assigment individu(azie).doc
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SMS 3113
STATISTICAL LABORATORY
Semester 2 Sessions 2012/2013
ASSIGNMENT 4:
Individual Assignment
LECTURER: R! NOR A"A# SAMAT
N$me M$tri% No!
A&e'$( Binti Is$ 200)103*02)
INSTRUCTIONS:
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1! T(is Assi+nment ,onsists o- T#REE
.estions! Anser ALL UESTIONS!
2! S(o 'or or! M$rs m$' e
e,te -or in,om56ete or!
3! Yo nee to t'5e 'or $nsers!
4! It is 'or res5onsii6it' to m$e sre
t($t t(is $ssi+nment e 'or ori+in$6
or!
7! 86e$se smit t(is $ssi+nment to
r!$&$(s$m$t9'$(oo!,om e-ore 11 $m
on 23rA5ri6 2013!
*! T(e -66 m$r -or t(is Assi+nment is
100 $n t(is $ssi+nment ,ontrites 20;
to 'or o??????????????
UESTION 1
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A major oil company developed a petrol additive that was
supposed to increase engine efficiency. Twenty-two cars were
test driven both with and without the additive, and the number of
kilometres per litre was recorded. Whether the car was automatic
or manual was also recorded and coded as ! manual and " !automatic.
#uring an earlier trial twenty-two cars were test driven using the
additive. The mean number of kilometres per litre was $.%.
&ou are interested in addressing the following 'uestions(
$@Are t(e ,$rs in t(e 5resent tri$6 rnnin+ more
e--i,ient6' t($n t(ose in t(e e$r6ier tri$6
)$ ( *+$.%
) ( * $.%claim
using /0//
One-Sample Statistics
N Mean Std. Deviation Std. Error Mean
withadd 22 13.86 2.748 .586
One-Sample Test
Test Value 1!.5
t d" Si#. $2%tailed& Mean Di""eren'e
(5) *on"iden'e +nterval o" the
Di""eren'e
,ower -er
withadd 5.741 21 .!!! 3.364 2.15 4.58
" using 1I2ITA3
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One-Sample T: withadd
Test of mu = 10.5 vs not = 10.5
Variable N Mean StDev SE Mean 95% CI T
!it"a## $$ 1.&'' $.()&1 0.5&59 *1$.')5$+ 15.0&$1, 5.() 0.000
4 using 56758
t-Test( 0aired Two /ample for 1eans
withadd
test
mean
1ean4.9:4:4
:4: $.%
;ariance9
$%" $
?bservations "" ""
0earson 7orrelation @#I;$B)ypothesiCed 1ean#ifference $.%
df "
t /tat
-".9$4"
4"9
0TD!t one-tail
".
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The cars in the present trial is running more efficiently than
those in the earlier trial because the mean is greater than $.%.
@oes en+ine e--i,ien,' im5ro
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4 using 56758
tTest: 8$ire To S$m56e -or Me$ns
$ri$6e 1 $ri$6e 2
Me$n 9.% 4.9:4:4:4:$ri$n,e .=$>
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,@ oes en+ine e--i,ien,' it( $n it(ot t(e $iti
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Estimate for #ifferene/ -5.'')
95% CI for #ifferene/ *-(.$$55 -.501(),
T-Test of #ifferene = 0 *vs not =,/ T-Value = -5.&$ -Value = 0.000 D2 =
)
4 using 56758
t-Test: Two-Sample Assuming Equal a!iances
Variable 1 Variable 2
"ean #$% 1&$#'&'&'&'
a!iance 11$110% $%%1*#0%2
+,se!ations 22 22
.oole/ a!iance $&&%*#
Hpotesie/ "ean 3i44e!ence 0
/4 *2t Stat -%$#222
.(T5=t) one-tail &$%#E-0
t 6!itical one-tail 1$'#1%2
.(T5=t) two-tail $1'E-0
t 6!itical two-tail 2$01#0#2
At E ! $.$% ,p-alue = 0$00
DECISION:
Te .-alue is 0$00 wic is less tan 7 alue Tus8 we !e9ect H0$
CONCLUSION:
Te!e4o!e8 engine e44icienc wit an/ witout te a//itie /i44e! ,etween manual
an/ automatic ca!s
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UESTION 2
?ne hundred car drivers who were stopped by police for some
violation were also checked to see if they were wearing their seat
belts. The following table records the results of this survey.
e$rin+ se$t e6t Not e$rin+ se$t
e6t
Men 4> "
omen 4" 4
Test at ".%G significance level whether being a man or a woman
and wearing or not wearing a seat belt are related by using
statistical software.
