hypotheses testing umi - use this copy.pptx

8/19/2019 hypotheses testing umi - use this copy.pptx

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Testing hypothesis JOSEPH KAMPUMURE

Consultant-UMI07!-"#$!

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A)te( *nishing this +hapte( youshoul, e ale to.

• Un,e(stan, the pu(pose o) hypothesistesting

•

/ist the steps inole, in hypothesis testing• Un,e(stan, the e((o(s inole, an, the use

o) signi*+an+e leels• Test hypotheses aout population 'eans• Use one- an, t1o-tail tests• E2ten, these tests to ,eal 1ith s'all

sa'ples•

Use the tests )o( a a(iety o) p(ole's3#%$"%$" J&a'pu'u(e-UMI !


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Int(o,u+tion

• Hu'an su(ial an, ,eelop'ent isa )un+tion o) the e2tent to 1hi+hpeople &no1 an, un,e(stan, thei(physi+al an, so+ial eni(on'ents3

• It is this knowledge an,understanding 1hi+h people use to

e2t(a+t thei( lielihoo,s3

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Int(o,u+tion5

6ays o) a+ui(ing knowledge an,understanding o) the physi+al an,so+ial eni(on'ents in+lu,e the)ollo1ing8

• Authoritarian way i3e3 )(o'so+ially9 e+ono'i+ally an, politi+ally

,e*ne, pe(sons3• Faith/Mystical method i3e3

&no1le,ge +o'es )(o' pe(sons

+lai'ing to hae +o''uni+ation o(#%$"%$" ;Pat(i+& 4aha1e


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Int(o,u+tion5

• The Rationalistic method i3e3 &no1le,ge+o'es )(o' the st(i+t +on)o('ity to (eason an,thought3 This 'etho, asse(ts that the 'in, +anun,e(stan, the 1o(l, 1ithout the e'pi(i+ale2pe(ien+e3

• The Empirical method i3e3 &no1le,ge +o'es)(o' (eal li)e e2pe(ien+e3

•

The Scientifc method i3e3 suggests that t(ue&no1le,ge +o'es )(o' a +o'ination o)thought an, e'pi(i+al e2pe(ien+e 1hi+h is)ollo1e, th(ough a lai, ,o1n p(o+e,u(e3

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Int(o,u+tion5

• Hu'an histo(y sin+e the $7th Centu(y9 see's to suggest that theScientifc method is supe(io( toothe( 'etho,s o) &no1ing sin+e ithas een su++ess)ully applie, to theso+ial9 e+ono'i+ an, politi+al

p(ole's o) ,eelope, +ount(ies9'a&ing the' e+ono'i+ally a=uent9so+ially a,an+e, an, politi+ally

stale3#%$"%$" "Pat(i+& 4aha1e


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Int(o,u+tion5

• In,ee, the only genuinely ,eelope,pa(ts o) the 6o(l, i3e3 the 6est9

Japan9 Aust(al-Asia an, no1 South-East-Asia happen to e the onlyso+ieties 1hi+h hae 'aste(e, theScientifc method an, 'a,e it to

e the only )un,a'ental asis )o(thei( e+ono'i+ 'o,es o) p(o,u+tionan, thei( institutional o(gani>ation3

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6hat is this S+ienti*+ 'etho, allaout?

• It is the a+uisition o) &no1le,ge an,un,e(stan,ing o) sel)9 so+iety an, natu(ey the )ollo1ing p(o+ess8

$3 Ose(ation o) so+ial an, physi+al (eality%p(ole'

!3 Suggesting e2planations o) the natu(e an,'e+hanis' o) the (eality

#3 The )o('ation o) e2pe+tations o(hypothesis o) the (eality ase, on thesuggeste, e2planations3

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S+ienti*+ 'etho,5

;3 The gathe(ing o) e'pi(i+al ,ata o(in)o('ation aout the (eality%pheno'ena


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What is a hypothesis?

• A hypothesis is a state'ent o)the (esea(+he(s p(e,i+tion o(

guess o) the (elation that e2istsa'ong the a(iales einginestigate,3

•

They a(e the Tentatie ans1e(sto the (esea(+h p(ole'3

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What is a hypothesis?!ontd

• Usually ,(a1n )(o' theo(y

• The *(st step in a (esea(+h is the

i,enti*+ation o) a (esea(+hp(ole' then 'a&ing e(i*alehypotheses3

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Hypothesis ,e*ne,

Resea(+h sta(ts out 1ith the i,eathat a++o(,ing to so'e theo(y o(

p(a+ti+e +e(tain (esults 1ill ee2pe+te,3 The (esea(+h stu,y is+a((ie, in o(,e( to +he+& on the

p(e,i+tion3

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• This p(e,i+tion aout the e2pe+te,out+o'e is 1hat is te+hni+ally+alle, a hypothesis3 A hypothesis isa )o('al aD('atie state'entp(e,i+ting the (esea(+h out+o'e3

