4-I agree with you that Sampling theory was developed to determine the most effective way of acquiring a sample that accurately reflects the population under study. A sample is the selected group of people or elements in a study. The sample selected should represent an identified population or a particular group of individuals or elements that is the focus of the research. And to add that Sampling theory is also the study of the relationship that exist between a target population and the samples that are drawn from the population and this only applies to samples that are drawn randomly. The main concepts of the sampling theory are the target population, representative samples and sampling plans or methods.
Target population is also known as research universe. The subject of investigation is the whole statistical data. A sampling plan normally states methods that are to be used to collect random samples from the population in such a way that there is very minimal to zero biasness. The methods can use random probability sampling techniques.
The following steps are normally involved when developing a sampling plan, they are as follows,
Identification of parameters to be measured.
Designing intervals of measurement.
Selection of sample sizes
Establishment of data storage formats
Assigning roles and responsible to the research teams.
Generalizability is the process of extrapolating the research findings of a sample population to the general population. The reason behind it, that the sample population that was selected represented the entire population. As such the research could extrapolate the findings and make a conclusion that represents the entire population.
Chambers, R, Chambers R, L & Skinner, C(2003), Analysis of Survey Data. Retrieved from https://www.powells.com/books/analysis.