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
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education