Final answer:
The type of statistical study that is most likely to answer the question about NBA teams with high-altitude home courts is an observational study. The study would involve comparing the records of NBA teams with high-altitude home courts to teams without high-altitude home courts. Lurking variables such as team talent and coaching staff could interfere with the study.
Step-by-step explanation:
The type of statistical study that is most likely to lead to an answer to the question about NBA teams with high-altitude home courts is an observational study. Since the study is asking about the records of different teams over a period of many years, it is not feasible to assign teams to different altitudes. In this case, the study would involve collecting data on the records of NBA teams with high-altitude home courts and comparing them to teams without high-altitude home courts.
In this observational study, the cases would be the NBA teams with high-altitude home courts and the controls would be the NBA teams without high-altitude home courts. The study would be retrospective since it involves looking at past records. Lurking variables that could interfere with this study could include factors such as team talent, coaching staff, and player injuries. Blinding is not necessary in an observational study.