008 hipotesis 001

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© 2002 Prentice-Hall, Inc. Chap 9-1

Basic Business Statistics(8th Editin!

Chapter 9

"unda#entals $ H%pthesis &estin' )ne-Sa#ple &ests

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© 2002 Prentice-Hall, Inc.Chap 9-2

*hat is a H%pthesis+*hat is a H%pthesis+

h%pthesis is aclai# (assu#ptin!

aut the ppulatinpara#eter Ea#ples $ para#eters

are ppulatin #ean

r prprtin &he para#eter #ust

e identi/ed e$reanal%sis

I claim the mean GPA of

this class is 3.5!

© 1984-1994 T/Maker Co.

µ =

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© 2002 Prentice-Hall, Inc.Chap 9-

&he ull H%pthesis, H &he ull H%pthesis, H00

States the assu#ptin (nu#erical! t etested

e.'. &he aera'e nu#er $ &3 sets in 4.S.H#es is at least three ( !

Is al5a%s aut a ppulatin para#eter( !, nt aut a sa#ple

statistic ( !

0 : 3 H µ ≥

0: 3 H µ ≥

0 : 3 H X ≥

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&he ull H%pthesis, H &he ull H%pthesis, H00

Be'ins 5ith the assu#ptin that the nullh%pthesis is true

Si#ilar t the ntin $ inncent until pren 'uilt%

7e$ers t the status u

l5a%s cntains the :; si'n

<a% r #a% nt e re=ected

(continued)

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© 2002 Prentice-Hall, Inc.Chap 9->

&he lternatie H%pthesis, H &he lternatie H%pthesis, H11

Is the ppsite $ the null h%pthesis e.'. &he aera'e nu#er $ &3 sets in

4.S. h#es is less than ( !

Challen'es the status u eer cntains the :; si'n

<a% r #a% nt e accepted

Is 'enerall% the h%pthesis that iselieed (r needed t e pren! te true % the researcher

1 : 3 H µ <

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© 2002 Prentice-Hall, Inc.Chap 9-?

Hypothesis Testing Process

Identify the Population

Assume thepopulation

mean age is 50.

( )

REJECT

Take a ample

!ull "ypothesis

No, not likely!

X 20 likely ifIs ? µ = = 50

0 : 50 H µ =

( )20 X =

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Chap 9-@

Sa#plin' Aistriutin $ Sa#plin' Aistriutin $

# 50

It is unliel%

that 5e 5uld'et a sa#ple#ean $ thisalue ...

... &here$re,5e re=ect the

nullh%pthesis

that m : >0.

7easn $r 7e=ectin' H7easn $r 7e=ectin' H00

µ$0

If H 0 is t%ue

X

... i$ in $act this5ere the ppulatin#ean.

X

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eel $ Si'ni/cance,eel $ Si'ni/cance,

Ae/nes unliel% alues $ sa#ple statistic i$Ae/nes unliel% alues $ sa#ple statistic i$

null h%pthesis is truenull h%pthesis is true Called re=ectin re'in $ the sa#plin'Called re=ectin re'in $ the sa#plin'

distriutindistriutin

Is desi'nated % , (leel $ si'ni/cance!Is desi'nated % , (leel $ si'ni/cance!

&%pical alues are .01, .0>, .10 &%pical alues are .01, .0>, .10 Is selected % the researcher at theIs selected % the researcher at the

e'innin'e'innin'

Prides the critical alue(s! $ the testPrides the critical alue(s! $ the test

α

α

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eel $ Si'ni/canceand the 7e=ectin 7e'in

H 0: µ ≥ 3

H 1: µ

< 3

0

0

0

H 0: µ ≤ 3

H 1: µ

> 3

H 0: µ 3

H 1: µ

≠ 3

α

α

α /2

Citical

al"e#s$

%e&ection%e'ions

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Errrs in <ain' Aecisins

Prailit% $ nt #ain' &%pe I Errr

Called the cn/dence ceDcient

( )1 α −

(continued)

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7esult Prailities

H 0& Inno'ent

The T%uth The T%uth

e%di't Innocent Guilty e'ision H0 True H0 False

Innocent Co%%e't E%%o% Do Not

e!ect

"0

* + α

Type II

E%%o% ( β )

Guilty E%%o% Co%%e't e!ect"0

Type IE%%o% (α

)

Po,e%

(* + β )

Ju%y T%ial "ypothesis Test

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&%pe I II Errrs Hae anInerse 7elatinship

α

β

If yo" e("ce the )o*a*ility of one

eo, the othe one inceases so that

e+eythin' else is "nchan'e(.

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Critical 3aluesCritical 3alues

pprach t &estin'pprach t &estin'

Cnert sa#ple statistic (e.'. ! ttest statistic (e.'. Z, t r F Fstatistic!

)tain critical alue(s! $r a speci/ed$r# a tale r c#puter I$ the test statistic $alls in the critical re'in,

re=ect H0

)ther5ise d nt re=ect H0

X

α

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p-3alue pprach t &estin'p-3alue pprach t &estin'

Cnert Sa#ple Statistic (e.'. ! t &estStatistic (e.'. Z, t r F Fstatistic!

