Question 3: (9 points) An experimenter working in an urban area desires to estim

Question

Question 3: (9 points) An experimenter working in an urban area desires to estimate the average value of a variable highly correlated with race. She thinks she should use cluster sampling, with city blocks as clusters and adults within blocks as elements. Explain why you would, or would not use cluster sampling in each of the following situations (a) Most of the adults in certain blocks are white, and most in other blocks are nonwhite (b) The proportion of nonwhites is the same in every block and is not close to 0 or 1 (c) The proportion of nonwhites differs from block to block in the manner that would be expected if the clusters were made up by randomly assigning adults in the population to clusters.

Explanation / Answer

We use cluster sampling when the clusters are assumed to be simple random samples of a large population.

(a)

In clusters, the propotion of whites/non-whites in different clusters are close to 0 or 1. So, in this case, clusters are not assumed to be simple random samples of a large population. So it is not advisable to use cluster sampling in this case.

(b)

In clusters, the propotion of non-whites in different clusters are not close to 0 or 1 but the proportion of non-whites are same in all clusters. So, in this case, random sample from clusters may be not provide a replica of simple random samples of a large population. So it is not advisable to use cluster sampling in this case.

(c)

Given, the propotion of non-whites in different clusters (blocks) are different in such a way that the clusters were made up by randomly assigning adults in the population to clusters. So, random sample from clusters may provide a replica of simple random samples of a large population. In other words, random sample from clusters may be considered as a random sample from large population. So it is advisable to use cluster sampling in this case.

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