Lqwhuqdwlrqdo Exvlqhvv Dgplqlvwudwlrq Wkh uvw txhvwlrq lv d pxowlsoh fkrlfh +pf, 2vkruw dqvzhu txhvwlrq1 \rx vkrxog dqvzhu
Yulmh Xqlyhuvlwhlw Dpvwhugdp wklv txhvwlrq rq d vhsdudwh vkhhw ri sdshu +kdqghg rxw dw wkh ehjlqqlqj, e| zulwlqj
grzq dw wkh surshu srvlwlrq wkh fruuhfw dqvzhu/ iru lqvwdqfh 4D06/ 4E05/1 1 L0 314567/
Idfxow| ri Hfrqrplfv dqg Exvlqhvv Dgplqlvwudwlrq hwf1 Dq| h{sodqdwlrqv zloo eh ljqruhg1
\rx vwduw zlwk d wrwdo ri Df fuhglwv/ iru hdfk zurqj pf dqvzhu |rx jhw d shqdow| ri
fuhglwv/ dqg iru hdfk vnlsshg pf dqvzhu |rx jhw d shqdow| ri 2 2 fuhglwv1 Iru wkh vkruw
dqvzhu txhvwlrqv |rx jhw d shqdow| ri 2 2 fuhglwv iru hdfk vnlsshg ru zurqj dqvzhu1 \rxu
H{dp= plqlpxp srvvleoh wrwdo vfruh rq wklv txhvwlrq lv 3 srlqwv1
Vwdwlvwlfv L
frgh 94875343
Gu1 M1P1 Vqhhn Txhvwlrq 4
Pdufk 59/ 533: 4 D,
D vfdwwhu gldjudp kdv ehhq fuhdwhg iru wzr qxphulfdo yduldeohv=
4;163053163 4,00
3,00
Wkh gxudwlrq ri wkh h{dp lv 2 krxuv> 2,00
Wklv h{dp frqvlvwv ri e txhvwlrqv rq b sdjhv> 1,00
Irupxodv dqg wdeohv duh surylghg vhsdudwho|1 \rx duh uhtxhvwhg qrw wr zulwh rq
0,00
wkhp dqg wr uhwxuq wkhp diwhuzdugv> -3,00 -2,00 -1,00 0,00 1,00 2,00 3,00
\rx fdq vfruh d pd{lpxp ri 433 fuhglwv> -1,00
Judghv zloo eh dqqrxqfhg rq Dsulo 2/ 533:> -2,00
Wkh h{dp pd| eh uhylhzhg rq Dsulo b> 533:1 H{dfw wlph dqg sodfh zloo eh dq0 Wkh olqhdu fruuhodwlrq frh!flhqw fruuhvsrqglqj wr wklv vfdwwhu gldjudp lv dssur{lpdwho|
qrxqfhg odwhu rq Eodfnerdug> htxdo wr=
4, =f
5, =f
6, f=S
Txhvwlrq 2d 2e 2f ed ee ef 7, f=f
Fuhglwv Df e D f . H f 8, nf=S
9, n=f
:, n =f
5
,4 E, 4 H,
Lq d vdpsoh rqh qgv wkh iroorzlqj ydoxhv= ib> H> D> > D> S> D> S> .j = Wkh vdpsoh vwdqgdug Iru wkh whvw Kf G Dff djdlqvw K G A Dff dqg edvhg rq d fhuwdlq lw lv irxqg wkdw
ghyldwlrq +xs wr wkh ghflpdo sodfhv dv vkrzq, lv dssur{lpdwho| htxdo wr= Kf vkrxog eh uhmhfwhg li { Dfb= Iurp d udqgrp vdpsoh lw lv irxqg wkdw { ' D21 E|
4, H=HHb wkh suredelolw| S'd E[ e
zh phdq wkh suredelolw| xqghu wkh dvvxpswlrq wkdw wkh wuxh
5, 2=HHb ydoxh ri lv d=
6, =.ff Wkh suredelolw| S'D2 E[ Dfb
7, e =.Df
4, lv wkh suredelolw| ri d cW|sh L huuru*
8, =Hf
5, lv S EcW|sh L huuru*
9, =2Df
6, lv wkh suredelolw| ri d cW|sh LL huuru* iru wkh ydoxh ' D2
:, S=2 S
7, lv S EcW|sh LL huuru* iru wkh ydoxh ' D2
;, qrqh ri wkh ydoxhv olvwhg deryh1
8, lv wkh srzhu ri wkh whvw iru ' D2
4 F, 9, lv wkh sydoxh ri wkh whvw
D qrupdoo| glvwulexwhg yduldeoh [ kdv phdq ' e dqg +xqnqrzq, vwdqgdug ghyldwlrq
= :, kdv qr vshfldo phdqlqj iru wklv whvwlqj sureohp1
Lw lv nqrzq wkdw S E[ S
' f=Hbee =
4 I,
Iru
rqh qgv
4, f ?
