Running head: Hypothesis Testing Testing
An assignment on Hypothesis Testing Nabeena Khatri LC00016000035 Third semester Nepa !usiness Coege !iratnagar"15# Nepa
Author Note
This This assign assignmen mentt $as prepare prepared d %or &uantit &uantitati ati'e 'e method# method# !!A"(5 !!A"(5(3 (3 departm department ent o% &uantitati'e method taught by )r* Ram !abu Ka%e
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Running head: Hypothesis Testing Abstract
Testing o% hypothesis is an important aspe+t o% theory o% de+ision ma,ing* -ne o% the most important +onsiderations $hen beginning your resear+h $or, and %ormuating the resear+h probem is +onstru+ting the hypothesis* .eneray# hypothesis pro'ides +arity so that you +an %o+us on a resear+h probem* Ho$e'er# this is not essentia %or a study or resear+h $or,* A resear+her +an +ondu+t a 'aid in'estigation $ithout +onstru+ting a hypothesis* Ho$e'er# it is a$ays good to +onstru+t a hypothesis as it $i hep to narro$ do$n your %o+us o% resear+h* The signi%i+an+e o% a hypothesis ies in its abiity to bring dire+tion and spe+i%i+ity to your resear+h $or,*
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Running head: Hypothesis Testing
Acknowledgement
This assignment is a $onder%u e/perien+e %or me be+ause it gi'es us ,no$edge o% di%%erent +on+eptua and pra+ti+abe +urri+uum o% our study* There is 'ery 'ast in saying and doing* 'ery study has +uriosity about their +on+eptua studies* $oud i,e to e/press my spe+ia than,s to my sub2e+t tea+her )r* Ramesh !abu Ka%ey $ho ga'e me su+h a goden opportunity to do this $onder%u assignment on the topi+ o% )easure o% o+ation $hi+h aso heps me in doing ots o% resear+h and +ome to ,no$ about so many things* am reay than,s to them %rom my inner heart that heps in this assignment* m ma,ing this assignment not ony %or the mar,s but aso %or in+reasing my ,no$edge* aso apoogies %or $ea,ness# speing# grammati+a error or any ,ind o% mista,e in this assignment
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Running head: Hypothesis Testing Introduction
4hat is Hypothesis Testing Hypothesis testing is an a+t in statisti+s $hereby an anayst tests an assumption regarding a popuation parameter* The methodoogy empoyed by the anayst depends on the nature o% the data used and the reason %or the anaysis* Hypothesis testing is used to in%er the resut o% a hypothesis per%ormed on sampe data %rom a arger popuation* or e*g* 7tudents $ho re+ei'e +ounseing $i sho$ a greater in+rease in +reati'ity than studen ts not re+ei'ing +ounseing
!RAKN. 8-4N Hypothesis Testing n hypothesis testing# an anayst tests a statisti+a sampe# $ith the goa o% a++epting or re2e+ting a nu hypothesis* The test tes the anayst $hether or not his primary hypothesis is true* % it isnt true# the anayst %ormuates a ne$ hypothesis to be tested# repeating the pro+ess unti data re'eas a true hypothesis** Characterticts of Hypothesis
Cear and pre+ise*
Capabe o% being tested*
7tated reationship bet$een 'ariabes*
Limited in s+ope and must be spe+i%i+*
7tated as %ar as possibe in most simpe terms so that the same is easiy understand by a +on+erned* !ut one must remember that simpi+ity o% hypothesis has nothing to do $ith its signi%i+an+e*
Consistent $ith most ,no$n %a+ts*
Responsi'e to testing $ithin a reasonabe time* -ne +a nt spend a i%e time +oe+ting data to test it*
/pain $hat it +aims to e/pain9 it shoud ha'e empiri+a re%eren+e*
Types of Hypothesis
* II.
