phat1 <- rep(NA,100)
 set.seed(132)
for(i in 1:100){
  phat1[i]=sum(sample(c(0,1),5,replace=T,prob=c(0.3,0.7)))/5
 }
phat2 <- rep(NA,100)
 set.seed(132)
for(i in 1:100) {
  phat2[i]=sum(sample(c(0,1),10,replace=T,prob=c(0.3,0.7)))/10
 }
phat3 <- rep(NA,100)
 set.seed(132)
for(i in 1:100){
  phat3[i]=sum(sample(c(0,1),50,replace=T,prob=c(0.3,0.7)))/50
 }
phat4 <- rep(NA,100)
 set.seed(132)
for(i in 1:100){
  phat4[i]=sum(sample(c(0,1),100,replace=T,prob=c(0.3,0.7)))/100
 }


windows(10,2.5)
par(mfrow=c(1,4),las=1,mar=c(4,4.5,2,2),oma=c(1,1,1,1),mgp=c(3,0.7,0.1))
hist(phat1,main="",prob=T,las=1,cex.lab=1.7,cex.axis=1.7,ylim=c(0,11),xlim=c(0,1),xlab="",breaks=c(0:27*0.038))
axis(side=1,lab=F)
#mtext(c("0.5","0.6","0.7","0.8","0.9"), at=c(0.5:0.9),side=1,cex.axis=1.7,line=1)
mtext(side=1,line=3,"Proportion",cex=1.2)  
mtext(side=3,line=1,"100 samples, size n=5",cex=1.2)
hist(phat2, main="",prob=T,las=1,cex.lab=1.7,cex.axis=1.7,ylim=c(0,11),xlim=c(0,1),xlab="",breaks=c(0:20*0.035+0.3))
axis(side=1,lab=F)
#mtext(c("0.5","0.6","0.7","0.8","0.9"), at=c(0.5:0.9),side=1,cex.axis=1.7,line=1)
mtext(side=1,line=3,"Proportion",cex=1.2)  
mtext(side=3,line=1,"100 samples, size n=10",cex=1.2)
hist(phat3,main="",prob=T,las=1,cex.lab=1.7,cex.axis=1.7,ylim=c(0,11),xlim=c(0,1),xlab="",breaks=c(0:10*0.04+0.5))
axis(side=1,lab=F)
#mtext(c("0.5","0.6","0.7","0.8","0.9"), at=c(0.5:0.9),side=1,cex.axis=1.7,line=1)
mtext(side=1,line=3,"Proportion",cex=1.2)  
mtext(side=3,line=1,"100 samples, size n=50",cex=1.2)
hist(phat4,main="",prob=T,las=1,cex.lab=1.7,cex.axis=1.7,ylim=c(0,11),xlim=c(0,1),xlab="",breaks=c(0.5+0.04*0:10))
axis(side=1,lab=F)
#mtext(c("0.5","0.6","0.7","0.8","0.9"), at=c(0.5:0.9),side=1,cex.axis=1.7,line=1)
mtext(side=1,line=3,"Proportion",cex=1.2)  
mtext(side=3,line=1,"100 samples, size n=100",cex=1.2)
mean(phat1); mean(phat2); mean(phat3); mean(phat4)
sd(phat1); sd(phat2); sd(phat3); sd(phat4)