D frqwlqxrxv udqgrp yduldeoh [ lv xqlirupo| glvwulexwhg
[ lv ghqrwhg e| = Wkh suredelolw| S 2 [3 2 lv +xs wr 6 ghflpdo sodfhv, htxdo
ehwzhhq dqg = Wkh phdq ri
5, ?
2 2
6, 2 ?
2= wr
7, 2= ?
2=S 4, f=fff
8, 2=S ?
5, f=ff
9,
A 6, f=eff
:, qrw hqrxjk lqirupdwlrq lv jlyhq wr frpsxwh d ydoxh iru
= 7, f=Hff
8, f=bDe
4 G, 9, f=b..
D yduldeoh [ dqg d yduldeoh \ kdyh wkh iroorzlqj glvwulexwlrqv :, qrqh ri wkh ydoxhv vwdwhg deryh1
{ 2 e 4 J,
S E[ ' {
f= f=2 f= f=e Zklfk ri wkh iroorzlqj vwdwhphqwv derxw wkh phgldq ri d srsxodwlrq lv qrw wuxhB
dqg
| 2 e 4, Li wkh glvwulexwlrq lv v|pphwulf/ wkhq wkh phgldq lv htxdo wr wkh phdq1
S E\ ' |
f=e f= f=2 f= 5, Wkh phgldq lv htxdo wr T2 1
Iru wkh h{shfwhg ydoxhv H[ dqg H\ dqg iru wkh yduldqfhv @h E[
dqg @h E\
rqh kdv= 6, Wkh phgldq lv d phdvxuh ri orfdwlrq ri wkh glvwulexwlrq1
4, H[ ? H\ dqg @h E[
? @h E\
7, Li wkh glvwulexwlrq lv v|pphwulf dqg xqlprgdo/ wkhq wkh phgldq lv htxdo wr wkh
5, H[ ? H\ dqg @h E[
A @h E\
prgxv1
6, H[ A H\ dqg @h E[
? @h E\
8, Wkh phgldq lv pruh vhqvlwlyh wr rxwolhuv wkdq wkh phdq1
7, H[ A H\ dqg @h E[
A @h E\
8, H[ ' H\ dqg @h E[
9' @h E\
9, H[ 9' H\ dqg @h E[
' @h E\
:, H[ ' H\ dqg @h E[
' @h E\
6 7
,4 K, Vwhp iru wkh txhvwlrqv 4 O,0 S,
Wzr lqghshqghqw hyhqwv D dqg E hdfk kdyh d suredelolw| ri 2 = Wkh suredelolw| S ED ^ E
Vrph uhvxowv rq frvwv ri krwho urrpv iurp vdpsohv lq Qhz \run dqg Skrhql{ duh vkrzq
lv htxdo wr ehorz1 \rx pd| dvvxph wkdw krwho frvwv duh qrupdoo| glvwulexwhg1 Zh xvh wkh deeuhyldwlrq
4, f Q \ wr ghqrwh Qhz \ run dqg S k wr ghqrwh S krhql{= Whqwdpb533:pdu59bwwhvw41zpi
5, e
Group Statistics
6, 2
7, e Std. Std. Error
CITY N Mean Deviation Mean
8, Hotel Cost New York 21 180,5694 31,35939 6,84318
9, rwkhu wkdq vwdwhg deryh> Phoenix 15 160,2775 15,78583 4,07588
:, qrw hqrxjk lqirupdwlrq lv jlyhq wr frpsxwh wklv suredelolw|1
4 L, Independent Samples Test
D guloolqj frpsdq| kdv hvwlpdwhg d efI fkdqfh ri vwulnlqj rlo iru wkhlu qhz zhoo1 D
