A well-designed experiment is the only legitimate way to establish a cause-and-effect relationship between two variables. We can use results from an observational study to test a claim about a population. We can use results from an observational study to test a claim about a population. When an observational study has a large sample and follows people for many years, we can use the results to establish a cause-and-effect relationship between two variables. When many observational studies together meet specific criteria, the results can provide varying degrees of evidence for a cause-and-effect relationship between two variables. But we should be cautious in interpreting such results.

A well-designed experiment, based on many observational studies, can give results to establish a cause-and - effect relationship between two large sampled variables, where the people are followed for many years, to test a claim about population, and the specific criteria met, can provide varying degrees of evidence, but we should be cautious in interpreting such results, as they are not absolute facts.

Step-by-step explanation:

Statistical studies are classified in two: observational studies and experiments.

As probably infered by its name, an observational study observes entities of interest to describe them, and to measure the variables that relate these entities, to be able to get answers in regards the association between these relationships variables.

Observational studies can be useful to give answers regarding population and the relationship between two variables, but consider that researchers are not to manipulate one of these variables involved so that it causes an effect in the other, that is why observational studies' cause-and-effect evidences are nor absolute or convincing the way experiments do.