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Sampling is a method used to select a subset of individuals from a population to estimate characteristics of the whole population. The main types include random sampling, where every individual has an equal chance of being selected; systematic sampling, which involves selecting every nth individual; convenience sampling, based on ease of access; stratified sampling, which divides the population into subgroups; and cluster sampling, where entire groups are randomly selected.

Random sampling is a technique where each member of the population has an equal probability of being chosen. This method helps to eliminate bias and ensures that the sample is representative of the population, which is crucial for the validity of statistical inferences. It is often achieved through methods like lottery or random number generators.

An observational study is a research method where the researcher observes and records behavior without manipulating any variables. In the context of the question, the study involved observing adults in public restrooms to gather data on handwashing habits. This type of study can provide valuable insights but does not establish cause-and-effect relationships.