In Exercises 18 20 identify the sampling technique used to

In Exercises 18 & 20, identify the sampling technique used to obtain a sample. Explain your answer.

18.       The businesses in Iowa City are grouped according to type: medical, service, retail, manufacturing, financial, construction, restaurant, hotel, tourism, and other. A random sample of 10 businesses from each type is selected.

20.      The Food and Drug Administration randomly selects five stores from each of four randomly selected sections of a large city and checks food items for freshness. These stores are used as a representative sample of the entire city.

Solution

18. This comes under stratified sampling.--

Here the population embraces different kinds of groups such as medical, service, retail, etc. Hence the whole population is divided into separate strata and samples from each strata is collected.

There are several potential advantages to stratified sampling.

First, dividing the population into distinct, independent strata can enable researchers to draw inferences about specific subgroups that may be lost in a more generalized random sample.

Second, utilizing a stratified sampling method can lead to more efficient statistical estimates . Even if a stratified sampling approach does not lead to increased statistical efficiency, such a tactic will not result in less efficiency than would simple random sampling, provided that each stratum is proportional to the group\'s size in the population.

Third data will be obtained easily than from the entire population as groupwise data are maintained already for some other purposes.

Different statistical applications can be applied to different strata according to the pattern, type and convenience of the stratas.

But major disadvantages are increase in cost to sort into strata, and the process sometimes turn out to be more complex than expected. Overlapping and repititions sometimes cannot be avoided thus misinterpreting the data.

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20) This is called random sampling.

In a simple random sample (SRS) of a given size, all elements of the frame are given an equal probability. Furthermore, any given pair of elements has the same chance of selection as any other such pair (and similarly for triples, and so on). This minimises bias and simplifies analysis of results. In particular, the variance between individual results within the sample is a good indicator of variance in the overall population, which makes it relatively easy to estimate the accuracy of results.

However, SRS can be vulnerable to sampling error because the randomness of the selection may result in a sample that doesn\'t reflect the makeup of the population. For instance, a simple random sample of ten people from a given country will on average produce five men and five women, but any given trial is likely to overrepresent one sex and underrepresent the other. (Systematic and stratified techniques), attempt to overcome this problem by \"using information about the population\" to choose a more \"representative\" sample.