and 2 = 0.10. Simulateamillionsample proportionsfromeachtreatmentwith n1 = n2 = 50. Constructhistogramsfor 1~2 and for log(1~2). Whichseemstohavesamplingdistributionclosertonormality?(This showsthatsomestatisticsmayrequireaverylargesamplesizetohaveanapproximate normal samplingdistribution.) (b) Fromamultivariateversionofthedeltamethod,astandarderrorforthelogrelativerisk is 11

and π2 = 0.10. Simulateamillionsample proportionsfromeachtreatmentwith n1 = n2 = 50. Constructhistogramsfor ˆπ1~ˆπ2 and for log(ˆπ1~ˆπ2). Whichseemstohavesamplingdistributionclosertonormality?(This showsthatsomestatisticsmayrequireaverylargesamplesizetohaveanapproximate normal samplingdistribution.)

(b) Fromamultivariateversionofthedeltamethod,astandarderrorforthelogrelativerisk is

¼

1−π1 n1π1

+ 1−π2 n2π2

. Forcomparingincidence of ararediseasebetweentwopopulations,state the conditionsforthedistributionsofcountstobeapproximatelyPoisson,andconclude that thestandarderrorintermsofthePoissonmeansisapproximately

¼

1

μ1

+ 1

μ2

.