ratio.est <- function(x, y, mux = NA, N = NA)
{
# estimate of a ratio and ratio estimate of population mean and total.
# x is auxiliary variable, y is response, mux is population mean
# of x (xbar is used if no value is given), 
# N is population size (assumed infinite if no value given), 
	if(length(x) != length(y)) stop("x and y must be same length")
	n <- length(x)
	fpc <- 1
	if(!is.na(N))
		fpc <- (N - n)/N
	r <- sum(y)/sum(x)
	sr2 <- (1/(n - 1)) * sum((y - r * x)^2)
	if(is.na(mux)) mx <- mean(x) else mx <- mux
	cat("r=", r, "  SE=", sqrt((fpc * sr2)/(mx^2 * n)), "\n")
	if(!is.na(mux))
		cat("mu-hat=", r * mux, "  SE=", sqrt((fpc * sr2)/n), "\n")
	if(!is.na(N) & !is.na(mux))
		cat("tau-hat=", N*r * mux, "  SE=", N*sqrt((fpc * sr2)/n), "\n")
}