Use sampling with probability proportional to size, with replacement, to estimate the mean or total of a population of your choice. One example would be the average elevation of lakes on a topographic map. In the process of carrying out the survey and making the estimate, think about or discuss with others the following:
(a) What practical problems arise in establishing a frame, such as a map or list of units, from which to select the sample?
(b) How is the sample selection actually carried out?
(c) What special problems arise in observing the units selected?
(d) Estimate the population mean or total.
(e) Estimate the variance of the estimator used above.
(f) Give a 95% confidence interval for the population proportion
(g) How would you improve the survey procedure if you were to do it again?