Surveying Phone Books
It is hypothesized that 10% of residential phone numbers in the 2010>2011 Melbourne White Pages end in one. However, due to the fact that random allocation may not be in effect this may not be true. The aim of this research is to use random samples generated by Minitab to estimate if 10% of residential phone numbers end in one using a cluster sampling method.
To complete the research the population has been selected randomly from the Melbourne White Pages. However, this may affect our final result as the residential phone numbers may not have been randomly allocated, and each column (cluster) may not contain the same number of ...view middle of the document...
However, using a random number table to choose the elementary units can be cumbersome. If the sample is to be collected by a person untrained in statistics, then instructions may be misinterpreted and selections may be made improperly. Simple random sampling is free of classification error and best suits situations where not much information is available about the population, and where data collection can be efficiently conducted on randomly distributed items, or where the cost of sampling is small enough to make efficiency less important than simplicity.
A systematic random sample is obtained by selecting one unit on a random basis and choosing additional elementary units at evenly spaced intervals until the desired number of units is obtained. As long as the list does not contain any hidden order, this sampling method is as good as the random sampling method. Its only advantage over the random sampling technique is simplicity.
A stratified sample is obtained by independently selecting a separate simple random sample from each population stratum. A population can be divided into different groups may be based on some characteristic or variable. These groups are referred to as strata. You can then randomly select from each stratum a given number of units which may be based on proportion. Stratified sampling is often used when one or more of the stratums in the population have a low incidence relative to the other stratums.
A cluster sample is obtained by selecting clusters from the population on the basis of simple random sampling. The sample comprises a census of each random cluster selected. Though very economical, cluster sampling is very susceptible to sampling bias.
In a cluster sample, the population is divided into non-overlapping subpopulations usually based on geographic or political boundaries. For a simple cluster sample, a random sample of subpopulations (clusters) is obtained and, within each selected cluster, each subject is sampled.
In theory, clusters are chosen to be as heterogeneous as possible, that is, the subjects within each cluster are diverse and each cluster is somewhat representative of the population as a whole. Thus, only a sample of the clusters needs to be taken to capture all the variability in the population. In practice, however, clusters are often defined based on geographic regions, political boundaries or occur in natural clusters, so that conducting a cluster sample reduces the time and cost associated with the survey. In this situation, the elements within the clusters may be rather homogeneous and, on average, the clusters may be very different from one another. Because of this, for a fixed sample size, the variance from a cluster sample is usually larger than that from a simple random sample, and therefore the estimates are less precise.
Some main advantages and disadvantages of cluster sampling are as follows.
- Only need to obtain list of units in the selected...