I feel embarrassed but I am confused with the below question.

An interviewer plans to stand at an entrance to a popular shopping mall and conduct interviews. $$$$Is the below statement true? $$$$ Because we cannot predict who will be interviewed, the sample obtained is an example of a random sample.

I think it is a False statement but I am not sure how to justify it nor clearly explain why.

  • 2
    $\begingroup$ This is a vague statement. Without precising the meaning of "random" (non-deterministic? uniform? exchangeable?) and the way people are chosen for interviews, there is no proper answer to this type of question. $\endgroup$
    – Xi'an
    Sep 7 at 9:27
  • $\begingroup$ A truly random sample would identify a population (such as all who are registered to vote in a county) and then draw a sample of $n$ subjects in such a way that each person not yet sampled has an equal probability of being chosen on each draw.// In the jargon of sampling methods, interviewing whoever happens to enter the mall while you're there might be called a "convenience" sample. (Maybe you can think of kinds of registered voters who are more likely to come to the mall than to be chosen at random, also who might be less likely.) $\endgroup$
    – BruceET
    Sep 7 at 16:12
  • $\begingroup$ In its broadest sense, a "random sample" may select subjects with varying probabilities, but the chance that any particular set of those subjects is selected for the sample must be well-defined. That goes (well) beyond being unable to predict what the sample will be beforehand. Thus, your question is answered by contemplating how you might (in principle) find the chance that the interviewer obtains a specific (but otherwise arbitrary) sample of interviewees. Consider an extreme case of just two shoppers in the mall: how would you determine the chances of the three possible samples? $\endgroup$
    – whuber
    Sep 7 at 18:03

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