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AP Stats: Inference Guidelines Remember to always use PANIC or PHANTOMS during inference!One or Two?ProcedureModelchart to useParameter use in HoEstimate from sampleFormulafor CI or test statisticAssumptions/ConditionsCalculatorSTAT TESTSProportionsFind z* on t-distribution at ∝ row in Confidence Level specifiedOne sample1-proportion z-intervalzppp±z*?pqnIndependentRandom < 10% of populationnp ≥ 10 and nq ≥ 10A: 1-Prop ZInt1-proportion z-testz=p-popoqon5: 1-Prop ZTestTwo independent groups2-proportion z-intervalp1-p2p1-p2p1-p2±z*?p1q1n1+p2q2n2IndependentRandom < 10% of populationIndependent groupsnp ≥ 10 and nq ≥ 10 for both groupsB: 2-Prop ZInt2-proportion z-testz=p1-p2-0ppoolqpooln1+ppoolqpooln2 Where ppooled=p1+p2n1+n26: 2-Prop ZTestMeansWith df=n-1For 2 groups, use df on calcOne samplet-intervaltμyy±tn-1*?sn Independent Random< 10% of populationNearly Normal8: TIntervalt-test t=y-μsn2: T-TestTwo independent groups2-sample t-intervalμ1-μ2y1-y2y1-y2±tdf*?s12n1+s22n2 Independent (from each other)RandomNearly Normal or large nIndependent groups0: 2-SampT int2-sample t-testt=y1-y2-(μ1-μ2)s12n1+s22n2 4: 2-SampT TestMatched pairsPaired t-intervalμddd±t*n-1?sdnPaired dataDifferences in pairs are independentRandom Differences nearly Normal8: TIntervalPaired t-testtn-1=d-0sdn2: T-TestDistributionsCategoricalOne sampleGoodness of fitχ2χ2χ2=Obs-Exp2Expdf = # of categories – 1 Counted dataIndependent cellsRandomExp counts ≥5D: χ2 GOF-TestMany groupsHomogeneity χ2=Obs-Exp2Expdf = (rows – 1)(columns – 1)C: χ2-TestMATRIX EDIT [A](obs) & [B](exp)Independence/Association categoricalMany groupsIndependenceSame as above, plus…< 10% of populationAssociation slopequantitativeOne sampleLinear-Regression conf. intervaltβ1b1b1±t*SEbdf = n–2Straight EnoughQuantitative DataRandom/IndependentRandom Residual PlotNearly Normal/No outlier Check histogram of residualsG: LinRegT IntLinear regression t-testt=b1-β1SEbdf = n–2F: LinRegT testPANICP = Parameters (DEFINE VARIABLES)A = Assumptions (EXPLAIN)N = Name of Interval I = Interval (WORK)C = Conclusion (IN CONTEXT)PHANTOMSP = Parameters (DEFINE VARIABLES)H = Hypothesis (Ho, Ha)A = Assumptions (EXPLAIN)N = Name of TestT = Test statistic (WORK)O = Obtain p-valueM = Make DecisionS = State Conclusion (IN CONTEXT)Sample Sizeto find the sample size, always use Margin of Error ME=CV*SEErrorsType I: Null is true, but we reject itType II: Null is false, but we fail to reject itAll Formulas are set up asCI = statistic ± (critical value)?(standard error)z or t = statistic-nullSEHypotheses for Tests1-proportion z-testHo: p≥, ≤, or= valueHa: p<, >, or≠ value2-proportion z-testHo: p1-p2=0Ha: p1-p2≠01-sample t-testHo: μ≥, ≤, or= valueHa: μ<, >, or≠ value2-sample t-testHo: μ1-μ2=0Ha: μ1-μ2≠0Matched pairs t-testHo: μd=0Ha: μd≠0χ2 goodness of fitHo: ___ are uniformly distributedHa: ___ are not uniformly distributedχ2 test of homogeneity Ho: ___ have the same distribution across ______(categories).Ha: ___ do not have the same distribution.χ2 test for independenceHo: ___ and ___ are independent.Ha: ___ and ___ are not independent.Linear Regression t-testHo: There is no association between ___ and ___. β1=0Ha: There is an association between ___ and ___. β1≠0 ................
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