)tain the p-alue $r# a tale r c#puter p-alue Prailit% $ tainin' a test statistic

#re etre#e ( r ! than the seredsa#ple alue 'ien H0 is true

Called sered leel $ si'ni/cance

S#allest alue $ that an H0 can e re=ected

C#pare the p-alue 5ith I$ p-alue , d nt re=ect H0

I$ p-alue , re=ect H0

X

≤ ≥

≤

≥ α

α

α α

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General Steps in H%pthesis &estin'General Steps in H%pthesis &estin'

e.'. &est the assu#ptin that the true #ean nu#er $$ &3 sets in 4.S. h#es is at least three ( n5n!σ

1. State the H0

2. State the H1

. Chse6. Chse n

>. Chse &est

0

1

: 3

: 3

=.05100

Z

H

H

n

test

µ

µ

α

≥

<

=α

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100 husehlds sure%ed

C#puted test stat :-2,

p-alue : .0228

7e=ect null h%pthesis

&he true #ean nu#er $

&3 sets is less than

(continuedontinued)

%e&ect H 0α

-1.645

Z

?. Set up critical

alue(s!

@. Cllect data

8. C#pute teststatistic and p-alue

9. <ae statistical

decisin

General Steps in H%pthesis &estin'General Steps in H%pthesis &estin'

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)ne-tail Z &est $r <ean( n5nn5n!

ssu#ptins Ppulatin is nr#all% distriuted

I$ nt nr#al, reuires lar'e sa#ples ull h%pthesis has r si'n nl%

Z test statistic

σ

≤ ≥

/

X

X

X X Z

n

µ µ

σ σ

− −

= =

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Chap 9-18

7e=ectin 7e'in

Z "

%e&ect H 0

Z "

%e&ect H 0

H 0: µ ≥ µ 0

H 1: µ

<µ 0

H 0: µ ≤ µ 0

H 1: µ

>µ 0

<ust BeSignifcantly Bel5 0

t re=ect H0

S#all alues $ dnJtcntradict H0

AnJt 7e=ect H0 K

α α

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Chap 9-19

Ea#ple )ne &ail &estEa#ple )ne &ail &est

. -oes an a+ea'e *o of

ceeal contain moe than

3/ 'ams of ceeal A

an(om sam)le of 25

*oes shoe( 4 32.5.

6he com)any has

s)ecifie( σ to *e 15 'ams.6est at the

α

0.05 le+el.

-/ gm.

H 0: µ ≤

368

H 1: µ

> 368

X

n n' r ca a ue nen n' r ca a ue ne

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Chap 9-20

n n' r ca a ue nen n' r ca a ue ne &ail &ail

Z ."4 ."#

1.# .15 .505 .9$1$

1.% .9$91 .9$99 .9#"8

1.8 .9#%1 .9#%8 .9#8#

.9%&8 .9%$"

Z " 1.645

."$

1.9 .9%44

StandardiLedCu#ulatie r#alAistriutin &ale

(Prtin!

*hat is Z 'ien α :0.0>+

α = .05

Citical al"e

4 1./75

.85

1 Z σ =

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Chap 9-21

Ea#ple Slutin )ne &ail &estEa#ple Slutin )ne &ail &est

α = 0.5

n 4 25

Citical al"e: 1./75

Cnclusin

A t 7e=ect at α : .0>

eidence that

true #ean is #re

Z " 1./75

.05

%e&ect

H 0: µ ≤

3/

H 1: µ > 3/

1.50 X

Z

n

µ

σ

−

= =

1.>

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Chap 9-22

p p -3alue Slutin-3alue Slutin

Z " 1.$"

P -Value =.0668

Z al"e of 9am)le

9tatistic

om Z 6a*le:

;ook") 1.50 to

*tain .8332

=se the

altenati+ehy)othesis

to fin( the

(iection of

the e&ectione'ion.

1.0000

.8332

.0//

pal"e is P # Z ≥ 1.50$ 4 0.0//

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Chap 9-2

p p -3alue Sluti-3alue Slutin(continued)

0*.50

Z

%e&ect

# pal"e 4 0.0//$ ≥ #α 4 0.05$

-o Not %e&ect.

p al"e 4 0.0//

α

4 0.05

Test Statistic 1.50 is in the Do Not RejectRegion

1./75

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Ea#ple &5-&ail &estEa#ple &5-&ail &est

. -oes an a+ea'e *o

of ceeal contain 3/

'ams of ceeal A

an(om sam)le of 25

*oes shoe( 4

32.5. 6he com)any

has s)ecifie(σ

to *e

15 'ams. 6est at the

α

0.05 le+el.

-/ gm.

