Carry out a survey to estimate a proportion in a population of your choice. Examples include the proportion of vehicles with only one occupant and the proportion of a university campus covered by tree canopy. For the latter, the campus can be partitioned into extremely small plots, so that each plot location may be determined to be either covered or not covered and the finite-population correction factor will be negligible. 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 proportion.
(e) Estimate the variance of the estimated proportion.
(f) Give a 95% confidence interval for the population proportion.
(g) How large a sample size would be needed to estimate the proportion to within 0.02 of the true value with 95% confidence? (Answer this first using your estimate proportion and second for the worst case.) (h) How would you improve the survey procedure if you were to do it again?