• E2a'ple8 /ease *nan+ing i'p(oesSME pe()o('an+e @hypothesis

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"ype o# hypothesis

$34ull hypothesis @H0

!3 Alte(natie hypothesis@HA

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This type o) hypothesis statesthat a pa(a'ete( has so'e

p(e+ise alue li&e The alue thato++u((e, in the past9 The alue+lai'e, y so'eone o( The

ta(get alue that is suppose, too++u(3

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$a% &ull hypothesis


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The 4ull Hypothesis- HO –

The alte(natie o) no ,ie(en+e –Usually not state, in the (esea(+h

p(oposal –

Tal&e, aout in the *n,ings se+tion –'ased on H( ) a decision ismade on whether therelationship is signifcant or not

–One eithe( (eFe+ts o( a++epts HOE3g3 /ease *nan+ing ,oes not i'p(oe SMEpe()o('an+e

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$*%"he Research Hypothesis H+

Also +alle, the alte(natie hypothesis

–Usually state, in the p(oposal

–Only tal&e, aout in the *n,ings i)the null hypotheses is (eFe+te,

–May e ,i(e+tional o( non-,i(e+tional

– Rep(esents the inestigato(Gs elie)3

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• The (esea(+h o( alte(natie hypothesis +an ta&e one o) th(ee)o('s3 An inestigato( 'ight eliee that the pa(a'ete( hasin+(ease,9 ,e+(ease, o( +hange,3 o( e2a'ple9 an

inestigato( 'ight hypothesi>e.• H$. 0 9 1he(e 0 is the +o'pa(ato( o( null alue @e3g39

0 L$B$ in ou( e2a'ple aout 1eight in 'en in !00" an,an in+(ease is hypothesi>e, - this type o) test is +alle, anuppertailed test8

• H$. 0 9 1he(e a ,e+(ease is hypothesi>e, an, this is+alle, a lowertailed test8 o(

• H$. N 09 1he(e a ,ie(en+e is hypothesi>e, an, this is+alle, a twotailed test3

• The e2a+t )o(' o) the (esea(+h hypothesis ,epen,s on theinestigato(Gs elie) aout the pa(a'ete( o) inte(est an,1hethe( it has possily in+(ease,9 ,e+(ease, o( is ,ie(ent)(o' the null alue3 The (esea(+h hypothesis is set up ythe inestigato( e)o(e any ,ata a(e +olle+te,3

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Hypotheses testing

Hypothesis testing sta(ts y'a&ing a state'ent ,es+(iing

so'e aspe+t o) the population @E3g3 SMEs in Ugan,a3

A sa'ple is then ta&en )(o' the

population to see i) ei,en+e +ansuppo(t the hypothesis3

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Steps in hypothesis testing

$3 State the null hypothesis an,alte(natie hypothesis

!3 Spe+i)y the leel o) signi*+an+e toe use,3 @Level of signicance is the probability of incorrectly rejecting a givennull hypothesis in favor of a second

alternative hypothesis )#3 Cal+ulate the a++eptan+e (ange

)o( the a(iale teste,

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http://en.wikipedia.org/wiki/Alternative_hypothesishttp://en.wikipedia.org/wiki/Alternative_hypothesishttp://en.wikipedia.org/wiki/Alternative_hypothesishttp://en.wikipedia.org/wiki/Alternative_hypothesis


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;3 in, the a+tual alue )o( thea(iale teste,


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E((o(s in hypothesis testing

i 6e 'ay (eFe+t a null hypothesisthat is t(ue. this is a type $ e((o(3

•

The p(oaility o) 'a&ing atype $ e((o( also +alle, the leelo) signi*+an+e o) the test is

usually ,enote, y i3e3 LP@Ho is (eFe+te,%Ho is t(ue

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• The leel o) signi)i+an+e9 9 is+hosen y the (esea(+he(3

•

Su+h a +hoi+e is ,epen,ent onthe (is& inole, in (eFe+ting anull hypothesis9 1hi+h is t(ue3

• An alue o) 030< is usuallya++epte,3

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ii 6e 'ay a++ept a null hypothesisthat is )alse. this is a type II e((o(3

•

Type II e((o( is +o''itte, 1hen anull hypothesis that is )alse in thepopulation is e((oneously a++epte,

on the asis o) the sa'ple ,ata3• The 'ost +o''on (eason )o( a Type II e((o( is a s'all sa'ple si>e3

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Ele'ents o) a hypothesistest

