Round all answers to at least 3 decimal places and assume, unless otherwise noted, that .05

1. TenpercentofpeopleintheUSareleft-handed.Aresearcherwantstotestthetheorythatcreativepeoplearemorelikelytobeleft-handedthantheaverageperson.Sherandomlyselects9artistsinthecommunityandfindsthat2ofthemarelefthanded a.Doesthisdataprovideevidencethatartistsarestatisticallymorelikelytobeleft-handed?Includeallstepsforfullcredit.(8pt)

b.Iftwooftheartistsinhersampleweresiblings,whichassumptionofthistestwouldhavefailed?(1pt)

2. Thereisavirusspreadingacrossthepopulationofacountry.Therearenoobvioussymptoms,soitisnotpossibletodetermineifsomeoneisacarrierunlesstheyaregivenabloodtest.Medicalofficialswanttostudyanindividualwhoiscarryingthevirus,sotheyplantorandomlyselectasampleofthepopulationtotest.However,thereissomeargumentindeterminingthesizeofthesample:ifthesamplesizeistoosmall,thereisariskofnotfindinganycarriers,butifitistoolarge,resourceswillbeusedinefficiently.

Adecisionismadetoobtainasampleof15individuals.Assumingthat3%ofthepopulationisactuallyinfectedwiththevirus,isthissamplesizeadequate?Justifyyouranswer.(3pt)