tmp=c(0.73953449, -0.07331137, -1.06387272, 0.91819290, -0.68997371, -0.1385866,-0.72969955, -1.66933685, 1.65363166, 0.18335139) rnorm(10,0,1) tmp-.Last.value curve(dnorm(x,0,1),-3,3) curve(pnorm(x,0,1),.001,.999) qnorm(.025,0,1) [1] -1.959964 rnorm(100,0,1) abs(.Last.value)>1.959964 sum(.Last.value) bernoulli E(x)=p, Var(x)=p(1-p) binomial: E(x)=np, Var(x)=np(1-p) mean: E(x)=p, Var(x)=p(1-p)/n n=100 p0=.5 p1=.49 curve(dnorm(x,p0,sqrt(p0*(1-p0)/n)),.3,.7) curve(dnorm(x,p1,sqrt(p1*(1-p1)/n)),.3,.7,col="red",add=T) n=10000 curve(dnorm(x,p0,sqrt(p0*(1-p0)/n)),.45,.55) curve(dnorm(x,p1,sqrt(p1*(1-p1)/n)),.45,.55,col="red",add=T) qnorm(.05,p0,sqrt(p0*(1-p0)/n)) [1] 0.4917757 #We reject null if p