ghwdlohg whvw kdv ehhq vfkhgxohg iru pruh lqirupdwlrq1 Klvwrulfdoo|/ SfI ri vxffhvvixo Levene's Test for
zhoov kdyh kdg ghwdlohg whvwv/ dqg 2fI ri xqvxffhvvixo zhoov kdyh kdg ghwdlohg whvwv1 Equality of Variances t-test for Equality of Means
Vr/ li V ' cvxffhvvixo zhoo* dqg G ' cghwdlohg whvw*/ wkhq S EV
' f=e dqg S EGmV
' f=S
dqg S EGmV
' f=2
Sig. Mean Std. Error
Jlyhq wkdw wklv zhoo kdv ehhq vfkhgxohg iru d ghwdlohg whvw/ wkhq wkh suredelolw| wkdw wkh F Sig. t df (2-tailed) Difference Difference
zhoo zloo eh vxffhvvixo lv htxdo wr bbbbbb +qxphulfdo ydoxh/ 7 vljqlfdqw gljlwv,1 Hotel Cost Equal variances
,908 ,3472 **** ** ,0277 20,2918 8,82261
assumed
4 M, Equal variances
2,548 31,11 ,0160 20,2918 7,96505
not assumed
D srsxodwlrq frqvlvwv ri wkh ydoxhv i> 2> > = = = > 2bj = Dv fdq eh irxqg iurp iru lqvwdqfh
H{fho/ wkh srsxodwlrq phdq htxdov D dqg wkh srsxodwlrq yduldqfh htxdov .f= D vdpsoh ri
vl}h f lv gudzq zlwkrxw uhsodfhphqw iurp wklv srsxodwlrq dqg wkh phdq ri wklv vdpsoh 4 O,
lv ghqrwhg e| [= Wkh yduldqfh ri [ lv htxdo wr bbbbbb +qxphulfdo ydoxh/ 7 vljqlfdqw Qrw dvvxplqj htxdo yduldqfhv/ zkhq whvwlqj wkh k|srwkhvlv Kf G S k Q\ djdlqvw
gljlwv,1 K G S k ? Q\ wkh sydoxh lv htxdo wr bbbbbb +qxphulfdo ydoxh/ 7 vljqlfdqw gljlwv,1
4 N, 4 P,
Rqh zdqwv wr vwxg| wkh wlphv ehwzhhq duulydov dw d edqn*v DWP +dxwrpdwhg whoohu pd0 Qrw dvvxplqj htxdo yduldqfhv/ wkh orzhu olplw ri wkh bDI frqghqfh lqwhuydo ri S k Q\
fklqh,1 Lw lv nqrzq wkdw wkhvh wlphv kdyh vrph frqwlqxrxv glvwulexwlrq dqg lw lv fodlphg lv htxdo wr bbbbbb +qxphulfdo ydoxh/ 7 vljqlfdqw gljlwv,1
wkdw wkh phgldq ri wklv glvwulexwlrq lv e plqxwhv1 Iru D duulydo wlphv rqh fkhfnv li wkh
wlph lv pruh wkdq e plqxwhv ru li lw lv ohvv wkdq ru htxdo wr e plqxwhv1 Wkh yduldeoh X lv 4 Q,
wkh qxpehu ri revhuydwlrqv wkdw duh pruh wkdq e plqxwhv1 Wkhq Qrw dvvxplqj htxdo yduldqfhv/ wkh hvwlpdwhg vwdqgdug ghyldwlrq ri [ S k [ Q\ lv htxdo
4, X kdv d qrupdo glvwulexwlrq wr bbbbbb +qxphulfdo ydoxh/ 7 vljqlfdqw gljlwv,1
5, X kdv d k|shujhrphwulf glvwulexwlrq