H 0: µ

3/

H 1: µ

≠ 3/

X

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© 2002 Prentice-Hall, Inc.Chap 9-2>

372.5 3681.50

1525

X Z

n

µ

σ

− −= = = = 0.05

n 4 25

Citical al"e: ?1.8/

Ea#ple Slutin &5-&ail &estEa#ple Slutin &5-&ail &est

Test Statistic:

Decision:

Conclusion:

A t 7e=ect at α : .0>

Eidence that &rue <ean is t ?8Z " 1.8/

.025

%e&ect

1.8/

.025

H 0: µ 3/

H 1: µ ≠ 3/

1.50

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© 2002 Prentice-Hall, Inc.Chap 9-2?

p-3alue Slutin

# p al"e 4 0.133/$ ≥ #α 4 0.05$

-o Not %e&ect.

0*.50

Z

%e&ect

α 4 0.05

1.8/

p al"e 4 2 x 0.0//

Test Statistic 1.50 is in the Do Not Reject

Region

%e&ect

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© 2002 Prentice-Hall, Inc.Chap 9-2@

( ) ( )

F! 372.5" 15 a#$ 25"

%&e '5( )#fi$e#)e i#%e!*al is:

372.5 1.'6 15/ 25 372.5 1.'6 15/ 25!

366.62 378.38

If %&is i#%e!*al )#%ai#s %&e &y+%&esi,e$ -ea# 368"

e $ #% !ee)% %&e #ull &y+%&esis.

I

X nσ

µ

µ

= = =

− ≤ ≤ +

≤ ≤

% $es. #% !ee)%.

Cnnectin t Cn/dence InteralsCnnectin t Cn/dence Interals

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t &est 4nn5n

ssu#ptin Ppulatin is nr#all% distriuted

I$ nt nr#al, reuires a lar'e sa#ple T test statistic 5ith n-1 de'rees $

$reed#

σ

/

X t

S n

µ −=

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Ea#ple )ne-&ailEa#ple )ne-&ail t t &est &est

-oes an a+ea'e *o of

ceeal contain moe than

3/ 'ams of ceeal Aan(om sam)le of 3/

*oes shoe( @ 4 32.5,

an( s 15. 6est at the

α 0.01 le+el.

-/ gm.

H 0: µ ≤ 3/

H 1: µ 3/

σ

is not 'i+en

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Ea#ple Slutin )ne-&ailEa#ple Slutin )ne-&ail

α = 0.01

n 4 3/, (f 4 35

Citical al"e: 2.73

6est 9tatistic:

-ecision:

Conclusion:

-o Not %e&ect at α 4 .01

No e+i(ence that t"e

mean is moe than 3/t 35

" 2.73

.01

%e&ect

H 0: µ ≤

3/

H 1: µ 3/372.5 368

1.80

1536

X t

S n

µ − −= = =

1.80

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p p -3alue Slutin-3alue Slutin

0*./0

t 35

%e&ect

# p al"e is *eteen .025 an( .05$ ≥ #α 4 0.01$.

-o Not %e&ect.

p al"e 4 .025, .05B

α

4 0.01

Test Statistic 1.80 is in the Do Not RejectRegion

2.73

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Proportion

Inles cate'rical alues

&5 pssile utc#es

Success; (pssesses a certaincharacteristic! and"ailure; (des nt pssesses a certaincharacteristic!

"ractin r prprtin $ ppulatin inthe success; cate'r% is dented % p

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© 2002 Prentice-Hall, Inc.Chap 9-

ProportionProportion

Sa#ple prprtin in the successcate'r% is dented % pS

*hen th np and n(1-p) are at least >,

pS can e appri#ated % a nr#aldistriutin 5ith #ean and standarddeiatin

(continued)

u-e! f u))essesa-+le i,e

s X pn

= =

s p p µ =1

s p

p p

n

σ −

=

E l Z & t $

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Ea#ple Z &est $rPrprtin

M. #aretin'c#pan% clai#s that itreceies 6N respnses

$r# its #ailin'. &test this clai#, arand# sa#ple $ >005ere sure%ed 5ith

2> respnses. &est atthe α : .0>si'ni/cance leel.

( )

( ) ( )

&e)k:500 .04 20

5

1 500 1 .04

480 5

np

n p

= =

≥

− = −

= ≥

Z & t $ P ti

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© 2002 Prentice-Hall, Inc.Chap 9->

( ) ( )

.05 .041.14

1 .04 1 .04

500

S p p Z

p p

n

− −≅ = =

− −

Z &est $r PrprtinSlutin

α 4 .05

n 4 500

A nt re=ect at α : .0>

H 0: p .07

H 1: p ≠ .07

Citical al"es: ± 1.8/

6est 9tatistic:

-ecision:

Concl"sion:

Z "

e!ect e!ect

."'$."'$

1.'6-1.'6

1.14

*e d nt haesuDcient eidence tre=ect the c#pan%Js

clai# $ 6N respnserate.

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p -3alue Slutin

# p al"e 4 0.2572$ ≥ #α 4 0.05$.

-o Not %e&ect.

0*.*1

Z

%e&ect

α 4 0.05

1.8/

p al"e 4 2 x .121

Test Statistic 1.1 is in the Do Not Reject

Re ion

%e&ect

008 hipotesis 001

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