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In: Statistics and Probability

(b) How can stratified random sampling and cluster sampling be combined? [4]

(b) How can stratified random sampling and cluster sampling be combined? [4]

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Expert Solution

Here, we have to show how can stratified random sampling and cluster sampling be combined.

Stratified random sampling : This is a type of sampling method in which the total population is divided into smaller equal size strata to complete the sampling process. The process which we use is usually simple random sampling with replacement or simple random sampling without replacement.

Cluster sampling : It is a probability sampling technique where we divide the total population into multiple clusters to perform the research. We use a simple random or systematic random sampling techinque for data collection and data analysis.

Let us consider a population having N population units. The population is divided into k stratas where the ith strata contains Ni population units. Now each strata having Ni units are divided into M clusters each of size m. From these M clusters n clusters are drawn by SRSWR or SRSWOR. Now the drawn clusters are enumerated completely where,

total population size = Mm

total sample size = nm

This is how we can combine the startified random sampling and cluster sampling together.

orchestra answered 2 years ago
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