6, X kdv d elqrpldo glvwulexwlrq 4 R,
7, X kdv d Srlvvrq glvwulexwlrq Dvvxplqj htxdo yduldqfhv/ wkh qxpehu ri ghjuhhv ri iuhhgrp ri wkh wvwdwlvwlf zkhq
8, X kdv dq h{srqhqwldo glvwulexwlrq whvwlqj wkh k|srwkhvlv Kf G Q\ S k djdlqvw K G Q\ ? S k lv htxdo wr bbbbbb
9, X kdv d glvwulexwlrq rwkhu wkdq phqwlrqhg deryh +qxphulfdo ydoxh,1
:, qrw hqrxjk lqirupdwlrq kdv ehhq jlyhq wr ghwhuplqh wkh glvwulexwlrq ri X=
4 S, Wkh orzhu olplw ri wkh bDI frqghqfh lqwhuydo ri S k lv htxdo wr bbbbbb
+qxphulfdo ydoxh/ 7 vljqlfdqw gljlwv,1
8 9
,4 T, Lpsruwdqw qrwh1
Lw lv fodlphg e| d jroi edoo pdqxidfwxuhu wkdw klv edoov duh surgxfhg zlwk d gldphwhu Iru hdfk rshq txhvwlrq |rx pxvw h{sodlq krz |rx fdph wr |rxu frqfoxvlrq1
ri e=2. fp dqg vwdqgdug ghyldwlrq f=fD fp1 \rx pd| dvvxph wkdw wkh gldphwhuv duh Iru k|srwkhvlv whvwlqj sureohpv wkh vdihvw dssurdfk lv wr iroorz wkh 80vwhsv
qrupdoo| glvwulexwhg1 surfhgxuh1 Lq dq| fdvh xqohvv h{solflwo| vwdwhg rwkhuzlvh |rx pxvw dw ohdvw
Vxssrvh wkdw d vhw ri b edoov kdv ehhq sxufkdvhg/ dqg wkdw lw pd| eh dvvxphg wkdw wkh vwdwh wkh k|srwkhvhv lqyroyhg/ wkh whvw vwdwlvwlf/ lwv glvwulexwlrq xqghu Kf > wkh
vhw lv d udqgrp vdpsoh iurp wkh edoov surgxfhg e| wklv pdqxidfwxuhu1 dvvxpswlrqv |rx pdnh/ zkhq wr uhmhfw wkh k|srwkhvlv +odujh dqg2ru vpdoo
gldphwhu ri wkhvh edoov/ wkhq 0 li wkh fodlp lv wuxh 0 wkh suredelolw| S [ e=2H lv htxdo ydoxhv,/ dqg wkh ydoxhv frpsxwhg iurp wkh vdpsoh ru uhdg iurp wkh frpsxwhu
Li [ lv wkh phdq
wr bbbbbb +qxphulfdo ydoxh/ 7 vljqlfdqw gljlwv,1 rxwsxw |rx xvh wr gudz |rxu frqfoxvlrqv1 Li |rx lqwurgxfh d qrq0vwdqgdug
qrwdwlrq/ |rx pxvw ghqh lwv phdqlqj1
4 U,
Wkh zdlwlqj wlph [ +lq plqxwhv, dw d fhuwdlq frxqwhu lv h{srqhqwldoo| glvwulexwhg zlwk
phdq e=
Wkh ydoxh ri S E[ 2
lv htxdo wr bbbbbb +qxphulfdo ydoxh/ 7 vljqlfdqw gljlwv,1 Txhvwlrq 5
Wkh pdqdjhu ri d uhvwdxudqw eholhyhv wkdw zdlwhuv dqg zdlwuhvvhv zkr lqwurgxfh wkhpvhoyhv
4 V, e| whoolqj fxvwrphuv wkhlu qdphv zloo jhw odujhu wlsv wkdq wkrvh zkr grq*w1 Lq idfw/ vkh
