Question

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2.26 Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. The filling processes can be assumed to be normal, with standard deviations of o, = 0.015 and o2 0.018. The quality engineering department suspects that both machines fill to the same net volume, whether or not this volume is 16.0 ounces. An experiment is per- formed by taking a random sample from the output of each machine. Machine 1 Machine 2 16.03 16.01 16.02 16.03 16.04 15.96 15.97 16.04 16.05 15.98 15.96 16.02 16.05 16.02 16.01 16.01 16.02 15.99 15.99 16.00 a) WE WANT TO OETERMIN iF THE a ma CHiaES ARE VOLUME of SofT DRIAK, VE HAVE NO PRioR xpeCTATICN TRAT ove wil BE HI6HER THAN THE PREouciNG TE SAME AveAie To BE Trro ExpLAi w reu STATED eTER HOU SHOULD ne STATE STATISTICALypeses iu wis maNER. MypenES iF PN EuivEER HANOFD you is D4TA WI e ExpiwATic , KIHAT GuesTions wouuD THE you of E CATn Peevioe AT EAST 3 io4icAL WANT TD AsK im/eR To DETEmine gues TroNs e) ExpuANATION oF AuO A usin E previoro o4TA Gpy iT laTe Jne IT is ResT To r e DTA N CAe coum puT A LAB foe mACHIN (MI oe A2) is A 2 m THE LABAR SHO LD BE T VEnsus A coNTINUeus wmBex d) Pier Tee OATA iuA THE mEnus Iucuoe AT LensT oe pe THAT uiLL Hep o4TEmiE it THERE is A Difreneuce in wAY WHAT DesRis per iNDICATE To 7 THE ANes hy wceusisTO w/youe yeasis How wouco you pai youre in part a . Temy hngpo TesT? Te 04T PaepuceD AnE what uOULO Be E COMELS/ON of A yen EPLAIN 17 w/THEUT usIs Any STATISTICAL Teams F) ReperT uasnew e B7 ASSume TanT E OATA n hy petuESis iN Pae 7 4-AppeaximaTay GOAKLDE Fiecy ceSiSTeT i e u wwa7 wouLD o Rave epetep weaT weD yo AwD Hwwouco mu ExpLA Tis 3/ ASTATSTICAL Tns ow a hoo wawn Jmr, wwic ees eT Am -Snpce t-Tes7 mpi TE papuATens memus iw Jmp.usE TRE OaT Tiaru pu VaRinecd. Pusuen TE Focewing wlerT K TRE PvRue, ASSuminé uE useD A tco-SToeD ATeRNATIV wuAT IS E PvALu if WE uSe THE ATERNATINE H -wy Ae HE AnsuEns Te THE Tuo Bree DinRTy AeOuG DFfene As Sumie6 e use ATeo-DED ATRATNE, weeT CAN WE CcuOE Aera Aypoesis ExpLN in STATISTICA TOms hp Aso is pAie Eweur A) AssumE kE A LD TeE ommCRCE DEPATng is AuoiTNG THE Pc moRRow, To L TRAT OUR e oz, Ser T DIES ArE 2 y ce e Avene, Assume TeAT TH Comm. Depr is NT NcEReo ABu7 mainC vs mACiA 3 Ihay oney careE ABru Ter papuATiON F SofT ORIAKS Cemine aut oF RE pLm WRAT wOup Be HyporTHESES PrpnapaimE EvacurTiNG THE peaT Feu THE Cemm, Dpr. T usE wHEu STATISTE To DETERMiag iF THERE 1S EVDENCE or D eAr Expni ETERMINE iF THE mACHinEs ARE pReouciNG 7HE SAME AVnAhe a WE WANT TO VOLUME of SofT DRINK, VE HAVE NO PAIOR EPECTATION THAT oNE WLL BE HIGHER THAN HE OTHER HOW SHOULD ne STATE STATISTICAL Hypoeses iu Tis mANNER To BE TSTEO ExpLAi WHy eu STATED Hypenies EugivEtR HAN OFD you s DATA WITH NO EpLAwATiCA, KIHAT uESTiONs wouuD THE you b-) IF AU of THE OATAProvioE eimpen To DETENMINE ExpLawATION gueiry AT LEAST 3 L0GICAL WANT TD ASK guesTioNS c) usint