Nu hypothesis Aternati'e hypothesis
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Running head: Hypothesis Testing
Null hypothesis
4hat is a Nu Hypothesis A nu hypothesis is a type o% hypothesis used in statisti+s that proposes that no statisti+a signi%i+an+e e/ists in a set o% gi'en obser'ations* The nu hypothesis attempts to sho$ that no 'ariation e/ists bet$een 'ariabes or that a singe 'ariabe is no di%%erent than its mean* t is presumed to be true unti statisti+a e'iden+e nui%ies it %or an aternati'e hypothesis*
!RAKN. 8-4N Nu Hypothesis The nu hypothesis# aso ,no$n as the +on2e+ture# assumes that any ,ind o% di%%eren+e or signi%i+an+e you see in a set o% data is due to +han+e* The opposite o% the nu hypothesis is ,no$n as the aternati'e hypothesis* Hypothesis is denoted by 0*% a popuation mean is eua to hypothesi;ed mean then Nu Hypothesis +an be $ritten as H0: = 0 Alternative hypothesis
The aternati'e hypothesis is the hypothesis used in hypothesis testing that is +ontrary to the nu hypothesis* t is usuay ta,en to be that the obser'ations are the resut o% a rea e%%e+t <$ith some amount o% +han+e 'ariation superposed=* The Aternati'e hypothesis is negation o% nu hypothesis and is denoted by . % Nu is gi'en as 0: > 0 Then aternati'e Hypothesis +an be $ritten as 0: > 0 : ? 0 : @ 0 : 0
Confidence levels
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Running head: Hypothesis Testing n sur'ey samping# di%%erent sampes +an be randomy see+ted %rom the same popuation9 and ea+h sampe +an o%ten produ+e a di%%erent +on%iden+e inter'a* 7ome +on%iden+e inter'as in+ude the true popuation parameter9 others do not* A +on%iden+e e'e re%ers to the per+entage o% a possibe sampes that +an be e/pe+ted to in+ude the true popuation parameter* or e/ampe# suppose a possibe sampes $ere see+ted %rom the same popuation# and a +on%iden+e inter'a $ere +omputed %or ea+h sampe* A B5 +on%iden+e e'e impies that B5 o% the +on%iden+e inter'as $oud in+ude the true popuation parameter**The +on%iden+e e'e indi+ates ho$ i,ey it is that the popuation parameter# su+h as the mean# is +ontained in the +on%iden+e inter'a* The +on%iden+e e'e represents the per+entage o% inter'as that $oud in+ude the popuation parameter i% you too, sampes %rom the same popuation again and again* Thus# i% you +oe+ted one hundred sampes# and made one hundred B5 +on%iden+e inter'as# you $oud e/pe+t appro/imatey B5 o% the inter'as to +ontain the popuation parameter# su+h as the mean o% the popuation# as sho$n in the %oo$ing %igure*
Here# the hori;onta ba+, ine represents the %i/ed 'aue o% the un,no$n popuation mean# D* The 'erti+a bue +on%iden+e inter'as that o'erap the hori;onta ine +ontain the 'aue o% the popuation mean* The red +on%iden+e inter'a that is +ompetey beo$ the hori;onta ine does not* A B5 +on%iden+e e'e indi+ates that 1B out o% (0 sampes
Significance evel
The nu hypothesis is re2e+ted i% the p"'aue is ess than a predetermined e'e# E* E is +aed the signi%i+an+e e'e# and is the probabiity o% re2e+ting the nu hypothesis gi'en that it is true
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Running head: Hypothesis Testing as %oo$s: irst# the di%%eren+e bet$een the resuts o% the e/periment and the nu hypothesis is determined* Then# assuming the nu hypothesis is true# the probabiity o% a di%%eren+e that arge or arger is +omputed* inay# this probabiity is +ompared to the signi%i+an+e e'e* % the probabiity is ess than or eua to the signi%i+an+e e'e# then the nu hypothesis is re2e+ted and the out+ome is said to be statisti+ay signi%i+ant* Traditionay# e/perimenters ha'e used either the 0*05 e'e