D frxqflo frqvlvwv ri H phq dqg D zrphq1 Wkuhh shrsoh ri wklv frxqflo duh vhohfwhg fodlpv wkdw wkh dyhudjh wls iru wkh iruphu jurxs lv HI zkloh wkdw ri wkh odwwhu lv rqo|
udqgrpo| iurp wklv frxqflo wr irup d frpplwwhh1 Ohw [ eh wkh qxpehu ri pdohv lq wkh DI=
frpplwwhh/ wkhq wkh suredelolw| S E[ ' 2
lv htxdo wr bbbbbb +qxphulfdo ydoxh/ 7 \rx pd| dvvxph wkdw wlsv +dv phdvxuhg lq shufhqwdjhv, duh qrupdoo| glvwulexwhg zlwk
vljqlfdqw gljlwv,1 vwdqgdug ghyldwlrq ri I= Vxssrvh f wlsv iurp zdlwhuv dqg zdlwuhvvhv zkr lqwurgxfh
wkhpvhoyhv duh ghqrwhg dv i[ > [2 > = = = > [f j dqg f wlsv iurp zdlwhuv dqg zdlwuhvvhv zkr
4 W, gr qrw lqwurgxfh wkhpvhoyhv duh ghqrwhg dv i\ > \2 > = = = > \f j1
D udqgrp yduldeoh [ lv Srlvvrq glvwulexwhg zlwk ' =bf =
Wkh suredelolw| S E [
lv htxdo wr bbbbbb +qxphulfdo ydoxh/ 7 vljqlfdqw glj0 d, Ilqg wkh suredelolw| wkdw d wls iru d zdlwhu ru zdlwuhvv zkr lqwurgxfhv klp2khuvhoi
lwv,1 lv dw ohdvw 2fI=
e, Zkdw shufhqwdjh ri wkh zdlwhuv dqg zdlwuhvvhv zkr gr qrw lqwurgxfh wkhpvhoyhv zloo
uhfhlyh d wls ehwzhhq DI dqg 2fI1
f, Ilqg wkh suredelolw| wkdw wkh phdq ri wkh wlsv iurp wkh zdlwhuv dqg zdlwuhvvhv
dqg zdlwuhvvhv zkr gr lqwurgxfh wkhpvhoyhv/ vr qg S \ A [ ru htxlydohqwo|
zkr gr qrw lqwurgxfh wkhpvhoyhv zloo h{fhhg wkh phdq ri wkh wlsviurp wkh zdlwhuv
S \ [ Af =
Txhvwlrq 6
D kljkzd| sdwuro r!fhu eholhyhv wkdw wkh dyhudjh vshhg ri fduv wudyhoolqj ryhu d fhuwdlq
vwuhwfk ri kljkzd| h{fhhgv wkh srvwhg olplw ri DD psk +plohv shu krxu,1 Wkh vshhgv ri f
fduv duh uhfrughg dqg ihg lqwr d frpsxwhu surjudp1 Iurp wkh vdpsoh lw lv irxqg wkdw wkh
dyhudjh vshhg lv Sf=e psk dqg wkh vwdqgdug ghyldwlrq lv D=f psk1
Gr wkhvh gdwd surylgh vx!flhqw hylghqfh wr vxssruw wkh r!fhu*v eholhiB Xvh d vljqlfdqfh
ohyho ri DI=
: ;
,
Txhvwlrq 7
Lq d whohylvlrq frpphufldo/ wkh pdqxidfwxuhu ri d wrrwksdvwh fodlpv wkdw dw ohdvw irxu rxw
ri yh ghqwlvwv uhfrpphqg wkh lqjuhglhqwv lq lwv surgxfw1 Wr whvw wkdw fodlp/ wkh Khdowk
Frpplwwhh ri d foxe iru Exvlqhvv Dgplqlvwudwlrq Vwxghqwv/ wkdw lv udwkhu vfhswlfdo derxw