Anser:
+ener se$te6t -re.en,'
4>
" "
" 4"
" " 4
)$ ! the two categorical variables are dependent
) ! the two categorical variables are related claim
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using 1I2ITA3
Tabulated statistics: GENDER; SEATE!T
3sin4 freuenies in 26E7
6o!s/ 8ENDE6 Columns/ SET:E;T
1 $ ll
1 ) $1 55
'.0 1&.(0 55.00
$ $ 1 )5
$9.(0 15.0 )5.00
ll '' ) 100
''.00 ).00 100.00
Cell Contents/ Count
E
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"ender # seatbelt $r%sstabulati%n
seatelt
Totalwear elt not wear elt
#ender en *ount 34 21 55
Ee'ted *ount 36.3 18.7 55.!
) within #ender 61.8) 38.2) 1!!.!)
) within seatelt 51.5) 61.8) 55.!)
) o" Total 34.!) 21.!) 55.!)
woen *ount 32 13 45
Ee'ted *ount 2(.7 15.3 45.!
) within #ender 71.1) 28.() 1!!.!)
) within seatelt 48.5) 38.2) 45.!)
) o" Total 32.!) 13.!) 45.!)
Total *ount 66 34 1!!
Ee'ted *ount 66.! 34.! 1!!.!
) within #ender 66.!) 34.!) 1!!.!)
) within seatelt 1!!.!) 1!!.!) 1!!.!)
) o" Total 66.!) 34.!) 1!!.!)
$hi-S&uare Tests
Value d"
s. Si#. $2%
sided&
Ea't Si#. $2%
sided&
Ea't Si#. $1%
sided&
/earson *hi%Suare .(52a 1 .32(
*ontinuit *orre'tion .583 1 .445
,ielihood 9atio .(5( 1 .327
isher0s Ea't Test .3(8 .223
,inear%%,inear sso'iation .(43 1 .332
N o" Valid *ases 1!!
a. ! 'ells $.!)& have ee'ted 'ount less than 5. The iniu ee'ted 'ount is 15.3!.
. *outed onl "or a 22 tale
from table ,
p-value! $.$4"=, E! $.$"%
ECISION:
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since p-value E, we do not reject )$
CONCLUSION:
so, the two categorical variables are dependent. Ten8 leel wete!
,eing a man o! a woman an/ wea!ing o! not wea!ing a seat ,elt a!e not !elate/$
UESTION 3
#iscuss the advantages and disadvantages of using 5Hcel, /0//
and 1initab in analysing statistical data. &our report must contain
the following information.
a Introduction to 1icrosoft 5Hcel, /0// and 1initab.
E%,e6 S8SS Minit$
5Hcel is the
spreadsheet program
created by 1icrosoft.
A powerfulspreadsheet that is
easy to use and
allows you to store,
manipulate,
analyCe, and
visualiCe data.
used "or surve authorin#
and deloent&: tet
analti's: statisti'al
analsis: and 'ollaoration
and deloent.
is concerned, pay
close attention to
how many decimal
places you allow in
each cell. If your
cell is too small,
the number will be
rounded up and its
possible it could be
radically different
from the number
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/0// J 1I2ITA3.
b Advantages and disadvantages of using 5Hcel, /0// and
1initab.#isadvantage(
E%,e6 S8SS Minit$ cannot miH
numbers with
letters in a cell.
does not have anundo option whenyou delete avariable.
default graphics
are poor and noteasily customiCableto make thembetter.
It is eHpensive.
There are oftencompatibility issueswith prior versions
time-consuming for
compleH
procedures.
Advantages(
E%,e6 S8SS Minit$
can use anyspreadsheetprogram foranalyCing data.
the instructionsgiven here arespecific.
is a versatileprogram presenton most computersat home and incomputer clusters.
very user friendly.
good for keeping
variables seperate
by category.
The range ofstatistical analysesthat 1initab canperform straightafter installation isnot as wide as inother packagessuch as /0//.
1initab has adynamic worksheetand loadmeasurementcolumn until >$$$.
easy to use, andoperates through
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an interface that isintuitive to anyonefamiliar with otherstatistics packages.
The result is more
accurate.
c 5Hample.
E%,e6:
tTest: 8$ire To S$m56e -or Me$ns
$ri$6e 1 $ri$6e 2
Me$n 9.% 4.9:4:4:4:$ri$n,e .=$>
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!it"a## $$ 1.&'' $.()&1 0.5&59
Differene $$ -5.'') $.9095 0.'191$
95% CI for mean #ifferene/ *-'.'511( -).0('10,
T-Test of mean #ifferene = 0 *vs not = 0,/ T-Value = -&.'' -Value = 0.000
d Keferences.
&ahoo answer
e)ow tech
http(office.microsoft.comen-$$web-apps-
helpintroduction-to-eHcel-web-app-)A$$4
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