4hen you do a hypothesis test# t$o types o% errors are possibe: type and type * The ris,s o% these t$o errors are in'ersey reated and determined by the e'e o% signi%i+an+e and the po$er %or the test* There%ore# you shoud determine $hi+h error has more se'ere +onseuen+es %or your situation be%ore you de%ine their ris,s*
Type I error
4hen the nu hypothesis is true and you re2e+t it# you ma,e a type error* The probabiity o% ma,ing a type error is E# $hi+h is the e'e o% signi%i+an+e you set %or your hypothesis test* A E o% 0*05 indi+ates that you are $iing to a++ept a 5 +han+e that you are $rong $hen you re2e+t the nu hypothesis* To o$er this ris,# you must use a o$er 'aue %or E* Ho$e'er# using a o$er 'aue %or apha means that you $i be ess i,ey to dete+t a true di%%eren+e i% one reay e/ists* Type II error
4hen the nu hypothesis is %ase and you %ai to re2e+t it# you ma,e a type error* The probabiity o% ma,ing a type error is F# $hi+h depends on the po$er o% the test* Gou +an de+rease your ris, o% +ommitting a type error by ensuring your test has enough po$er* Gou +an do this by ensuring your sampe si;e is arge enough to dete+t a pra+ti+a di%%eren+e $hen one truy e/ists* The probabiity o% re2e+ting the nu hypothesis $hen it is %ase is eua to 1F* This 'aue is the po$er o% the test 8e+ision
True
ase
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Running head: Hypothesis Testing ai to re2e+t
Corre+t
8e+ision Type rror " %ai to
1 " E= Re2e+t
re2e+t the nu $hen it is
%ase F= Type rror " re2e+ting Corre+t 8e+ision the nu $hen it is true
1 " F=
E=
Hypothesis testing is an important a+ti'ity o% empiri+a resear+h and e'iden+e"based medi+ine* A $e $or,ed up hypothesis is ha% the ans$er to the resear+h uestion* or this# both ,no$edge o% the sub2e+t deri'ed %rom e/tensi'e re'ie$ o% the iterature and $or,ing ,no$edge o% basi+ statisti+a +on+epts are desirabe* "hat is critical value and critical region#
n hypothesis testing# a +riti+a 'aue is a point on the test distribution that is +ompared to the test statisti+ to determine $hether to re2e+t the nu hypothesis* % the absoute 'aue o% your test statisti+ is greater than the +riti+a 'aue# you +an de+are statisti+a signi%i+an+e and re2e+t the nu hypothesis* Criti+a 'aues +orrespond to E# so their 'aues be+ome %i/ed $hen you +hoose the tests E
igure A
igure !
critical values on the standard normal distribution for $ % &.&'
igure A sho$s that resuts o% a one"taied I"test are signi%i+ant i% the test statisti+ is eua to or greater than 1*6J# the +riti+a 'aue in this +ase* The shaded area is 5
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Running head: Hypothesis Testing the test statisti+ is eua to or greater than 1*B6# the +riti+a 'aue in this +ase* The t$o shaded areas sum to 5
The +riti+a region o% the samping distribution o% a statisti+ is aso ,no$n as the E region* t is the area# or areas# o% the samping distribution o% a statisti+ that $i ead to the re2e+tion o% the hypothesis tested $hen that hypothesis is true*
a= 4hat is test statisti+ 4hat is its %ormua A test statisti+ is a standardi;ed 'aue that is +a+uated %rom sampe data during a hypothesis test* Gou +an use test statisti+s to determine $hether to re2e+t the nu hypothesis* The test statisti+ +ompares your data $ith $hat is e/pe+ted under the nu hypothesis* A test statisti+ measures the degree o% agreement bet$een a sampe o% data and the nu hypothesis* ts obser'ed 'aue +hanges randomy %rom one random sampe to a di%%erent sampe* A test statisti+ +ontains in%ormation about the data that is ree'ant %or de+iding $hether to re2e+t the nu hypothesis* The samping distribution o% the test statisti+ under the nu hypothesis is +aed the nu distribution* 4hen the data sho$ strong e'iden+e against the assumptions in the nu hypothesis# the magnitude o% the test statisti+ be+omes too arge or too sma depending on the aternati'e hypothesis* This +auses the tests p"'aue to be+ome sma enough to re2e+t the nu hypothesis* or e/ampe# the test statisti+ %or a I"test is the I"statisti+# $hi+h has the standard norma distribution under the nu hypothesis* 7uppose you pe r%orm a t$o"taied I"test $ith an E o% 0*05# and obtain a I"statisti+
