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LECTURE 15

TESTING FOR EQUALITY OF VARIANCES FROM 2 INDEPENDENT POPULATIONS:

Why is this test important?________________________________

___________________________________________________________

Test statistic:____________________________

where s 1 2 is the larger of the two ariances

the hypotheses are: _________________

_________________

the ! "istri#$tion loo%s li%e:

so the "ecision r$le is always: __________________________

__________________________

To fin" the critical al$e:

1& !in" n$merator "egrees of free"om: n 1 '12& !in" "enominator "egrees of free"om: n 2 '1(& Loo% $p the critical al$e on Ta#le )*+ page ,-( .ass$ming */5 le el

of significance which m$st #e "i i"e" #y two #eca$se this is a two'taile"test&

0R CE ! R 3 4 6 T'TE T ! TW 0 0UL)T4 : flow chart

1&__________________________________

2&__________________________________

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(&__________________________________

e7ample 1: ) professor in the )cco$ntancy "epartment of a #$siness schoolclaims that there is "ifferent aria#ility in the final e7am scores ofst$"ents ta%ing the intro"$ctory acco$nting co$rse as a a re8$irement thanfor st$"ents ta%ing the co$rse as part of their ma9or Ran"om samples of 1(non'acco$nting ma9ors an" 1/ acco$nting ma9ors were ta%en from theprofessor;s class roster in his large lect$re an" the following res$lts werecomp$te" #ase" on the final e7am scores:

n )

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Minitab Instructi ns:To test equality of variances:

Data must be in one column with the code for groups in asecond column.Choose stat

Choose ANOVA Choose Homogeneity of VarianceSelect data variable in "response"Select code variable in "factors"Click OK

ASSIGNMENT:

Rea" in yo$r te7t#oo%: pages -/,'-1(

Written assignment:#y han": pg -1( @1/*5(#y comp$ter: 1& pg -1( @1/*5=

2& Using the pro#lem written #elow or on the ne7t page"o the complete in"epen"ent t'test process* 3o not ma%e anyass$mptions a#o$t the ariances'yo$ m$st test to "eterminewhether the ariances are e8$al or not then choose an" "othe appropriate t'testA

0ro#lem: The "irector of training for a company man$fact$ring electronice8$ipment is intereste" in "etermining whether "ifferent training metho"sha e an effect on the pro"$cti ity of assem#ly line employees* he ran"omlyassigne" -2recently hire" employees into two gro$ps of 21 each* The firstgro$p recei e" comp$ter'assiste" in"i i"$al'#ase" training an" the secon"gro$p recei e" team'#ase" training* Upon completion of training theemployees were e al$ate" on time .in secon"s& it too% to assem#le a part*The res$lts are as follows:

Comp$terBin"i i"$al training Team'#ase" training

1,*- 1=*+ 22*- 1(*2/*+ 1,*( 1 *+ 1 */21* 1=* 1,*( 2/*1-*1 1+*+ 15*= 1+*11=*1 1,* 1 */ 2 *21=* 1,*( 21*+ 2/*1-*+ 1=*/ (/*+ 2-*+16.5 1+*+ 2(*+ 1+*-

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1=*2 1+*- 2(*2 2/*11=*- 1=* 12*( 15*218.5 1=*/

Using a */5 le el of significance is there e i"ence of a "ifference in thea erage assem#ly times .in secon"s& #etween employees traine" in a comp$ter'

assiste" in"i i"$al'#ase" program an" those traine" in a team'#ase" program?