$3 Hypothesis Q a si'ple state'entaout a population

!3 Test (esult - a+tual (esult )(o' thesa'ple

#3 Test statisti+ Q a +al+ulation aout asa'ple assu'ing that the

hypothesis is t(ue3;3 Con+lusion Q eithe( (eFe+t the

hypothesis o( not#%$"%$" J&a'pu'u(e-UMI !<


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Meaning o# the ,"a*lereading

• A tale uses statisti+al in)o('ation ta&en )(o'a sa'pling o) ,ata to 'a&e p(e,i+tions aout theoe(all population )(o' 1hi+h the sa'ple 1asta&en3

• Spe+i*+ally9 the tale esti'ates ho1 'u+h,ata @e2p(esse, as a p(oaility o( pe(+entage1ill )all aoe o( elo1 a gien alue o) inte(estin the population3

• tale p(e,i+tions assu'e that the population,ata is normally distributed, an, that the sa'ple,ata is in )a+t (ep(esentatie o) the population3

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Meaning o# the ,"a*lereading

• Cal+ulate the alue using the)o('ula L @2-%9 1he(e 2 is thepoint o) inte(est9 us the ae(age9

an, is the stan,a(, ,eiation3•


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, test This test is use, to ,ete('ine 1hethe( t1o

'eans ,ie( )(o' ea+h othe(3 It +an also euse, to ,ete('ine 1hethe( a single 'ean,ie(s signi*+antly )(o' a population 'ean3

L 2 -

6he(e - is the stan,a(, ,eiation

. is the population 'ean

is a alue ta&en )(o' the population

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Eample0"esting a mean *asedon a sample 1alue

A alue is ta&en at (an,o' )(o' apopulation an, )oun, to e $7!3

Test9 at the


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Solution

State HO an, H$

HO . L $


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e+i,e on the leel o) the test9 ,e+i,e on(eFe+tion +(ite(ia

1e 1ill test at W $3B"

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Cal+ulate the alue o) the teststatisti+

L 2 -

L $7! Q $


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• Ma&e +on+lusion

sin+e W>W $3B"9 1e (eFe+t HO

an, +on+lu,e that the(e issigni*+ant ei,en+e9 at the


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amp e0 ypo es stesting

*ased on a sample mean!3 The ae(age in+o'e pe( +apita in ana(ea is +lai'e, to e X$


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E2a'ple

• State the null an, alte(natie hypotheses

HO. L $


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E2a'ple

• 6ith a


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The stan,a(, e((o( L %Yn

L !000%Y;<

L !B3$;

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in, the stan,a(, alue o) eithe( 9 )(o'statisti+al tales at a gien leel o)+on*,en+e o( signi*+an+e3

The alue o) at


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O(

$;;$" to $


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• e+i,e 1hethe( to a++ept o((eFe+t the null hypothesis

• The a+tual alue is outsi,ethe a++eptan+e (ange9 so thenull hypothesis 'ust e(eFe+te,

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• State the +on+lusion (ea+he,

the ei,en+e )(o' the sa'ple

,oes not suppo(t the o(iginal+lai' that the ae(age in+o'epe( +apita in the a(ea is

X$


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• 6ith a $ signi*+an+e leel9 thea++eptan+e (ange 1oul, e 1ithin !3


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$;!#$ to $


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• Ka'pala City Coun+il Autho(ity ta&esa su(ey o) the 'onthly +osts o) )oo,an, housing )o( a pa(ti+ula( type o)

)a'ily3 They thin& that the 'ean +ostis [$9"00 1ith a stan,a(, ,eiationo) [;B3 A sa'ple o) $00 )a'ilies has

an ae(age e2pen,itu(e o)[$97$!3


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E2e(+ise $

• John /o thin&s that the 'ean alue o)o(,e(s (e+eie, y his *(' is [!"03He +he+&s a sa'ple o) #" a++ounts

an, *n,s a 'ean o) [!;0 an,stan,a(, ,eiation o) [;


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E2e(+ise !

• Eli>aeth Ho(st is a 'anage'ent +onsultant1ho has (e+ently int(o,u+e, ne1 p(o+e,u(esto a (e+eption oD+e3 The (e+eptionist shoul,,o at least $0 'inutes o) pape(1o(& ea+hhou(3 Eli>aeth 'a,e a +he+& on ;0 (an,o'hou(s o) 1o(& an, )oun, that the 'ean ti'espent on pape(1o(& is 3B< 'inutes 1ith astan,a(, ,eiation o) # 'inutes3 Can she(eFe+t the hypothesis that the ne1 p(o+e,u(es'eet spe+i*+ations at $ leel o)signi*+an+e?

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hypotheses testing umi - use this copy.pptx

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