问题标题:
HypothesisTestingInastudyofirondeficiencyamonginfants,thebloodhemoglobinlevelswerecomparedbetweentwosamplesofinfants,whofollowdifferentfeedingregimes.Onegroupconsistedofbreastfedinfants,whiletheothergroupwasfedwi
问题描述:
HypothesisTesting
Inastudyofirondeficiencyamonginfants,thebloodhemoglobinlevelswerecomparedbetweentwosamplesofinfants,whofollowdifferentfeedingregimes.Onegroupconsistedofbreastfedinfants,whiletheothergroupwasfedwithastandardbabyformulawithoutanyironsupplements.Thesummaryofresultsonbloodhemoglobinlevelsforinfantsat12monthsofageisasfollows:
GroupSamplesizeMeanStandarddeviation
Breast–fed2313.31.7
Babyformula1912.41.8
Istheresufficientevidencetoindicatethatthemeanbloodhemoglobinlevelishigheramongthebreast-fedbabies?Testat=0.05.
[sp2=3.0475;t=1.663;DonotrejectH0]
李琥回答:
Hypothesis:Astatementaboutthevalueofapopulationparameterdevelopedforthepurposeoftesting.
Hypothesistesting:假设检验Basedonsampleevidenceandprobabilitytheory;Usedtodeterminewhetherthehypothesisisareasonablestatementandshouldnotberejected,orisunreasonableandshouldberejected.
StepOne:Statethenullandalternatehypotheses
NullHypothesisH0零假设或空假设:Astatementaboutthevalueofapopulationparameter
AlternativeHypothesisH1备择假设:Astatementthatisacceptedifthesampledataprovideevidencethatthenullhypothesisisfalse
Threepossibilitiesregardingmeans(Thenullhypothesisalwayscontainsequality.)
H0:μ=0H0:μ≤0H0:μ≥0
H1:μ≠0H1:μ>0H1:μCriticalz
p-Value:Theprobability,assumingthatthenullhypothesisistrue,offindingavalueoftheteststatisticatleastasextremeasthecomputedvalueforthetest
DecisionRule:Ifthep-Valueislargerthanorequaltothesignificancelevel,a,H0isnotrejected.Ifthep-Valueissmallerthanthesignificancelevel,a,H0isrejected.
Calculatedfromtheprobabilitydistributionfunctionorbycomputer
P-valuelevelofsignificance:failtorejectH0
StepFive:Makeadecision.
One-TailedTestsofSignificance:Thealternatehypothesis,H1,statesadirection
Two-TailedTestsofSignificance:NodirectionisspecifiedinthealternatehypothesisH1.
Testforthepopulationmeanfromalargesamplewithpopulationstandarddeviationknown
Proportion:Thesampleproportionispandpisthepopulationproportion.
Thefractionorpercentagethatindicatesthepartofthepopulationorsamplehavingaparticulartraitofinterest.
TestStatisticforTestingaSinglePopulationProportion
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