Stats Lec8

7/28/2019 Stats Lec8

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HypothesisTesting(2)

Barrow, Statistics for Economics, Accounting and Business Studies, 4th edition Pearson Education Limited 2006


2/14

HypothesisTesting

(2)

So

far

we

have

looked

at

hypothesis

testing

about

a

single

H0:=5000

Nowwe

look

at

testing

hypotheses

about

differences

between

twopopulationparameters

E.g.arewomenpaidlessthanmen?



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FormalLayout

of

aProblem

1. Specifythenullandalternativehypothesis

. , . .

3. Lookupcriticalvaluefromzorttables

4. Calculatethe

test

statistic

. ec s on:re ec or ono re ec 0



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Testingthe

Difference

of

Two

Means

Totestwhethertwosamplesaredrawnfrompopulationswith

thesame

mean

H0:1 =2 orH0:1 2 =0

H : orH : 0

Theteststatisticis

2

2

2

1

2121

ss

z

21 nn



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isOutputtheSame?

Average daily output for 30 420 408

Standard dev of daily output 25 20

H : = or =0

H1:12 0

Significancelevelof1%impliesz*0.005=2.57



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05.2

2025222

2

2

1

2121

ss

z

303021 nn

z


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Proportions Totestwhethertwosampleproportionsareequal

H : =

or

H :

=

0

H1:1 2 orH1:1 2 0

11z

21

2211

nn

pnpn

21



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Example:Customer

Satisfaction

proportion who say they are satisfied 45/75 48/90

H0:12=0

H1:120

Si nificance level of 5 z* =1.96

.



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564.0533.0*906.0*75

2211

pnpn

21 nn

11

z

86.0

0533.06.0

21

90

564.01564.0

75

564.01564.0

z


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ma

amp es:

est ngt e

erence

Thetest

statistic

is

)2(~ 21

22

2121

nnt

xxt

21 nn

2 w ere s epoo e var ance

112

22

2

112 snsn221

nn



11/14

Sofarassumedoursamplesaredrawnindependently

tenwe ave epen ent samp es e.g. e orean a tertests,orscoresonmacroandmicroexams)

Weuse

adifferent

approach

to

use

the

info.

that

the

data

comesfromthesameobservation



12/14

or er

Before 21 24 23 25 28 17 24 22 24 27

After 23 27 24 28 29 21 24 25 26 28

Improve

ment2 3 1 3 1 4 0 3 2 1

10,10.3,5.23 nsxBB

10,55.2,5.25

nsx AA


,.,. tmprovementmprovemen


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0: timprovemen0 H

0:

*

timprovemen HA

00.2

.9,05.0

.247.1 2

> so we re ec e nu ypo es s an conc u e atraining has improved worker productivity



14/14

Theprinciplesarethesameforalltests:calculatethetest

statisticand

see

if

it

falls

into

the

rejection

region

Theformulafortheteststatisticdependsupontheproblem(mean,proportion,etc)

Therejection

region

varies,

depending

upon

whether

it

is

aone

ortwotailedtest

Forlargesampleswecanalwaysuseaztest

If n is small we can still use z test if the o ulation variance is

known


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