Carry out a survey to estimate the mean or total of a population of your choice, in which an auxiliary variable is available along with the variable of interest. Examples include the average amount of pocket change carried by attendees to a lecture, as in Example 1, or eyeball estimates and careful measurements of any sort of object. 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 using the sample mean.
(e) Give a 95% confidence interval for the population mean or total based on the sample mean.
(f) Estimate the population mean or total using the ratio estimator.
(g) Give a 95% confidence interval for the population mean or total based on the ratio estimator.
(h) How would you improve the survey procedure if you were to do it again?