This function demonstrates the advantage of ratio estimation when further information (ratio) about x and y is available.

From this demonstration we can clearly see that the ratio estimation is
generally better than the simple sample average when the ratio **R**
really exists, otherwise ratio estimation may not help.

```
library(animation)
ani.options(interval = 1, nmax = 50)
## observe the location of the red line (closer to the population mean)
res = sample.ratio()
```

```
## absolute difference with the true mean
matplot(abs(cbind(res$ybar.ratio, res$ybar.simple) - res$Ybar), type = "l")
legend("topleft", c("Ratio Estimation", "Sample Average"), lty = 1:2, col = 1:2)
```

plot of chunk demo-a

```
## if the ratio does not actually exist:
sample.ratio(X = rnorm(50), Y = rnorm(50))
```

plot of chunk demo-b

```
## ratio estimation may not be better than the simple average
```