diff.mean=function(data,x,y,N,mux){
  data=as.name(data); x=x; y=y; n=length(x); N=N; mux=mux
  fpc=(1-n/N); plot(x,y,main=data)
  ybar=mean(y); xbar=mean(x); d=y-x
  dbar=mean(d); vard=var(d); muhat.yD=mux+dbar
  vhat.muhat.yD=(fpc)*(vard/n)
  bound=2*sqrt(vhat.muhat.yD)
  lower=muhat.yD-bound; upper=muhat.yD+bound
  cat("","\n","Results from SRS: Data =",data,"\n",'Estimation method = Difference estimator of muy','\n',"N =",N,"n =",n,
      "\n","FPC =",fpc,"\n","MuyD =",muhat.yD,'Variance of differences =',vard,'\n',"Vhat muhat.yD =",vhat.muhat.yD,
      "\n","Bound =",bound,"\n","Lower Bound =",lower,"Upper Bound =",upper,"\n","")
  results=list(mux=mux,data=data,muhat.yD=muhat.yD,n=n,vard=vard,N=N,fpc=fpc,x=x,y=y,vhat.muhat.yD=muhat.yD,bound=bound,
               lower=lower,upper=upper)  
}

# to use the function with its call:
# diff.mean(data,x,y,N,mux)

# data: name of dataset, in quotes
# x: vector (data)
# y: vector (data)
# N: population size
# mux: mean of X