
—
‘
.
I
I
F
/ -
i-
:
r
(b) The Coffee Party leaders claim that they have
the support of 42% of the electorate. Does
your
interval in part (a) suggest that this claim
is plausible? Explain your reasoning.
7
/
.—
/
y- /
i:. 3/_;
/. )/
/
45/
4’
S.f /
.
Ic) The random sample was actually 1200 peop
le, hut 17 people never responded. Does this
change
‘our anster to part (b> Fplain hv or why
not
F
I
S.AJ
04’
1
4
I
I F,;
/
Ij
i-rccc cu 5aucuc Or AP. 51e
S.I
/1
—
1
•
I 2, There are many ways to measure the reading ahigv of childre
n. Research designed to impro’:e
reading performance is dependent on good nv’asures uf the outcom
e. One frequently used test is
the DRP, or Degree of Reading Power Ares ircher supecrs
that the mean %core a of all third—
grackrs in H
is dltlLrcnt rrom the uauon iiu ‘ad ich is 32 To tst
her
uspiuon ‘hL dn1Inlster% the DRP to in RS
jH.nnLo Eoim h iJ-grid. ‘ttfdLnt The
distrthution of scores is summarized in the Miniab output below:
.
MIN
STDEV
—
SEMEAN
MIN
QI
MEDIAN
QI
MAX
-—
(a) Construct a 90% confidence interval to estimate the mean DRP
score in Flenrico County
Schools.
/
-
/
2 11
rn,
,p
/
t
-
.
‘
/
I
er
i
j}
I’
2
—
tf9
—
I
—
-)LI
j
5
—.
.
I
—
4
1,
(
_..
4)
(3
.+-
5
:;
)
1
N
2
t
L
4-
5rv/
rj
2
T
-
-
L.
:.
‘s
..
.
/...
4.
/
5
.fD.
(b) Use the confidence interval you constructed in (a) to
comment on whether you agree with the
researcher’s claim. Explain your reasoning clearly.
5
-
(
I’)
/
r’
—
/ ç
*/
a55 s’
‘