and draw10,000randomsamplesof size 20each.Lookatthesimulatedsamplingdistributionof , whichishighlydiscrete.Is it bell-shapedandsymmetric?UsethistohelpexplainwhytheWaldconfidenceinterval performspoorlyinthiscase. (c) When = 0, showthattheWaldconfidenceintervalis(0,0).As approaches0,explain

and draw10,000randomsamplesof size 20each.Lookatthesimulatedsamplingdistributionof ˆπ, whichishighlydiscrete.Is it bell-shapedandsymmetric?UsethistohelpexplainwhytheWaldconfidenceinterval performspoorlyinthiscase.

(c) When ˆπ = 0, showthattheWaldconfidenceintervalis(0,0).As π approaches0,explain why P(ˆπ = 0) approaches1,andthustheactualprobabilitythattheWaldinterval contains π approaches0.

(d) NowusetheWilson’sscoreinterval(formula(4.7))withsimulationorinthe ExploreCov-

erage app. Draw1000samplesofsize20eachwhen π = 0.06. Whatpercentageofthe95%

confidence intervalsactuallycontained π? Explainhowthisrelatestotheinterpretation for confidenceintervals.