Question

The mayor of a small city (of approximately 60,000 people) has been requested to sign off on a new casino to be built near the city. Casinos being built are usually contentious affairs as some citizens worry it can encourage gambling addiction and attract unwanted people to the community while others believe it can bring an economic boom to the city. As such, the mayor is interested in the townspeople’s view of having the new casino built; specifically whether or not they support having the casino built. The mayor is planning on taking a sample of citizens to get their opinions. The mayor is planning on personally doing an in-person survey to be able to hear all concerns the citizens have. The mayor has several ways to obtain a sample. The city is broken into 9 distinct neighborhoods. Each neighborhood is a relatively homogeneous collection of people with similar demographics and socio-economic status. The neighborhoods are named for the directions they are in from the center of the city. They are referred to as: NE, E, SE, S, SW, W, NW, N and C. The “C” stands for center and is the neighborhood in the dead center of the city. Roughly 6650 people live in each neighborhood. More so, each neighborhood is split further into smaller city blocks with approximately 50 blocks each. Each block has about the same number of people living on it. Further, the mayor has access to city records giving the names and addresses of all citizens in the city. The picture on the following page gives you a general idea of how the city is broken up, it does not include all blocks but is meant to give you the “flavor” of the organization. How should the mayor sample in order to get a simple random sample, a cluster sample and a stratified sample? That is the goal of this section of the test. For each of the following, please write at least a small paragraph worth for each sampling plan. You need to be very specific in your response. There should be no ambiguity of how you will sample from the citizens.

1. How should the mayor sample to get a Simple Random Sample?

2. How should the mayor sample to get a Stratified Sample?

3. How should the mayor sample to get a Cluster Sample?

4. Which do you think is the most correct method, especially given the mayor’s goals?

5. Should a census be used? Why or why not?

Answer 1

Here total 10 district are there & each neighbourhood district contains 5 blocks in it . In each district there are about 6650 peoples & each block contain same(133) people.

As, each district is relatively homogeneous collection of people with similar geographical and socio -economics status . So here we can say that district are between homogeneous and within heterogeneous .

1) Here simple random sampling can be done by drawing ni units from eact district . as there are 9 districts so one can draw ni*9 o of people from whole populations . By ignoring blocks from each district . Here we have large no of peoples . So by considering srs for each district one can draw sample I think simple random sample may be possible. But it doesn't take unto account blocks.

2) As stratum are formed in such a way that they are within homogeneous and between heterogeneous . So selecting n district by srs method and then deviding each district into homogeneous blocks one can apply stratified random sampling to each block . For that purpose we have to select (k ) no of people from each block so that all blocks will represented in the population . So we get total nk people from each selected district . Ex if 4 district are selected by srs then 3*nk will be total selected people for sample .

3) If we consider population as a whole and each district as a whole then as each district is within heterigrneous and between homogeneous . So by selecting(n<9) clusters at 1st level and (k<50) from each selected blocks all (133) people in the each selected block will be consider as a sampling element  . But this method is too muvh complicated . No need of two stage samoling for such a simple reason .

4)I think, here stratified random sampling is the better method of the sampling. Since district are similar with repect to all properties  so need not be select all district . And blocks in yhe distruct are heterogeneous so they all must be reprsented in the population . So sample  of k people represent each block to sample .

5) As,we know that census means complete inomuration . Taking into accounts each and every person opinion. I think it may be time consuming. We can overcome this issue by using sampling also .So there is no need of census .