Usesimulationoranapp,suchasthe ExploreCoverage app at www.artofstat.com/web-apps, to exploretheperformanceofconfidenceintervalsforaproportionwhen n is notverylarge and maybenear0or1,byrepeatedlygeneratingrandomsamplesandconstructingthe confidence intervals.Takethepopulationproportion =

Usesimulationoranapp,suchasthe ExploreCoverage app at www.artofstat.com/web-apps, to exploretheperformanceofconfidenceintervalsforaproportionwhen n is notverylarge and π maybenear0or1,byrepeatedlygeneratingrandomsamplesandconstructingthe confidence intervals.Takethepopulationproportion π = 0.06, n = 20, andconfidencelevel 95%.

(a) UsetheWaldconfidenceinterval(formula(4.8)).Choose10samplesofsize n = 20. Now drawanother10.Howmanyofthe20Waldintervalscontainedthetruevalue, π = 0.06?

Howmanywouldyouexpecttocontainit?Toseethatthisisnotafluke,simulateby drawing1000randomsamplesofsize n = 20 and constructing1000confidenceintervals.

What percentagecontain π = 0.06? Whatdoesthissuggest?

(b) Usingsimulationoranapp,suchasthe Sampling DistributionoftheSampleProportion app at www.artofstat.com/web-apps, let π =