b= Ho$ de+isions are made on the basis o% statisti+a +a+uations 7tatisti+a de+isions are de+isions made on the basis o% obser'ations o% a phenomenon that obeys probabiisti+ a$s that are not +ompetey ,no$n* As an e/ampe# et us +onsider the disin%e+tion o% $ater by +horination* The amount o% +horine to be added shoud depend on the a'erage number o% ba+teria per unit 'oume* The 'aue o% # ho$e'er# is not ,no$n and is estimated %rom the resuts M1# M(#****Mn o% a +omputation o% the
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Running head: Hypothesis Testing number o% ba+teria in n independenty see+ted unit 'oumes o% $ater* n the simpest mode it is assumed that Mi# %or i > 1#***#n# has a oisson distribution $ith the un,no$n mean
+= 4hat is the importan+e o% hypothesis testing in business !usiness o$ners i,e to ,no$ ho$ their de+isions $i a%%e+t their business* !e%ore ma,ing de+isions# managers may e/pore the bene%its o% hypothesis testing# the e/perimentation o% de+isions in a PaboratoryP setting* mportan+e o% hypothesis in business are: (ata Collection
As hypothesis testing is purey a statisti+a e/er+ise# data is amost a$ays needed be%ore per%orming a test* 8ata may be obtained %rom e+onomi+ resear+h agen+ies or management +onsutan+y %irms# $ho may e'en +arry out the hypothesis testing on beha% o% the business* 8ata are +ompied %or a gi'en hypothesis* 7o i% a business $ishes to e/pore ho$ e+onomi+ gro$th a%%e+ts a %irms pro%its# the management +onsutan+y $i i,ey +oe+t data +on+erning gross domesti+ produ+t gro$th and the pro%it margins o% the +ompan y o'er the past 10 or (0 years* The )rocess
Hypothesis testing is per%ormed $ith spe+iai;ed statisti+a so%t$are that e/amines the reationship bet$een 'ariabes o% 'ery arge sampes* 8ata are %ed into the system and the program does the rest* t is up to the statisti+ian to interpret the resuts* There are t$o main 'ariabes the statisti+ian is oo,ing %or* The %irst is that o% PaP itse%* The arger the 'aue o% Pa#P the greater the impa+t o% P/P on Py*P The other is that o% the +riti+a 'aues* Criti+a 'aues di%%er depending on the type o% statisti+a test +arried out# but o%ten 'aues represent signi%i+an+e e'es o% 1# 5 or 10 per+ent* Re2e+ting the nu at 1 per+ent impies absoute +on%iden+e that P/P has no e%%e+t on Py*P -n the %ip side# i% the statisti+ian is unabe to re2e+t the nu e'en at the 10 per+ent
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Running head: Hypothesis Testing e'e# then he +oud say $ith a reasonabe e'e that P/P does ha'e an impa+t on Py#P and at a magnitude o% Pa*P
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Running head: Hypothesis Testing Conclusion
A hypothesis is generay a spe+uati'e statement that needs to be 'eri%ied in a resear+h $or,* 8uring hypothesis %ormuation# it is important to ,eep the statement simpe# re+ise and +ear# and deri'e it %rom an e/isting body o% ,no$edge* T$o types o% hypothesis +ategories are resear+h and aternate* Resear+h hypothesis +an be +assi%ied as nu hypothesis# hypothesis o% di%%eren+e# hypothesis o% asso+iation and hypothesis o% point"pre'aen+e* The main %un+tion o% an aternate hypothesis is to e/pi+ity spe+i%y the reationship that $i be +onsidered *
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