TRANSCRIPT:
There areafewassumptionsassociatedwiththet‐statistic.First,itisassumedthatallobservationsareindependent.
Second,thet‐statisticassumesthatthedatacomefromapopulationforwhichthedatawouldbenormallydistributedif
datawereobtainedfromallmembersofthepopulation.
Wedohypothesistestswiththet‐statisticthesameaswiththez‐statistic.Totesthypotheseswiththet‐statistic,westart
withthepopulationforwhichwedonotknowthemeanandvariance.Usually,thispopulationisatreatmentgroupof
somesort,fromwhichwehavedataonasample.
Thegoalistouseasampleofthetreatedpopulationtodetermineifthetreatmenthadanyeffectonthepopulation.
Thenullhypothesisfortestingwiththet‐statisticisthesameaswiththez‐statistic.Thenullhypothesisisalwaysthatthe
treatmenthadnoeffect;
or,thatthepopulationmeanisunchanged.Justlikeinunit2,thenullhypothesisprovides
specificvaluesforthepopulationmean.
Differentfromz‐statistichypothesistests,isthatt‐statistictestsusethesampledatatoprovideavalueforthesample
mean,andthevarianceandestimatedstandarderrorarecomputedfromthesampledatainsteadoffromthepopulation
parameters.
So,fromjustlookingattheformulaforthet‐statistic,wecanmakeafewinferencesabouttherelationshipbetweenthe
differenceinthemeans(thenumerator)andtheestimatedstandarderrorofthemean.Forinstance,
whenthe
differenceinmeansismuchlargerthantheestimatedstandarderror,wegetalargertvalue(positiveornegative).
Ifthedifferencebetweenthesampleandpopulationmeansislargerelativetotheestimatedstandarderror,weare
morelikelytorejectthenullhypothesisbecausethedifferencesindicatesthesamplemeanisverydifferentfromthe
populationmean.
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