TE proviaep 04TA opy iT 1ATO Jmp IT is BesT To r A OTA oE Co puT A LABEL Foa MACHIAR CMI oF coums THE LABAR SHOKLD BE XT in A 2 coLumA OR CONTINUOUS umBeR VEnsus A d) PuT Tre OATA iu A THAT nuil Hap DETenmise it Ttene is A DifrERencer in Way THE mEnNs, lucuoe A7 LenST one pur you ABeuT WHAT DUES is per INDICATE TO THE AVERAES Vhy hayparesis you Epiain your yon IN part a. TOTMY weeusisTOUT wlyoue Aupermesis TosT? Muu ARE e) Suppese THE DATA PaopuceD How wouLD what vuayLD Be THE cOMCLusioN or A ONCusiON TO A How wouo ENGINEER WHo HAS NO BACINGROUD N STATISTies memwiN ExplaiN 17 wiTHeuT usING Ary STATISTI CAL TEnms P RepenT gSTeN e Bu7 ASSume TuAT THE OATA AnE hy potHESi's iN PAR 74 -praximaTeay COACLUDE AMow penfoRm DetnclT GPTion FniRly CONSISTENT wiTH Te uL WHAT weruLD you HavE EpecTep WHAT WOUD you STATISTICAC TAns AND Hw wouco vou EXDLAIA Tuis vsiA No memus in Jmp.USE TRE two-sampue t-Tes7 ampmin TuE papuLATION JmP, wyiu ees eT ASume que VARIANces. AesuEn TE FoLLOuinG KHAT iS TRE PVAue, ASSuminG WE uSeD A teo-SioeD ALTERNA7e WHAT IS TE PVALUE If we uSe THE ATERNATIVE He Ans THE AnsuEns To THE Two guesrens DinRTY why PBOUE DIFFemrUT As Sumia6 ue use A Two-SiDED ATERUATINE, WHA7 CAN WE CCUOE ABerd F u Ay poTAESISExpLN A) AssumE kE ARE Bro THE GemmEnce Depar Temeut is AuDitING THE Pim PmoRRow, TO Vemify TAT aun looz. Sof7 DRukS AnE FTu ACy er en Avene, Assume TRAT THE Comm. Pept. iS AaT ONCENNED ABUUT macHinE I us macuiae 3Thay oncy cace Ashu in STATISTICAL TErms AND ASo IN pLAiw ENtuse. OF SorT ORIAKS cerninG aur Of THE PimT WRAT wouuD B ApprapriArE The papueATION HypuTHEses Fore THE Comm DepT. To uSE nHEN STATISsTi sremy Evacurrias TE peaNT nloT Expeain, To DETERMINN iF THERE Is EVIDENCE or he

Answer 1

2.26

a)

Null Hypothesis(H0):

Two machines are producing the same average volume of soft drink. The difference between the average volumes of soft drink for two machines is not significantly different from 0.

μιΕμΕ Ρ μ0 μΕμ2Ε0

Alternative Hypothesis(H1):

Two machines are not producing the same average volume of soft drink. The difference between the average volumes of soft drink for two machines is significantly different from 0.

(two-tailed test)

μ14μ2 -μ70 μ- μ2Η0

We stated the hypotheses in this manner because we do not have any prior expectation that one will be greater than the other or less than the other. So, we will used two-tailed test procedure.

($\mu1$ =Population mean volume of soft drink for machine 1 and =Population mean volume of soft drink for machine 2).

42

b)

1. What is the given data about?

2. What are the units?

3. Do the population standard deviations for 2 machines is known? If known, what are they?

Questions 1 and 2 are asked in order to interpret the conclusions of the test.

Question 3 is asked because if population std.deviations are given, they have to be used in calculations. Otherwise sample std.deviations are to be used.