The "law of large numbers" indicates that as sample size increases, sample statistics become less variable and more closely estimate their corresponding population parameters. Different research studies investigating how people consider sample size when evaluating the reliability of a sample statistic have found a wide range of responses, from no consideration of sample size to over consideration of sample size. This paper provides a qualitative meta-analysis of studies that have used what we dub the "Hospital Task" for investigating peoples' thinking about the role of sample size in parameter estimation. This paper aims to investigate what the Hospital Task can tell us about how people make decisions under uncertainty and the usefulness of the task for developing models of students' statistical reasoning. To achieve these goals, we review the original task, synthesize results of other studies which have used some version of this task, provide a critique of the different versions of the task, discuss implications of the task for research, and provide insights and viewpoints from a small group of statisticians. The paper concludes with implications for further research.