wklv fodlp/ udqgrpo| vdpsohv f ghqwlvwv dqg dvnv hdfk rqh zkhwkhu kh ru vkh zrxog
uhfrpphqg wrrwksdvwh wkdw frqwdlqhg wkh lqjuhglhqwv1 Wkh uhvsrqvhv duh ' \ hv dqg
f ' Q r=
Vxssrvh wkdw wkh pdqxidfwxuhu lv frqvlghulqj wr vsrqvru wkh foxe1 Ri frxuvh/ vsrqvrulqj
fdq qrw eh dffhswhg e| wkh foxe li wkh fodlp lv uhixwhg e| wkh gdwd1
d, Vwxghqw D/ zkr rqo| ydjxho| uhphpehuv d vwdwlvwlfv ohfwxuh kh dfflghqwo| vwxpeohg
xsrq lq wkh sdvw/ vxjjhvwv wr uhmhfw wkh fodlp zkhq rqo| 2 ru ohvv ghqwlvwv lq wkh
vdpsoh gr qrw uhfrpphqg wkh lqjuhglhqwv iurp wkh wrrwksdvwh ri crxu* pdqxidfwxuhu1
Lw zrxog eh d glvjudfh iru wkh foxe wr kdyh d vsrqvru wkdw surgxfhv surgxfwv wkdw
duh uhfrpphqghg e| DfI ri wkh ghqwlvwv ru ohvv1 Li d vdpsoh ri vl}h f lv vhohfwhg/
qg wkh suredelolw| wkdw d vdpsoh lv vhohfwhg vxfk wkdw wkh fodlp lv qrw uhmhfwhg
xvlqj D*v vxjjhvwlrq +vr pruh wkdq wzr ghqwlvwv gr qrw uhfrpphqg wkh wrrwksdvwh,
zkhq wkh wuxh sursruwlrq ri uhfrpphqglqj ghqwlvwv lv lq idfw DfI=
Qrz vxssrvh wkdw wkh vdpsoh uhvxowv lq wkh iroorzlqj gdwd=
Ghqwlvw 4 5 6 7 8 9 : ; < 43
Uhvsrqvh 4 4 3 4 3 3 4 3 4 3
e, \rx duh vxssrvhg wr dgylfh wkh foxe wr uxq d surshu whvw1 Irupxodwh wkh k|srwkhvhv
li wkh sxusrvh lv wr csuryh* wkdw wkh fodlp lv idovh1 Gr wkh whvw dw d vljqlfdqfh ohyho
ri DI= Lqfoxgh wkh dvvxpswlrqv |rx qhhg lq rughu wr vroyh wklv whvwlqj sureohp1
Rq wkh rqh kdqg wkh foxe zrxog olnh wr kdyh d vsrqvru/ exw rq wkh rwkhu kdqg qrw d vsrqvru
wkdw surgxfhv lqihulru surgxfwv1 Vr wkh vwxghqwv ghflgh wr wdnh d odujhu vdpsoh1 Vxssrvh
wkh| udqgrpo| vhohfw d vdpsoh ri ff ghqwlvwv1 Rxw ri wkhvh ghqwlvwv .f uhfrpphqg
wrrwksdvwh zlwk wkh lqjhglhqwv ciurp rxu pdqxidfwxuhu*1
f, Whvw wkh k|srwkhvhv iurp e, djdlq/ xvlqj wkh qhz gdwd1 Djdlq xvh d vljqlfdqfh ohyho
ri DI> exw iru wkh whvwlqj |rx kdyh wr xvh d ydolg dssur{lpdwlrq ri wkh glvwulexwlrq
ri wkh whvw vwdwlvwlf1
Qrwh= vhh lpsruwdqw qrwh rq sdjh ;$ Li |rx xvh irupxodv/ yhuli| wkh frqglwlrqv wkdw
|rx pd| xvh wkhp$
<