Question

choose one of the three random sampling methods we studied in this chapter, state which method you've chosen, and describe exactly how you would conduct a completely randomized survey of 100 Montgomery County, Tennessee, residents using this method. Make sure that the sample is truly and purely random. Assume you have unlimited resources (money, workers, time, etc.) and unlimited access to information. Describe exactly what steps you would take to choose each person in the sample. Would you be able to draw conclusions about the entire population of Montgomery County residents using just a sample of size 100? Why or why not?

Answer 1

I am assuming that you are talking about the possible three random sampling methods

i)Simple Random Sampling

ii) Stratified Random Sampling

iii) Cluster Sampling (or its particular case Systematic Sampling)

i would choose Stratified Random Sampling, in Stratified random sampling we divide whole population of size N into L strata, h^th strata containing N_h units, such that

which are within homogeneous and between heterogeneous then we use Simple Random Sampling Without Replacement to select a sample of size n=100(here) by selecting n_h units from h^th stratum such that

.

Since we are assuming that there is no resources limitation and all information is available, so we can use Neyman's allocation, in which the sample size(n_h) for each stratum requires prior knowledge of Stratum size(N_h) and Variation(S_h)for each stratum, Now S_h depends on the objective of the survey, according to the objective, we can make S_h as small as possible, and then can divide the whole population into strata having small within Variation(S_h) and then we can select a Simple random sample without replacement of size n_h from h^th stratum.

By doing stratification, we are ensuring that each type of person is able to be chosen in the overall sample(n).

and by using simple random sampling , we are ensuring that the sample is drawn randomly from each stratum.

Now, drawing conclusions, yes we will be able to draw conclusions about the entire population of Montgomery County residents, because we have taken the whole sample from entire population, that is, for taking the sample, we have taken into consideration the each and every segment(stratum) of population.

Although the conclusions drawn will have some sampling error.