Summary STAT 2000 Unit 3

statisticsunit3Test
hypothesistestsignificancetest determineswhethertorejectaclaimabouta populationofinterestbasedonevidencestrength
weconducthypothesisteststoseewhetherdatasupportsaclaimaboutavaluefortheparameter theystartbyestablishing
nullhypothesis Ho representssomestatusquoorbaseline alternativehypothesis Ha representssomedifferentclaim
whenhypothesistestsareconductedwealwaysconsiderclaimsaboutapopulationmean m orpopulationproportion p
p valueprobabilityofobservingoursampleoutcomeifthenullhypothesisweretrue significancelevel a cutoffvalve 1.05
2competingclaimsdataprobability decisionbasedonsampledataandprobabilityformalizedinferenceprocedure
significancetestusesdatatosummarizetheevidenceabouta hypothesis categorical proportion quantitativemean
theHovaluerepresentsnochangetheHavaluerepresentsachangesmallpvaluerejectHo largepvalue donotrejectHo
onesided2testmeansyouonlytestonesideofthenullvalue cord usea 2teststatisticnormalmodel toconducta HT
wosided testmeansyoutestbothsides cands ofthenullvalue teststatistic z p po Pogo n
typeIerrorHoistruebutrejected typeIIerrorHoisfalsebutnotrejected Pd it x mo s F dt n t
sointestimatesinglenumberthatisourbestguessfortheparameter conti
vaivedfffneihptafatle.plfusible
vspossiblecontainspvalues
intervalestimateintervalofnumbersthatisbelievedtocontaintheactual centermeanofsampling dist
confidenceinterval
pgighpepetif.gg marginoferror marginoferrorcritical value standarderror

thesamplingdist ofPtellsushowfarweexpect5tovaryfromthetrue population parameter
sample's
plnavg.tt samples
accordingtotheempiricalruleDiswithin about 2SDofpin951of piswithinabout 2s of
interpretingaconfidenceintervalwearect confident thatourinterval lowerboundupperbound capturesthetruepopparameter
constructingaconfidenceintervalforapopulationproportion pointestimate criticalvalue standarderrorofsamplingdist
samplesizenp 215 and all 51215shape statcrunch I be z Plypt
randomsample center independentobservationsspread
SD PqSE Pg

Éfianftp.afhYpiYnpfpYYn yyfuel flap
halftime
af ah
if ifyYajvheyYa Yisve

themarginoferrorforaconfidenceintervalincreasesastheconfidencelevelincreasesanddecreases asthesamplesizeincreases
moreconfident highercapturerate largercriticalvalue largermarginoferror
argersamplesize lessvariability smallerstandarderror smallermarginoferror
estimatingpopulationproportion no p 11 p ME use0.5 estimatingpopulationmean n m roundup
twosidedhypothesistestwithsignificancelevel givesthesameconclusiona confidenceintervalwith11 a 100 confidence

iniaiie in iii iai i stmiiidiiiiiiioin
stepsforperformingaHypothesisTest
Istatethehypothesis onesidedgreaterlessthanHotwosideddifferentfromHovalue
2Checkconditions
3Teststatisticandpvalue
4makeconclusions
symbols
D sampleproportion statistic x̅ samplemean
PohypothesizedproportionfromHo m hypothesizedmean fromHo
n samplesize s SDfromthesample
n samplesize
usestatcrunchforpvalue
2scorenormalcalculator mean o SD



i iiiiii initiatia.in


I t.isiiii iiia i i ini
useTcalculator DF n 1 whenJDcomesfromthesample
usenormalcalculatorwhenJDcomesfromthepopulation akaacalculator
Irare

alwaysmakeyourconclusionsin contextoftheHa
alwayssayyouhavesufficientinsufficientevidenceforHa

significancelevel istheprobabilityofmakingatypeI error