Math 140
Prof Silva
Mod 8, 9 Review
Disclaimer: Anything done in class, homework, or in OLI is fair game for the exam, so
please make sure to study everything! This is just meant as a reminder of the topics we
covered, it is not what the test will necessarily look or be like.
Topics:
• Confidence intervals for proportions (1 and 2 proportions)
• Finding error, critical values, and CI's
• Hypothesis testing for proportions (1 and 2 proportion)
• Inferences about one and two proportions
Practice Questions: Show all work
1. In a recent survey of 4276 randomly selected households showed that 94% of them
had telephones. Using these results, construct a 99% confidence interval estimate
of the true proportion of households with telephones using PANIC or PHANTOMS,
whichever applies. Assume the assumptions are met.
A~
As.sV.P>1ff'1oi1s
to be
tire
ct55(1t111@d
/\
Lio/ q
.
p -= (?, q lf
:::
4 :2 76
s+«t~C{ ,~ rroblervt
a..s ~e.+
1
2. In a Gallup poll, 1025 randomly selected adults were surveyed and 29% of them said
that they used the Internet for shopping at least a few times a year.
a) Find a 90% confidence interval estimate of the percentage of adults who
use the Internet for shopping using the formula, (this means no Minitab!).
You do not need to use PANIC/PHANTOMS for this.
er:-
p+
i?c~
~
+ I. 6L/5
(J, 2 Cf
<£:~~>;_0;!'1
o, :;2. q ± I. 6 L/ fr ( 0,
0.:2..q +
O I 4;i..)
0,,0-=:l3Lf
b) What is the point estimate?
c) What is the Margin of Error?
[E:::
o.o;,3Li ]
d) What is the Standard Error?
/sE - o,01L, 2]
2
3. A survey of 300 union members in New York State reveals that 112 favor the
Republican candidate for governor. Construct a 97% confidence interval for the
true population proportion of all New York State union members who favor the
Republican candidate using PANIC or PHANTOMS, whichever applies .
./'\p P~
I
A~
f op id ei +·, o '"I
f r ofo r-+ ,o ..-,
Rctndorvi? No+ s+c-t+e.o/ ..
an cl
f
t'o cee
np= 300(0,,373)=
= B~
n :J73
300
v ...
tj; =
l-
p' :=:; 0,
W'./l-Cf5S'ln'le .~·v.-l'v-<y·
J
6 -;;i. 7
w,r:s randtJr'v)
w 1 +"1 cez ""+10 '"'
11=<:>to'-"
n~-=: 300(&,6:J?)= l8'8'?1V ./
N .,; I
.I7
p1"opOt"i-tOt1
CI
(0,313)0Pl.f34)
of{
0,313.C:: p<0,43Lf
C-,. We C<v~ q 7% co.,,,.-f:'id-evt+ -t.J)C<+ -+~€"
-1-v-ue poptA/CA+ ~;,,
f'l"opo,+ 1 OV> o-( _cdl New Yov-k S+4-te un1011 meM bev.S vvho
.fa.ver +he Re.p«bl1can C'ir>ohda-t~ +o·.'' !}ov e.;. -n.o r is Jbe+vV'e-ev1
CJ. 313 and 0, 43Lf.
4. Given:
Ho: The dog does not bite
H1: The dog bites
a. Write a conclusion that would result from a type I error.
Wtc vie.· e<.-t ti-l,~+ -the do'} does no+ bi+eJ so i.M€_ -1-I-\,;,, k
1
·
wi-\tvJ J,~ -fctc+ -th~
Jo:} doe.sn -t b',t,e C c::n-H ( us10,.,."W ~
~ht> do9 b;+es
+ b 1 H€ ' 1
<J<!..
clon 4
1
.,
b. Write a conclusion that would result from a type II error.
'wl?. {q', I
-<;o V-ej--c.c+ t:h.C{+ th-e ()03 oltJes r10+ b/+e.J so v..1€
+h;vik
-k;h e clo:} cloe.5 Vi o+ b 1'+. e VJ'1 et) ,_·n -f.et c+ "'=~-e d O!J does b t'+-e .
Co v, c / ~ s i·c,"): We J€ i "
b ;tfe fl.
5. Test the_claim that the proportion of drowning deaths of children attributable to
beaches 1s more than 25'¾o. A sampIe of 61 5 drownmg
. deaths showed that 30'¾0 of
them were attributable to beaches. Use a= 0.01. Use PANIC or PHANTOMS
18' 5'
whichever applies. -~
'
P = 0,"30=
­
615"
·H~ Ha= p ~= o. ~!:>-e H,: p>o.~5" A~
f{cmdotJ-1?
np:::.(o.;ii;)(6t5)%15"'-l2IV,/ t-l'S.SurYte
Vl
s+a+-ed -to be vondom_ \;V'< vv;tt_
1+ v,Nt5 rondo,'>') cu,J proc@ed \},ll+h
Stiwip{e nof
Gy =(o. 7S)(6i!i)= 46 f 2il)./ Ca u+io n4
T-:,
0 ,--:,
=c=~.91
p--va Iue = o.. oo::i.. <. 0~ I
S ~ The,e
C(a;,n
·,.s su-f-f,c,€o11+ ev.,dev1c<c.
+iict-f t~~
drovJ~1V1Cj dea+Vl5
bect ch e..s t S
Mo re
--to supptu+ -;;-he.
-hrl-4€'
fopc,d~ttOr} propol-tt<Jt1 t:rf a/(
o-F
c'1ildve"1 a++v1bu+c.lbl~ -to
·-th ~V> 0,. ::i. 5 ~
4
6. The Harris Poll conducted a survey in which they asked "How many tattoos do you
currently have on your body?" Of the 1,205 males surveyed, 181 responded that
they had at least one tattoo. Of the 1,097 females surveyed, 143 responded that
they had at least one tattoo. USE PANIC or PHANTOMS, whichever applies for the
following
a. At level of significance of 0.05, is the proportion of females that have at
least one tattoo different from the proportion of males that have at least
one tattoo.
·P; =- ( 8" 1 -= 0.15"
f; = _lj}
rM
IF
1:205'
A
0-!:,
q;M
= O.. o
H- 7
1-1-o '.
..-!'\
'}p
-o
!0'17- ,I
3
=- &. S--7
Prvi = PF
HA : PM ·=f::. PF
b. Now find an estimate for the difference in population proportions between
males and females that at least one tattoo. That is, find the confidence
interval for the difference between males and females who have at least one
tattoo
p~
;z
A 4 Same
N
p,opor-f;o,1s
pop1.1./CI-f1c,t")
aloc;ive
Cl.S
'::?'f''l'C)fOf'+tO~'\
7
I -=, ( - {) rO OCf I
C _.....:, W e
o-f:.
.re..
t< v
c-r
-...1...
be
v
"10
\I\) Ch'Y'I
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Of\
(),
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.,
-o•0 0 Cf <. Ptyt - PF < (} r O l/ 8'
.
.
0
.
,t
. h~ -f r'IA € p opu. ( C< -f t tlr} f' Ii' Of'CN -f-1th1
q5-% C(l~'l-(,Jevl+ -c ,a+ ~+,·e
OOCf less t-htH? -t-o
- .
f q .s+ 0 1>1 ,e -1-C< ;- ,,; (/ :;; v.,
L-/ 8)
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+"',
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r, en/
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.
..s-t..S -ti,C(+ -tv1ev'e 1 /
1 5 S.iA9 ~p:
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.•
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7. A stu9y was conducted to assess the effects that occur when children are exposed
to cocaine before birth. Children were tested at age 4 for object assembly skills.
Of the 190 children born to cocaine users, 139 of them passed the test. Of the 186
children not exposed to cocaine, 153 of the children passed the test. USE PANIC
1,;~ :: (),73:;.
or PHANTOMS, whichever applies. Use a= 0.01 for both parts.
a. Test the claim that prenatal cocaine exposure is associated with lower ;
cl,,. - 0, :.26 if'
scores of four year-old children on the test of object assembly.
c _
:1 pop,.d&(·f; 0111 f•Df'Ot,..+•ot'/.S (Pi'·f{e,re.-1<.e)
~-=0_,8'..2.3
It~
Ho; Pc.= PN
f::
it=
H;:
A-,
PN
f<Q.,Jo,,,,.,? Nd· 5tcded1 w·, It q$,Si;1;,v1e
flc.
i.3"1 ~IV n,J f'rJ;. /5'3 ">- f(J
i:
f1c
N~
ft ..c..
tfw -~
'tc. :: SI .:!"IV
;2 f•"Opt't"-f
nN
'"'"1
1N = 33 .':~ to
-f~>+
D{
> 0 .01
Ho
s -~ The,,-e
tn
~s
5u-f+;c:: i:~V\+
t~ ~. -f-v u ~ pv·f)p»CJ 1-f, 'H'\ hctve lc1.~.rer or /e.s.s YlO~"l- Cc.'7'cc?IY/E'
user.>,
b. Find the confidence interval for the difference in pass rates between those
&,
17 7